Science in the City 2022 Prof J Jamesv[2022]

What would a scientist do at a bank?
Prof Jessica James, for Imperial College, Feb 2022
Science in the City

1
1. Introduction – a scientist in the city 2
2. Case Study (1) – FX Carry Trade 6
3. Case Study (2) – Fair Value of Options 23
4. Case Study (3) – Out of the Money 40
5. Case Study (4) – Emerging Market Currency Options 51
6. Case Study (5) – Puts and Calls 64
7. Conclusions 81
Contents

2
7. Conclusions 81

3
Introduction
Why go into finance?
Interesting
Mathematical
Fast moving
Much to learn

4
Careers
What skills does a bank need?
Mathematics, coding, analysis, economics
Languages, people skills, organisation
Design, journalism, writing
Specialist legal, corporate, politics

5
How?
It’s harder than it used to be!
Milk round
Summer schools, internships
Web applications
CV building

6
7. Conclusions 81

7
The FX Carry Trade
After 1971 when the USD peg to gold was broken, exchange
rates became free floating until by the 1980’s most were
trading freely.
It was assumed that these new floating rates would have their
underlying value determined by interest rates and inflation in
their own country.
This lead to the idea of Uncovered Interest Parity (UIP) – that
FX rates will on average track the forward rates determined by
the relative interest rates between two countries. Source: Bloomberg, Commerzbank
Returns to long term quarterly carry trade
However, it became clear early on in the free floating FX
regime that in fact FX rates utterly decline to obey these rules.
The actual profits (Total carry) closely track the forward point
component. On average, the carry trade delivers almost
exactly the carry.
-40
-30
-20
-10
0
10
20
30
40
50
1987 1991 1995 1999 2003 2007 2011 2015
Cumulative
return
(%)
Total carry Forward point component
Spot component Required spot path for UIP

8
UIP is a key building block in many open economy
macroeconomic models
Under UIP, the difference between interest rates for two
currencies is equal to the expected change in the exchange
rate for those currencies
• Or put slightly differently, one should not be able to
realise the interest rate carry as it should be negated by
the change in the spot rate over the investment period
(see example to the right)
The concept of UIP goes back at least as far as the 1920s,
but from the early 1980s a succession of papers suggested
that the parity relationship might not hold…
…or that there are at least distortions due to deviations
from the underlying assumptions
Views on UIP are most likely to be expressed through
currency forwards given that the forward rate is related to
the spot rate and both interest rates if UIP holds
The theory behind the carry trade
Uncovered Interest Parity (UIP)
Exchange for
euros
Invest at euro
deposit rate
Exchange for
dollars
EURUSD =
1.250
EURUSD =
1.214
Invest at dollar
deposit rate
r = 2%
$10,000,000
€8,000,000 €8,400,000
r = 5%
$10,200,000

9
The forward point contribution to the carry return is
calculated by assuming that spot rates remain unchanged
(that is, the full interest differential is earned)
The expected spot rate contribution under UIP should be
the inverse of the forward point contribution (so that the
total return is zero)
The actual spot rate contribution can be calculated from the
start and end values of the spot rate
The schematic illustration to the right displays how we
might expect the carry trade to be decomposed if UIP holds
Data and methodology
Breaking down the return into forward-point and spot components
Return
(%)
Forw ard point contribution
Spot rate contribution
Time

10
Results
The chart on the right displays the aggregated results
We note that:
1. The carry trade in aggregate has made money, not
lost it, delivering close to the ‘carry’
2. During the years immediately prior to the crisis, spot
rates actually moved away from forwards rather than
towards them – exactly the opposite of the behaviour
expected under UIP
3. Since the start of 2009, the average spot rate
contribution has once again acted to reduce carry
returns, but has not been negative enough to
completely negate the forward point contribution
Aggregation for all 45 G10 currency pairs
Source: Bloomberg, Commerzbank
-40
-30
-20
-10
0
10
20
30
40
50
1987 1991 1995 1999 2003 2007 2011 2015
Cumulative
return
(%)
Total carry Forward point component
Spot component Required spot path for UIP

11
7. Conclusions 81

12
Introduction
FX options are incredibly widely used instruments.
From long term hedges of overseas income, right through
to opportunistic volatility selling, they are used as
protection, as positioning tools, and as return drivers.
They are some of the most widely used derivatives in the
world.
But are they good value? Are they too cheap, or too
expensive?
The corporate user will be convinced that they are paying
too much for protection.
The investor will be wary of using them to deliver returns in
case they are biased to be cheap or expensive.
And all this confusion is because no-one really knows.
We show that it is possible to answer these questions by
calculating the historical premium values and comparing
them to the historical pay-outs.
We performed this calculation for every day since 1995, for
every currency pair available, for every traded tenor of
option.
By the end of the process the answer was clear: short
dated options are expensive; long dated options are better
value.
This answer explains why so many people will say one
thing or another with such conviction!
Both are right – or wrong – but without understanding the
tenor effect it is easy to make the wrong decisions.

13
Motivation for our study
We are interested in the most basic definition of fair value;
payout vs premium.
• However, we recognise that the issue of marked-to-
market variation, which we do not examine in this paper,
is important.
From the point of view of the protection buyer, it would be
highly valuable to know whether FX options on average
deliver value.
A corporate typically has to make long term hedging
decisions and the premium outlay on these structures
can be high.
Without knowing whether the hedges are likely to pay
out or not, the company is operating in the dark.
For the investor, it is more interesting to wonder if a
profitable trading strategy may be derived from this
information
Above, we show the daily premia of one week FX at-the-
money straddle options since 1995, together with the
payouts that those options generated.
It is immediately obvious that the payouts can be greatly
different from the premia, though they are related.
They rise and fall at similar times, but the values of the
premia are far more bounded and constrained than those
of the payouts.

14
A volatile data period
We can focus in on an interesting data period, the fall and
winter of 2008 (figure 2)
The huge variability of the payouts relative to the premium
costs become clearly apparent, with payouts going from
close to zero to almost 8% of notional value.
• The premia vary much less; from about 1% to 6% at the
peak.
• There is an interesting lag effect due to the fact that the
payouts happen later than the premia are calculated.
For simplicity we plot the pay-out of the option on the same
day that the premium is calculated.
Thus you can see that on 20th October 2008, a one week
straddle cost 2.35% of notional amount – but paid back
7.71% a week later. Nice trade!

15
Creating a trading strategy
Though it looks as if the averay payout and average
premium for the USDJPY 1 week options are similar, they
are not quite the same.
The average value for the premium is 1.31% of notional
amount (if we are buying, including costs), and the average
value for the payout is 1.13% of notional amount.
Is this difference enough to use? Indeed it is.
In the chart we have produced an estimate of the returns of
a simple straddle writing strategy
While it should be emphasised that these results include
only final payouts and not marked to market variation, it is
encouraging that such a simple strategy looks promising.
Clearly there is value to be gained from understanding
option fair value!

16
Data used in the study
To value options on historical dates, it is essential to have
all the relevant data available at the time – in particular the
implied option volatility
While some option studies may be able to estimate
historical implied option volatility values from realised
actual volatility levels, in this case that approximation may
not be made.
Often those small differences are those which can drive a
trading strategy.
Over the longer term small differences in volatility can lead
to large differences in payout and price.
So we can only perform the backtest on those days where
we have the full data set.
This is, for each separate tenor,
• Spot FX Rate
• Option Volatility
Then two out of
• Forward rate
• Term (foreign) deposit rate
• Base (domestic) deposit rate

17
Currency pairs
These are the start dates for 1 month tenor data.
Not all tenors have all of this data.
For the G10 pairs, we have data for tenors
• 1w
• 1m
• 3m
• 6m
• 12m
• 2y
• 3y
For the EM pairs, the 2y and 3y data is mostly unavailable
or insufficient.
Currency
pair
USDJPY GBPUSD EURUSD USDCHF EURCHF
Start
date
Dec 95 May 96 Dec 98 May 96 Jan 99
Currency
pair
USDAUD USDCAD USDDKK USDNOK USDSEK
Start
date
Dec 95 Aug 98 Feb 01 Feb 99 Aug 98
Currency
pair
USD
MXN
USD
TRY
USD
ZAR
USD
SGD
USD
TWD
USD
KRW
Start
date
Dec 99 Dec 03 Feb 99 Dec 00 Apr 99 Aug 04

18
Methodology
For each premium and payout calculation, we need to value
the option on the day it is bought or sold, and then calculate its
payout at expiry.
To calculate the premium, we use a straightforward FX Black-
Sholes method, and we use straddles throughout, to immunise
the study as much as possible from overall directionality of the
currency pair
If we wish to compare the relative performance of some of the
main tenors (say 1W, 1M, 3M, 6M, 12M, 2Y and 3Y) for the
main G10 and emerging market currencies, then it is clear that
the task at hand is not a trivial one.
Assuming seven tenors for 34 crosses over an average
historical period in the region of 10 to15 years, the scale of the
challenge becomes clear. If we wish to compare forwards with
at-the-money and out-of-the-money options, for puts, calls and
straddles and long and short positions then somewhere in
excess of 2 million payoff calculations will be required
In all cases the premium is calculated in per cent of underlying
notional, in the base currency.
This is unambiguous and enables easy comparisons among
the various currency pairs.
Note that we discount the payout of the option as it occurs at a
different date to the premium. The effect is very small up to
the 12m tenor; after that point it can become noticable
There are two possible types of result from this study. The
first would be perhaps the expected one – that FX options are
on the whole fairly priced. In this case, we would expect to see
the premia and payouts approximately equal to each other
over time, albeit with some noise
The second type of result would be much more interesting.
In this case we would see persistent deviations from fair value,
with options tending to pay out more or less than the premium
cost over time.

19
Costs
It is essential to include costs in this study; they can make
the difference between success or failure of a strategy.
As premium is a linear function of volatility, we calculate the
costs as an additional percentage of the premium.
We take the whole series average and apply this to the
daily premium calculations.
Bid-offer costs in % premium
Tenor USDJPY GBPUSD EURUSD USDCHF EURCHF
1w 9.9% 11.6% 8.8% 10.4% 24.8%
1m 4.5% 4.7% 3.1% 4.2% 9.7%
3m 4.3% 4.1% 2.8% 3.8% 8.5%
6m 3.2% 3.9% 2.4% 3.5% 7.7%
12m 2.7% 3.6% 2.3% 3.4% 7.3%
2y 3.5% 4.0% 3.2% 4.0% 8.9%
3y 4.4% 5.2% 3.9% 5.5% 10.7%
1w 9.6% 10.8% 16.1% 14.9% 14.5%
1m 3.7% 4.3% 7.1% 6.1% 5.8%
3m 3.6% 4.0% 5.3% 5.0% 5.2%
6m 3.4% 3.7% 4.6% 4.5% 4.6%
12m 3.9% 4.1% 4.2% 4.2% 4.2%
2y 4.2% 4.0% 5.2% 5.8% 6.4%
3y 5.4% 5.1% 5.0% 5.9% 6.6%
*data is from start dates given in Tables 1 and 2 up until May 2012
USD
MXN
USD
TRY
USD
ZAR
USD
SGD
USD
TWD
USD
KRW
1w 20.3% 12.5% 17.0% 27.6% 30.2% 24.4%
1m 10.6% 10.9% 10.1% 11.2% 14.2% 12.7%
3m 9.5% 9.2% 8.6% 10.4% 13.0% 11.1%
6m 8.8% 7.5% 8.1% 9.6% 11.2% 10.0%
12m 8.0% 5.4% 7.7% 9.0% 11.1% 9.5%
*data is from start date

20
What do we expect to see?
There are two possible types of result from this study.
The first would be perhaps the expected one – that FX
options are on the whole fairly priced.
• In this case, we would expect to see the premia and
payouts approximately equal to each other over time,
albeit with some noise
The second type of result would be much more interesting.
In this case we would see persistent deviations from fair
value, with options tending to pay out more or less than the
premium cost over time.
For this to be meaningful we would expect to see these
results, whatever they are, confirmed across different
currency pairs.
Most of our analysis will focus on the payout/premium ratio,
that is, the value of the payout of an option divided by the
value of the premium.
This quantity is comparable across currency pairs, which is
essential when we have pairs ranging from EURCHF
(average 1w premium =0.67%) to USDKRW (average 1w
premium = 2.13%).
If options were fairly priced, we would expect to see this
value centred on 100% for all option tenors.

21
Average Premium and Payout Values – G10
Average Payout in % Underlying Notional
1w 1.13% 1.00% 1.13% 1.21% 0.55%
1m 2.42% 2.00% 2.48% 2.55% 1.15%
3m 4.15% 3.27% 4.40% 4.37% 1.79%
6m 5.85% 4.85% 6.55% 6.22% 2.56%
12m 8.33% 6.79% 9.50% 8.05% 4.30%
2y 13.70% 12.89% 10.33% 11.51% 10.46%
3y 17.38% 14.48% 10.20% 15.12% 16.41%
1w 1.37% 1.01% 1.12% 1.31% 1.32%
1m 2.78% 1.93% 2.43% 2.68% 2.81%
3m 4.70% 3.37% 4.36% 4.74% 4.82%
6m 7.48% 5.25% 6.59% 7.02% 7.70%
12m 11.59% 7.53% 8.76% 9.44% 10.90%
2y 18.52% 8.86% 9.10% 11.49% 14.00%
3y 20.29% 8.60% 6.86% 9.27% 7.80%
Average Premium in % Underlying Notional
1w 1.32% 1.09% 1.24% 1.28% 0.67%
1m 2.63% 2.16% 2.53% 2.56% 1.26%
3m 4.48% 3.76% 4.40% 4.42% 2.11%
6m 6.27% 5.32% 6.21% 6.18% 2.88%
12m 8.60% 7.37% 8.62% 8.44% 3.71%
2y 10.48% 10.92% 11.22% 10.79% 4.50%
3y 10.56% 11.65% 12.42% 11.62% 5.00%
1w 1.46% 1.10% 1.30% 1.47% 1.49%
1m 2.77% 2.20% 2.59% 2.95% 2.98%
3m 4.67% 3.80% 4.48% 5.07% 5.11%
6m 6.40% 5.33% 6.35% 7.12% 7.11%
12m 8.64% 7.43% 8.84% 9.86% 9.78%
2y 13.08% 11.45% 11.42% 13.84% 13.56%
3y 14.30% 12.29% 13.48% 15.15% 15.00%

22
Average Premium and Payout Values - EM
USD
MXN
USD
TRY
USD
ZAR
USD
SGD
USD
TWD
USD
KRW
Average
over all
1w 1.02% 1.46% 1.80% 0.58% 0.49% 1.59% 1.13%
1m 2.12% 3.12% 3.89% 1.26% 1.18% 2.56% 2.33%
3m 3.86% 5.58% 6.49% 2.25% 2.26% 4.41% 4.05%
6m 5.33% 8.15% 10.26% 3.36% 3.82% 7.21% 6.14%
12m 7.98% 11.66% 15.71% 4.69% 4.96% 10.71% 8.81%
2y 12.09%
3y 12.64%
Note that we have added half the full bid-offer costs to the premia in all cases, as we assume we are buying the options.
Also note that the “Average” column averages over all currency pairs, G10 and EM.
USD
MXN
USD
TRY
USD
ZAR
USD
SGD
USD
TWD
USD
KRW
Average
over all
1w 1.35% 1.61% 2.11% 0.76% 0.75% 2.13% 1.32%
1m 2.68% 3.45% 4.17% 1.39% 1.46% 2.96% 2.55%
3m 4.70% 6.26% 7.06% 2.44% 2.60% 4.88% 4.39%
6m 6.84% 9.35% 9.95% 3.49% 3.92% 6.61% 6.21%
12m 10.27% 14.67% 14.24% 4.87% 5.59% 8.80% 8.74%
2y 11.13%
3y 12.15%

23
Payout/Premium Ratio
We begin to understand what is going on when we look at
the ratio of payout/premium
Note that we have not taken account of the fact that
different currency pairs have different amounts of data; the
averages are simple averages over the currency pairs.
The payout/premium figures are calculated by dividing
payout by premium for each day, then averaging over time.
Average Payout/Premium Ratio
1w 88.3% 93.1% 93.1% 95.3% 80.5%
1m 95.3% 95.5% 100.8% 100.4% 90.2%
3m 95.7% 89.5% 104.9% 101.5% 88.5%
6m 97.3% 94.0% 112.5% 104.7% 96.0%
12m 101.0% 98.7% 120.9% 100.6% 121.6%
2y 144.8% 150.7% 97.3% 108.8% 225.4%
3y 177.6% 149.5% 86.6% 134.2% 337.4%
1w 95.6% 91.6% 88.3% 91.0% 89.8%
1m 102.2% 89.9% 96.6% 95.2% 97.4%
3m 103.7% 95.2% 103.2% 98.2% 97.8%
6m 120.0% 104.6% 111.4% 102.2% 112.5%
12m 142.8% 107.5% 111.7% 103.5% 119.4%
2y 144.4% 84.4% 87.9% 90.2% 114.1%
3y 139.5% 73.1% 63.5% 63.4% 51.8%
USD
MXN
USD
TRY
USD
ZAR
USD
SGD
USD
TWD
USD
KRW
Average
over all
1w 78.7% 92.2% 86.8% 77.2% 68.1% 77.2% 86.7%
1m 85.1% 94.3% 97.0% 94.8% 88.9% 98.0% 95.1%
3m 94.4% 95.7% 99.4% 98.4% 95.1% 110.4% 98.2%
6m 98.8% 92.6% 113.4% 103.5% 111.2% 135.7% 106.9%
12m 99.8% 82.1% 124.6% 106.5% 100.7% 195.3% 114.8%
2y 124.8%
3y 127.7%

24
Patterns begin to emerge
Now we begin to see some structure emerging. There are
various points worth noting about the Payout/Premium
Ratio
• For all currency pairs, 1 week options have payout less
than premium, on average 86.8%.
• For thirteen out of sixteen currency pairs, 1 month
options have payout less than premium, on average
95.1%
• For all pairs except Turkey, the 12 month pay-
out/premium ratio is significantly larger than the 1 week
payout/premium ratio
• Though there is dispersion, the longest dated options
have payouts significantly greater than premia. How-
ever, there is less good data for these tenors.
• The difference in mispricing is considerable. 1 week
option payouts are 86.7% of premium value, 3 year
options are 127.7%.
All of this information points towards a simple fact:: short
dated options are overvalued, and long dated options are
better value.
Particularly in the short tenors where the data quality is
best, we can see how very different currency pairs clearly
exhibit this pattern.

25
A view on the whole data set
Perhaps the simplest view on the data comes about when
we look at the overall average value of the payout/premium
vs tenor
Once we have sufficient averaging (and it is worth
remembering that about 200,000 premium/payout
calculations went into this graph!) then a clear pattern
emerges.

26
Analysis of Results
Why are short dated options expensive?
Short dated FX options are usually bought to cover short
dated and perhaps unexpected risks, so would be priced
for buyers who have less choice than usual
A short dated option may need its hedges adjusted every
day in a volatile market, and the trader may want to be
compensated for this time and effort.
Perhaps the most important contribution is simply that it is
human nature to be too focussed on near term risks.
• The market fears the risks of tomorrow more than it
should
How can we use this information?
We could make money by selling short dated options.
This is a courageous strategy, which would involve
selling volatility in high risk times
A more sophisticated development of the strategy would
include an element of hedging.
Why are long dated options better value?
Buyers of long term protection can usually take time to
consider different structures and let their counterparties
compete.
Long dated options can be simpler to hedge
It is likely that human nature provides for much of the long
term mispricing.
• Long term volatlities are not very different to short term,
but long term outcomes contain vast and unknowable
risks.
How can we use this information?
Long term option data is primarily of interest to hedgers
and protection buyers
For investors, ‘black swan’ type funds, which make money
on rare but extreme outcomes, use this effect.
However, interim volatility needs to be taken into
consideration

27
Conclusions
We can now answer a number of questions
Is it worth hedging long term FX risk with an option?
• Yes. On average, long dated bought options paid out
more than their premia
Can I tell which options are good value now?
• Yes. One can look at long term averages relative to
current prices. Care should be taken where there is not
much historical data, however
What tenor should I be using to hedge?
In general, longer is better with 12m appearing to be a
good tenor. After that the data is less good and
discounting becomes more important.
Remarkably, there seems to be a consistent and
significant mispricing of FX options.
Over history, and across currency pairs, we find that
short dated options are overpriced relative to their
payouts, while longer dated options are better value.

28
7. Conclusions 81

29
Out-of-the-money options
Based on their likelihood of expiring in the money, OTM options should clearly cost less
Source: Commerzbank
Distribution of final spot rates
OTM strikes less likely to be reached
If exchange rates followed a lognormal process,
OTM options should be cheaper due to the lower
probability of them expiring in the money
If we knew the form of the process (as assumed by
Black-Scholes), we could accurately price options
of varying strikes based on probability arguments
There should be no reason why options of different
strike prices should not provide similar value over
time
ATM Strike
Spot rate
OTM Strike
Most
likely
result
ATM Strike
Spot rate
OTM Strike
ATM Strike
Spot rate
OTM Strike
Most
likely
result
This result is encoded in the Black-Scholes model
and its analytic expressions for option prices, e.g.
)
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30
The volatility smile
In reality, return distributions have ‘fat tails’ so OTM options often have higher implied volatilities
Implied volatility smiles
As at 1 July 2013
Despite the fact that OTM options are cheaper in
dollar terms, option markets are usually discussed
in terms of implied volatility
In implied volatility terms, OTM options are often
said to be ‘expensive’
Markets price in higher volatilities for large moves
that are likely to be associated with market stress,
accounting for fat tails observed in historic data
We can restate our question of OTM option value in
terms of how these tail risks are priced; if risks are
overestimated, OTM options will offer poor value
Since the form of the volatility smile varies between
currency pairs and with time, it is not clear whether
OTM options are worth their (lower) cost
6
7
8
9
10
11
10d 20d 30d 40d ATM 40d 30d 20d 10d
Implied
volatility
(%)
EURGBP EURUSD USDGBP
Strike price (delta)

31
Dataset and methodology
Calculate c. 31,000 payoff-to-premium ratios
Currency dataset constituents and data series
start dates (mm/yy)
G10 crosses Emerging market crosses
AUDUSD 12/95 EURCZK 06/99
EURGBP 12/98 EURHUF 10/03
EURUSD 12/98 EURPLN 09/99
GBPUSD 05/96 USDBRL 10/03
USDCAD 08/98 USDKRW 08/04
USDCHF 05/96 USDMXN 11/99
USDDKK 06/03 USDSGD 12/00
USDJPY 12/95 USDTRY 08/02
USDNOK 02/99 USDTWD 04/99
USDSEK 08/98 USDZAR 02/99
In order to determine the relative value offered by out-
of-the-money currency options one faces an involved
set of computations
Calculate the premiums of options for a number of
representative currencies over a meaningful period of
time (ideally covering at least a full business cycle)
For each date/currency-pair/tenor combination, require
implied volatilities, FX spot price and two of forward
rate, foreign deposit rate and domestic deposit rate
Use straddles throughout in order to immunise the
study as much as possible from overall directionality of
currency pairs
Calculate premiums and payoffs for a range of tenors
(1W, 1M, 3M, 6M and 12M) for 20 currency pairs since
the end of 1995 where possible
Calculate one payoff-to-premium ratio per month for
ATM, 25-delta and 10-delta options Source: Commerzbank

32
ATM and OTM option premiums
How much cheaper are OTM options?
Average ATM and 25-delta option premiums
Percent of notional amount, since 1995 where possible
On average, halving the delta of an FX option more
than halves the dollar cost of the option
For our dataset, a 3M ATM option typically costs 4-
5% of the notional amount while a 3M 25 delta
OTM option costs nearer 2% of the notional
0
2
4
6
8
USDTWD
USDSGD
EURCZK
EURGBP
USDCAD
GBPUSD
EURPLN
EURUSD
USDCHF
USDJPY
EURHUF
USDDKK
AUDUSD
USDKRW
USDMXN
USDNOK
USDSEK
USDTRY
USDBRL
USDZAR
1M ATM 3M ATM 1M 25-delta 3M 25-delta

33
ATM and OTM option payouts
As expected, lower premiums mean lower payouts on average
Average ATM and 25-delta option payouts
Percent of notional amount, since 1995 where possible
Payouts are discounted to account for the period of
time that passes between an upfront premium
being paid and any payout being received
As expected, the reduced premiums of OTM
options result in smaller payoffs
To get to the nub of the matter regarding OTM
option value we must combine the information on
premiums and payouts
0
2
4
6
8
USDTWD
USDSGD
EURCZK
EURGBP
GBPUSD
USDCAD
USDMXN
EURHUF
USDKRW
USDDKK
USDCHF
EURUSD
USDJPY
EURPLN
USDNOK
USDSEK
AUDUSD
USDTRY
USDZAR
USDBRL
1M ATM 3M ATM 1M 25-delta 3M 25-delta

34
Payout-to-premium ratios by currency pair
Underperformance of OTM options versus ATM options is largest for shorter tenors
Average payout-to-premium ratios (%)
Since 1995 where possible
For 1M options, the results are fairly conclusive; in
almost all cases OTM options paid out less than
ATM options as a percentage of the premium paid
For longer tenors the picture becomes slightly less
clear
Moving further out in expiry to the 6M tenor sees
the average difference in payout ratios between
ATM and OTM options reduced even further
At the 3M tenor (not shown), while ATM options
provided the best value overall, there were some
example of 10-delta options having performed best
0
50
100
150
EURCZK
USDMXN
EURHUF
USDNOK
USDTWD
USDKRW
EURGBP
USDSEK
GBPUSD
USDJPY
USDSGD
USDDKK
USDCAD
EURPLN
EURUSD
USDZAR
USDCHF
USDTRY
USDBRL
AUDUSD
1M ATM 1M 25-delta 1M 10-delta
0
50
100
150
200
EURGBP
USDMXN
EURCZK
GBPUSD
USDSGD
EURHUF
USDKRW
USDTWD
USDDKK
USDNOK
USDCAD
USDCHF
USDSEK
USDTRY
USDJPY
EURUSD
EURPLN
USDZAR
AUDUSD
USDBRL
6M ATM 6M 25-delta 6M 10-delta

35
Aggregated results for all currency pairs
Simple averages for EM and G10 crosses
Average payoff ratios
G10 (top chart) and EM (bottom chart)
Aggregate results for the currency pairs, grouping
them into G10 and EM baskets
Note that we did not take into account the fact that
different cross rates had different amounts of data;
the averages are simple averages over the pairs
Despite their apparent cheapness, out-of-the-
money options on the whole offer poor value
Tendency for implied volatilities to be higher
increases the cost of OTM options beyond a level
consistent with probability of expiring in-the-money
Difference between ATM and OTM option payout
ratios becomes much smaller for longer tenors and
is greatest for short tenors/deeply OTM options
40
50
60
70
80
90
100
110
1W 1M 3M 6M 12M
ATM 25-delta 10-delta
40
50
60
70
80
90
100
110
1W 1M 3M 6M 12M
ATM 25-delta 10-delta

36
Compare results for EM and G10 currencies
Plot contents of previous two charts on common axes
Average payout-to-premium ratios (%)
By tenor, since 1995 where possible
Relative outperformance of longer-tenor options is
present for both EM and G10 pairs. This effect
could be due to:
• Short-tenor options being priced for short-
notice/limited choice buyers
• Short-dated options needing to be hedged more
regularly, with traders charging for the additional
time and effort involved
• Perhaps most importantly, it may simply be
human nature to focus on near-term risks while
being blasé about the longer term outlook
Variation with tenor seems to be greater for crosses
that include an emerging market currency than for
the G10 crosses
It would appear that overall long-term risks have
historically been underestimated slightly for EM
currencies, but not for G10 currencies
60
70
80
90
100
110
1W 1M 3M 6M 12M
G10 ATM EM ATM G10 25-delta EM 25-delta
Short-term risks appear to have been
overestimated to a greater degree for EM
currencies than for G10 currencies

37
Alternative measures of OTM option value
Before writing off OTM options as ‘too expensive’ we should consider other measures of value
Example of cashflow benefit for option hedges
Frequency distribution of quarterly cashflows (% notional)
Despite their apparent lack of payoff-to-premium
value, OTM options are valuable in other respects
E.g. companies with a mandatory hedging policy
may find OTM options an ideal vehicle for occas-
ions when ‘insurance’ is not deemed necessary
In a scenario in which a hedged currency steadily
appreciates, an OTM option could provide the
compulsory hedge at half the cost of an ATM option
OTM options also offer an attractive cashflow
structure; not only could the corporate benefit from
FX appreciation, but the small ‘insurance’ cashflow
of an OTM option replaces the potentially large
negative cashflow that would fall due under a
forward hedge
0
5
10
15
20
25
-5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5%
Forwards Options

38
Conclusions
Out-of-the-money options are expensive in terms of average payout-to-premium ratios
Over a historical test period, out-of-the-money options on the whole proved more expensive in terms of
payoff ratios than at-the-money options. The relative performance gap is large for short tenors and much
smaller for longer tenors
As we have shown previously for at-the-money options, longer-tenor out-of-the-money options offered
better value
Long-term risks have historically been underestimated for EM currencies while short-term risks appear to
have been overestimated to a greater degree for EM currencies than for G10 currencies
Comparing G10 and EM crosses suggests that there are several biases in the relative pricing of short-
and long-tenor options, both at the money and out of the money

39
7. Conclusions 81

40
Currency pairs
Available currency pairs under consideration
Currency Pairs
Dataset from 1999
The currency pairs we considered were all of those
for we could source good quality data, which went
back several years in time at least
The data set begins in 1999, though not all
currency pairs go back to that date
EURBRL EURPLN EURRUB USDARS USDBRL
USDCLP USDCNY USDCOP USDCZK USDHUF
USDIDR USDILS USDINR USDKRW USDMXN
USDMYR USDPHP USDPLN USDRON USDRUB
USDSGD USDTHB USDTRY USDTWD USDZAR
The data needed are spot rates, implied ATMF and
OTM option volatilities, forward rates and interest
rates

41
Hedge Strategies – Forward contracts
The most liquid and traditional hedge
Source: Commerzbank
Forward payoffs
Payoffs can be significantly positive or negative
Forward contracts are popular and highly liquid.
The hedger locks in the forward rate, which for the
higher yielding EM currency inevitably implies a
depreciation.
To hedge a positive EM exposure, a long forward
contract on the FX rate is entered into; for a
negative EM exposure, the hedge will be a short
forward
If this occurs then long forward contracts will lose
money, and short forward contracts will make
money
In general, the EM currency does not depreciate as
much as is implied by the forward rate
Forward rate
Long forward
payoff
Short forward
payoff
EM currency depreciation
Spot at Expiry
Forward rate
Long forward
payoff
Short forward
payoff
Spot at Expiry

42
Hedge Strategies – ATMF Options
The most liquid and widely traded option type
Source: Commerzbank
ATMF Option payoffs
Payoffs have limited loss but unlimited gain
To hedge a long (short) exposure in an EM
currency, the hedger would buy a call (put) option
on the FX rate.
This costs a premium which is fixed at the time of
purchase, and pays out when the EM currency
depreciates (appreciates) further than the forward
rate.
Because an option is the right but not the obligation
to enter into the exchange at expiry, the maximum
loss is the premium amount
Forward rate
Long
call payoff
Long put payoff
Long forward
payoff
Short forward payoff
Forward rate
Long forward
payoff
Short forward
payoff
Spot at Expiry
Forward rate
Long
call payoff
Long put payoff
Long forward
payoff
Forward rate
Long forward
payoff
Short forward
payoff
Spot at Expiry
Forward rate
Long forward
payoff
Short forward
payoff
Spot at Expiry

43
Hedge Strategies – OTM Options
Good quality data is available for 25 delta options
Source: Commerzbank
OTM Option payoffs
OTM options are cheaper but have lower payoffs
OTM options pay out only for large spot moves;
they are sometimes referred to as ‘disaster
insurance’
For this reason their premium costs are lower, as
they offer less protection
Determination of their value will depend upon
protection offered vs premium cost
Forward rate
Long ATMF
call payoff
Long forward
payoff
Forward rate
Long forward
payoff
Spot at Expiry
Long OTM
call payoff
Forward rate
Long ATMF
call payoff
Long forward
payoff
Forward rate
Long forward
payoff
Spot at Expiry
Long OTM
call payoff
We show only the call options for simplicity but the
case is symmetrical for puts and short forwards

44
Hedging long EM exposures – forwards vs ATMF options
Both forwards and options on average lose money – but options lose less
Average 3m hedge cashflows
Results for long forwards or long ATMF calls
We simulated the cashflows from both a 3m long
forward and a 3m long call ATMF option hedge
program
To represent the full impact of the purchased call
option, we netted both premium and option payoff
into a single number
Twenty out of the twenty-five currency pairs tested
have the option cost as less than the forward cost,
and the five exceptions have smaller data sets
The difference between forward and option hedges
is unambiguous – even including the full premium
and bid-offer costs, the options cost on average is
just over half of the forward cost
The forward hedge is short of the EM currency, so if a
depreciation occurs which is greater than that implied by the
interest rate differential, the forward hedge will have a
positive return. However, usually the depreciation is rather
less than this, or the emerging currency will even appreciate,
so the forward contracts tend to lose money.
-5%
-4%
-3%
-2%
-1%
0%
EURBRL
EURPLN
EURRUB
USDARS
USDBRL
USDCLP
USDCNY
USDCOP
USDCZK
USDHUF
USDIDR
USDILS
USDINR
USDKRW
USDMXN
USDMYR
USDPHP
USDPLN
USDRON
USDRUB
USDSGD
USDTHB
USDTRY
USDTWD
USDZAR
Average
net
cashflow
3m Long Forward Hedges 3m ATMF Long Call Option Hedges

45
Hedging long EM exposures – forwards vs OTM options
OTM options cost significantly less than ATMF
Results for long forwards or long OTM calls
We repeated the backtest using 25 Delta out-of-the
money long call options
It is not necessarily the case that they will be
cheaper overall; if the payoffs to these options are
disproportionally small then they will prove to be
poor value overall
They are on average less than half the cost of the
forwards, once more including premium and bid-
offer costs
The supposedly more exotic OTM options are
actually cheaper hedges again than both the ATMF
options and the long forward contracts
OTM call options are cheaper long EM exposure hedges
than ATMF call options, which themselves are cheaper than
forward contracts
-5%
-4%
-3%
-2%
-1%
0%
EURBRL
EURPLN
EURRUB
USDARS
USDBRL
USDCLP
USDCNY
USDCOP
USDCZK
USDHUF
USDIDR
USDILS
USDINR
USDKRW
USDMXN
USDMYR
USDPHP
USDPLN
USDRON
USDRUB
USDSGD
USDTHB
USDTRY
USDTWD
USDZAR
Average
net
cashflow
3m Long Forward Hedges 3m OTM Long Call Option Hedges

46
Hedge Strategies – comparing the worst cases
Did the options protect the hedger during depreciations?
OTM Option payoffs
OTM options are cheaper but have lower payoffs
Over time the options have offered better value
than forwards, but how do they perform in periods
of EM currency depreciation?
For each currency pair, we looked at the very worst
3m EM depreciation in the data set, when the long
forward payoff had been highest
For that same period, we looked at the ATMF and
OTM long call option payoffs
We see that in the overwhelming majority of cases,
the options provided a very effective hedge
-20%
-10%
0%
10%
20%
30%
40%
EURBRL
EURPLN
EURRUB
USDARS
USDBRL
USDCLP
USDCNY
USDCOP
USDCZK
USDHUF
USDIDR
USDILS
USDINR
USDKR
USDMXN
USDMY
USDPHP
USDPLN
USDRON
USDRUB
USDSGD
USDTHB
USDTRY
USDTW
USDZAR
Payoff
in
%
notional
Long forward Long ATMF call Long 25D call

47
Hedging short EM exposures – forwards vs ATMF options
Forward hedges are the clear winner here
Results for short forwards or long ATMF puts
We simulated the cashflows from both a 3m short
forward and a 3m long put ATMF option hedge
program
We saw previously that long forward hedges tend
to lock in a loss; conversely, short forward hedges
tend to lock in a profit
The ATM options also had a positive return on
average, but less than half of the forward return
We saw previously that long forward hedges tend
to lock in a loss; conversely, short forward hedges
tend to lock in a profit
The forward hedge is long of the EM currency, so if a
depreciation occurs which is less than than that implied by
the interest rate differential, the forward hedge will have a
positive return. Usually the depreciation is rather less than
this, or the emerging currency will even appreciate, so the
forward contracts on average make money.
-1%
0%
1%
2%
3%
4%
5%
EURBRL
EURPLN
EURRUB
USDARS
USDBRL
USDCLP
USDCNY
USDCOP
USDCZK
USDHUF
USDIDR
USDILS
USDINR
USDKRW
USDMXN
USDMYR
USDPHP
USDPLN
USDRON
USDRUB
USDSGD
USDTHB
USDTRY
USDTWD
USDZAR
Average
net
cashflow
3m Short Forward Hedges 3m ATMF Long Put Option Hedges

48
Hedging short EM exposures – forwards vs OTM options
OTM options deliver lower returns than ATMF
Results for short forwards or long ATMF puts
We repeated the backtest using 25 Delta out-of-the
money long call options
The OTM options lag behind the ATMF, on average
delivering zero return
So we have a hierarchy where short forward
hedges have been the best for short EM
exposures, followed by ATMF and OTM options
Despite costing less, the OTM options deliver lower returns
than the ATMF, as the bias introduces by the carry trade
ensures that the spot rates rarely move past the strike rate
of the option
-2%
-1%
0%
1%
2%
3%
4%
5%
EURBRL
EURPLN
EURRUB
USDARS
USDBRL
USDCLP
USDCNY
USDCOP
USDCZK
USDHUF
USDIDR
USDILS
USDINR
USDKRW
USDMXN
USDMYR
USDPHP
USDPLN
USDRON
USDRUB
USDSGD
USDTHB
USDTRY
USDTWD
USDZAR
Average
net
cashflow
3m Short Forward Hedges 3m OTM Long Put Option Hedges

49
Hedge Recommendations
It becomes possible to see a highly consistent pattern in the historical data
The situations we analyse are those where hedging is passive and constant rather than dynamic
For those institutions with the capacity to vary their hedges with the market environment, other hedge strategies become
available.
Hedge Recommendations
A surprisingly simple result emerges
Exposure Risk Optimal hedge
instrument
Optimal hedge
tenor
Long EM
currency
EM depreciation 25D OTM call
option 1
12m
Short EM
currency
EM appreciation Short forward no clear signal
[1] The call option is on the FX rate, so is a call on the developed currency, and a put on the EM currency

50
7. Conclusions 81

51
Why investigate Put and Call FX Options?
Any kind of put-call asymmetry will be significant to the financial community
Previous work revealed significant mispricings with FX straddle options. A straddle is
a put plus a call; we used these structures to eliminate long term trend effects
We now turn our attention to the separate puts and calls to see how they contribute to
this overall result.
This is of interest because, for hedging purposes, the natural position for the option
buyer will always be one way round, depending on their country of origin. Also, if
investors will want to know if trading strategies can be developed.
We found that on average, in terms of premium versus payout, long dated options are
better value than short dated, with mispricings of up to 20% at each end of the term
structure.
If there is any kind of put-call asymmetry, it will be of very broad interest to the
financial community.

52
Previous Work
Our earlier work concentrated on ATMF (At The Money Forward) FX straddle options
If the premium of the option is ‘fair’ we would
expect that neither of the buyer and seller
consistently makes or loses money
We discovered that on average, short dated
options are expensive, but long dated options can
often be cheap.
Payout/premium ratio for ATMF Straddles
On average long dated options are better value
Almost every currency pair conformed to this
pattern, with the feature of better value associated
with longer tenors holding constant.
The rationale for this effect was not entirely clear,
though risk perception is certainly part of it
70%
75%
80%
85%
90%
95%
100%
105%
1W 1M 3M 6M 12M 2Y 3Y
Payout/Premium Ratio for ATMF Straddles - average over 34 pairs
Series1

53
How might mispricings arise?
Quick recap of the calculation of the premium of an ATMF call option
There are two parameters which would have the
potential to have a systematic effect on the
premium/payout ratio
Either the forward rate is not in general the mean of
the future distribution, or the implied volatility is a
biased estimate of the standard deviation. Or both.
These are the forward rate K and the option implied
volatility 
)
(
)
( 2
1
0 d
N
K
d
N
e
S
c
T
r
T
r f
f 



T
d
d
T
T
r
r
K
S
d
f









1
2
2
0
1
)
2
/
(
)
/
ln(
c = premium of a call option on the foreign currency
S0 = FX rate at inception (value of 1 unit of foreign currency in base
currency)
K = Forward rate
r = interest rate for tenor of the deal in the base currency
rf = interest rate for the tenor of the deal in the foreign currency
T = tenor of the deal
 = implied volatility of the option
We would expect that by analysing put and call
payout/premium ratios separately, we would gain
some insight as to the source of the mispricing
This is because they will react differently to
forward rate effects (asymmetric) and distribution
effects (more likely to be symmetric).

54
Methodology and results
Testing option performance over time
In all cases, we will refer to options on the rate, so
a call option will pay out when the rate rises. eg for
EURUSD this is when the EUR appreciates relative
to the USD.
We used 34 available currency pairs, for all
available tenors, from 1995 or as early as it was
available. We included trading costs
We then looked forward to the payout date for each
contract and calculated the option payout
For all FX ATMF option data available in
Bloomberg, we took weekly data to calculate the
average historical premia of put and call options
Payout/premium ratio for ATMF put and
call options
Finally we divide the payout by the discounted
premium to find whether the option overall
delivered value or cost money.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
1W 1M 3M 6M 12M 2Y 3Y
Payout/Premium Ratio for ATMF Calls
Series1
60%
70%
80%
90%
100%
110%
120%
130%
140%
1W 1M 3M 6M 12M 2Y 3Y
Payout/Premium Ratio for ATMF Puts
Series1

55
How should we interpret this?
This is a remarkable result
Consider that the results found in previous work for ATMF straddles show a strong
tendency for longer dated options to be better value. We now see in more detail how
these results originate.
But in fact, all of the tendency for better value in longer tenors is coming from the puts!
The calls show a strong tendency in the opposite direction, for longer dated options
to be much worse value.
A straddle is just a put and a call added together, so the upwards tendency of the data
with tenor is coming from the average of the put and call data
How should we interpret this? Looking at the currency-by-currency results gives
us a clue as to the cause.

56
Currency by currency results – put options
Put options generally have better value in longer tenors
Currency-by-currency results for ATMF put
options
Put options generally have better value in longer tenors
Puts, which pay out for appreciation of the foreign
currency, are very good value indeed.
The avearge payout/premium ratio reaches 160%
for the 3 year tenor.
We might take the 2 year and 3 year tenor results
as coming from less good data but even the 12
month tenor has a payout/premium ratio of 140%
0%
50%
100%
150%
200%
250%
300%
350%
400%
1W 1M 3M 6M 12M 2Y 3Y
Payoff/Premium Ratio for ATMF puts for different currency pairs
AUDUSD EURAUD EURCHF EURCZK EURGBP EURHUF EURJPY
EURNOK EURPLN EURUSD GBPUSD USDARS USDBRL USDCAD
USDCHF USDCLP USDCOP USDCZK USDDKK USDHKD USDIDR
USDILS USDINR USDJPY USDKRW USDMXN USDNOK USDPHP
USDPLN USDSEK USDSGD USDTRY USDTWD USDZAR Average

57
Detailed results for put options (1)
Payout/Premium Ratios for ATMF Puts Payout/Premium Ratios for ATMF
1W 1M 3M
Premia Payoff Ratio Premia Payoff Ratio Premia Payoff Ratio
AUDUSD 0.71% 0.62% 86.8% 1.33% 1.26% 94.9% 2.30% 2.11% 91.5%
EURAUD 0.64% 0.62% 96.0% 1.21% 1.34% 111.2% 2.13% 2.69% 126.1%
EURCHF 0.32% 0.27% 83.9% 0.60% 0.55% 92.0% 1.03% 0.94% 90.4%
EURCZK 0.43% 0.36% 82.2% 0.83% 0.76% 91.1% 1.43% 1.45% 101.0%
EURGBP 0.47% 0.41% 87.1% 0.93% 0.82% 89.0% 1.65% 1.39% 84.4%
EURHUF 0.64% 0.56% 87.3% 1.25% 1.14% 91.2% 2.21% 2.33% 105.5%
EURJPY 0.72% 0.63% 87.8% 1.42% 1.24% 87.6% 2.47% 2.17% 87.9%
EURNOK 0.44% 0.38% 85.4% 0.84% 0.81% 96.3% 1.45% 1.47% 101.0%
EURPLN 1.25% 1.09% 87.3% 2.15% 2.16% 100.7%
EURUSD 0.60% 0.54% 89.9% 1.21% 1.15% 95.2% 2.16% 2.03% 94.1%
GBPUSD 0.53% 0.47% 87.8% 1.04% 0.92% 88.1% 1.85% 1.50% 81.0%
USDARS 1.34% 0.92% 68.3% 2.95% 2.66% 90.1%
USDBRL 0.88% 0.87% 98.6% 1.71% 2.16% 126.2% 2.99% 4.91% 164.1%
USDCAD 0.52% 0.50% 96.5% 1.04% 1.03% 99.7% 1.78% 1.87% 105.1%
USDCHF 0.63% 0.60% 95.6% 1.24% 1.27% 102.9% 2.19% 2.20% 100.5%
USDCLP 1.39% 1.34% 96.4% 2.48% 2.80% 113.0%
USDCOP 1.71% 1.74% 102.0% 2.97% 3.56% 120.0%
USDCZK 0.80% 0.76% 94.5% 1.56% 1.70% 108.7% 2.72% 3.07% 112.8%
USDDKK 0.64% 0.53% 83.9% 1.25% 1.20% 95.7% 2.21% 2.01% 91.0%
USDHKD 0.06% 0.02% 36.0% 0.09% 0.03% 32.4% 0.18% 0.05% 26.5%
USDIDR 1.46% 1.17% 80.1% 2.78% 2.42% 87.2%
USDILS 0.99% 1.14% 115.3% 1.68% 2.24% 133.6%
USDINR 0.99% 1.01% 102.6% 1.81% 1.97% 109.1%
USDJPY 0.66% 0.54% 81.8% 1.28% 1.11% 86.3% 2.24% 1.94% 86.6%
USDKRW 0.65% 0.54% 83.3% 1.20% 1.17% 97.6% 2.12% 2.10% 98.8%
USDMXN 0.67% 0.55% 81.1% 1.29% 1.15% 89.4% 2.33% 2.32% 99.7%
USDNOK 0.72% 0.68% 94.5% 1.40% 1.40% 100.3% 2.45% 2.70% 109.9%
USDPHP 1.23% 0.86% 70.2% 2.31% 1.89% 81.7%
USDPLN 1.70% 1.93% 113.5% 2.99% 3.74% 125.3%
USDSEK 0.72% 0.65% 90.9% 1.42% 1.39% 98.0% 2.48% 2.50% 100.7%
USDSGD 0.36% 0.30% 82.3% 0.67% 0.67% 100.6% 1.21% 1.29% 106.1%
USDTRY 0.72% 0.78% 107.5% 1.57% 1.87% 119.1% 2.82% 3.66% 129.4%
USDTWD 0.33% 0.21% 62.8% 0.57% 0.48% 84.0% 1.07% 0.93% 87.0%
USDZAR 1.01% 0.91% 89.4% 1.98% 2.01% 101.3% 3.41% 3.74% 109.7%
Average Ratio
1W 86.11%
1M 94.54%
3M 101.52%
6M 110.81%
12M 117.63%
2Y 113.31%
3Y 127.17%

58
Detailed results for put options (2)
Payout/Premium Ratios for ATMF Puts
6M 12M 2Y 3Y
Premia Payoff Ratio Premia Payoff Ratio Premia Payoff Ratio Premia Payoff Ratio
AUDUSD 3.19% 3.15% 98.6% 4.44% 4.50% 101.4% 6.21% 2.24% 36.1% 6.88% 0.85% 12.3%
EURAUD 3.06% 4.55% 148.7% 4.37% 7.98% 182.4% 6.09% 15.42% 253.1% 6.63% 22.78% 343.6%
EURCHF 1.47% 1.40% 95.0% 2.07% 2.35% 113.6% 3.23% 7.15% 221.5% 3.11% 10.63% 341.2%
EURCZK 2.01% 2.30% 114.2% 2.82% 3.87% 137.5%
EURGBP 2.37% 1.87% 79.1% 3.37% 2.46% 73.1% 5.03% 2.12% 42.1% 5.83% 2.42% 41.5%
EURHUF 3.15% 3.51% 111.6% 4.45% 4.58% 102.9%
EURJPY 3.51% 3.15% 89.8% 4.90% 4.42% 90.2% 7.17% 9.34% 130.3% 8.98% 14.79% 164.7%
EURNOK 2.03% 2.17% 107.0% 2.83% 3.66% 129.5% 4.17% 5.01% 120.2% 4.82% 6.61% 137.2%
EURPLN 3.02% 3.35% 110.9% 4.26% 5.36% 125.9%
EURUSD 3.08% 2.93% 95.0% 4.37% 3.94% 90.0% 6.09% 3.06% 50.3% 6.75% 3.38% 50.1%
GBPUSD 2.65% 2.24% 84.5% 3.75% 2.96% 79.0% 5.86% 6.94% 118.5% 6.81% 8.83% 129.7%
USDARS 4.82% 4.79% 99.3% 8.00% 8.16% 101.9%
USDBRL 4.30% 8.97% 208.9% 6.33% 16.37% 258.8%
USDCAD 2.53% 3.05% 120.9% 3.60% 4.90% 136.3% 5.97% 5.90% 98.9% 7.26% 5.35% 73.7%
USDCHF 3.11% 3.15% 101.4% 4.36% 4.38% 100.5% 5.91% 7.41% 125.3% 6.47% 9.42% 145.7%
USDCLP 3.57% 4.23% 118.4% 5.15% 6.29% 122.3%
USDCOP 4.24% 5.68% 134.1% 6.45% 7.38% 114.5%
USDCZK 3.85% 4.62% 120.2% 5.43% 6.25% 115.2%
USDDKK 3.17% 3.21% 101.1% 4.54% 4.10% 90.1% 6.18% 4.04% 65.4% 6.77% 3.20% 47.2%
USDHKD 0.32% 0.06% 18.7% 0.63% 0.09% 14.7%
USDIDR 4.16% 4.58% 110.1% 6.39% 7.75% 121.3%
USDILS 2.35% 3.76% 160.1% 3.29% 6.09% 185.1%
USDINR 2.61% 2.80% 107.2% 5.15% 3.43% 66.7%
USDJPY 3.15% 2.68% 85.1% 4.39% 3.46% 78.8% 5.97% 7.68% 128.6% 6.70% 9.74% 145.2%
USDKRW 3.00% 3.36% 111.9% 4.25% 5.18% 122.0%
USDMXN 3.36% 3.50% 104.1% 4.91% 5.73% 116.7%
USDNOK 3.47% 4.21% 121.4% 4.88% 6.66% 136.5% 7.18% 6.83% 95.2% 8.08% 6.36% 78.8%
USDPHP 3.48% 3.15% 90.5% 5.12% 5.75% 112.3%
USDPLN 4.22% 5.85% 138.7% 5.95% 8.94% 150.3%
USDSEK 3.50% 3.94% 112.6% 4.91% 6.21% 126.6% 7.28% 7.34% 100.8% 8.36% 5.82% 69.6%
USDSGD 1.77% 1.99% 112.5% 2.57% 3.06% 119.2%
USDTRY 4.18% 6.15% 147.1% 6.29% 10.51% 167.1%
USDTWD 1.60% 1.27% 79.5% 2.42% 1.51% 62.7%
USDZAR 4.81% 6.22% 129.4% 6.79% 10.47% 154.2%

59
0%
50%
100%
150%
200%
250%
300%
1W 1M 3M 6M 12M 2Y 3Y
Payout/Premium Ratio for ATMF calls for different currency pairs
AUDUSD EURAUD EURCHF EURCZK EURGBP EURHUF EURJPY
EURNOK EURPLN EURUSD GBPUSD USDARS USDBRL USDCAD
USDCHF USDCLP USDCOP USDCZK USDDKK USDHKD USDIDR
USDILS USDINR USDJPY USDKRW USDMXN USDNOK USDPHP
USDPLN USDSEK USDSGD USDTRY USDTWD USDZAR Average
Currency by currency results – call options
The results are remarkably consistent – apart from AUD
Currency-by-currency results for ATMF call
options
Call options generally have worse value in longer tenors
One glaring outlier, particularly for the calls, is the
AUD/USD currency pair.
Where the average payout/premium ratio for all the
calls for the 3 year tenor is 41%, the AUD/USD pair
comes in at 179%.
For the puts, the 3 year tenor for the AUD is 13%,
in complete contrast to the average of 157%
AUD
This leads us in the direction of the answer. The
AUD currency on average has had much higher
interest rates, over time, than the USD.
Most of the currency pairs in the sample are the
other way round. This seems to be a carry trade
effect

60
Detailed results for call options (1)
Payout/Premium Ratios for ATMF Calls Payout/Premium Rat
1W 1M 3M
Premia Payoff Ratio Premia Payoff Ratio Premia Payoff Ratio
AUDUSD 0.71% 0.69% 96.1% 1.33% 1.47% 110.6% 2.30% 2.64% 114.7%
EURAUD 0.64% 0.53% 82.7% 1.21% 1.01% 83.6% 2.14% 1.42% 66.2%
EURCHF 0.32% 0.25% 80.0% 0.60% 0.52% 86.5% 1.04% 0.80% 77.2%
EURCZK 0.43% 0.31% 72.2% 0.84% 0.56% 67.0% 1.44% 0.83% 57.6%
EURGBP 0.47% 0.41% 87.3% 0.93% 0.80% 86.1% 1.65% 1.40% 84.5%
EURHUF 0.64% 0.48% 74.6% 1.26% 0.83% 66.4% 2.22% 1.36% 61.3%
EURJPY 0.72% 0.68% 94.3% 1.42% 1.44% 101.2% 2.48% 2.65% 107.0%
EURNOK 0.44% 0.34% 76.5% 0.84% 0.64% 76.1% 1.45% 0.99% 68.0%
EURPLN 1.25% 0.95% 76.3% 2.16% 1.66% 77.1%
EURUSD 0.60% 0.55% 91.0% 1.21% 1.21% 99.5% 2.16% 2.18% 100.7%
GBPUSD 0.53% 0.47% 89.2% 1.04% 1.02% 98.1% 1.86% 1.71% 92.2%
USDARS 1.34% 0.15% 11.1% 2.92% 0.29% 10.1%
USDBRL 0.88% 0.63% 71.5% 1.71% 1.19% 69.5% 3.00% 1.82% 60.9%
USDCAD 0.52% 0.45% 85.9% 1.04% 0.76% 73.3% 1.79% 1.17% 65.2%
USDCHF 0.63% 0.56% 89.1% 1.24% 1.21% 97.9% 2.20% 2.12% 96.3%
USDCLP 1.39% 1.08% 77.9% 2.49% 1.96% 78.8%
USDCOP 1.72% 1.14% 66.1% 3.00% 1.85% 61.7%
USDCZK 0.80% 0.71% 88.9% 1.57% 1.46% 93.3% 2.73% 2.41% 88.2%
USDDKK 0.64% 0.52% 80.9% 1.25% 1.11% 88.5% 2.22% 1.79% 80.6%
USDHKD 0.06% 0.03% 51.2% 0.09% 0.06% 64.8% 0.18% 0.14% 74.5%
USDIDR 1.46% 0.84% 57.9% 2.77% 1.47% 53.3%
USDILS 0.99% 0.74% 74.9% 1.68% 1.11% 66.2%
USDINR 0.99% 0.81% 82.0% 1.79% 1.56% 86.9%
USDJPY 0.66% 0.55% 83.6% 1.29% 1.29% 100.6% 2.24% 2.44% 109.2%
USDKRW 0.65% 0.47% 72.2% 1.20% 0.92% 76.7% 2.13% 1.52% 71.1%
USDMXN 0.67% 0.51% 75.8% 1.29% 0.92% 71.2% 2.32% 1.47% 63.3%
USDNOK 0.72% 0.61% 84.8% 1.40% 1.08% 77.4% 2.46% 1.78% 72.5%
USDPHP 1.23% 0.55% 44.8% 2.32% 1.00% 43.1%
USDPLN 1.70% 1.28% 75.2% 3.00% 2.11% 70.6%
USDSEK 0.72% 0.61% 84.6% 1.42% 1.21% 85.3% 2.49% 2.00% 80.5%
USDSGD 0.36% 0.25% 69.6% 0.67% 0.52% 77.8% 1.22% 0.82% 67.8%
USDTRY 0.72% 0.63% 86.5% 1.57% 1.17% 74.6% 2.84% 1.94% 68.4%
USDTWD 0.33% 0.22% 64.9% 0.57% 0.54% 93.7% 1.07% 1.14% 106.7%
USDZAR 1.01% 0.82% 81.2% 1.98% 1.60% 80.8% 3.41% 2.66% 78.0%
Average Ratio
1W 80.58%
1M 78.44%
3M 75.30%
6M 73.87%
12M 66.01%
2Y 62.29%
3Y 49.98%

61
Detailed results for call options (2)
Payout/Premium Ratios for ATMF Calls
6M 12M 2Y 3Y
Premia Payoff Ratio Premia Payoff Ratio Premia Payoff Ratio Premia Payoff Ratio
AUDUSD 3.19% 4.15% 130.0% 4.45% 6.54% 146.9% 6.19% 12.59% 203.4% 6.85% 16.56% 241.6%
EURAUD 3.06% 2.06% 67.5% 4.39% 2.18% 49.7% 6.06% 1.19% 19.7% 6.59% 0.98% 14.9%
EURCHF 1.47% 1.12% 76.5% 2.07% 1.68% 81.1% 3.17% 1.91% 60.2% 3.00% 0.72% 23.9%
EURCZK 2.02% 0.97% 48.3% 2.82% 1.21% 42.8%
EURGBP 2.37% 1.97% 82.9% 3.37% 2.89% 85.8% 5.01% 5.58% 111.3% 5.77% 8.15% 141.2%
EURHUF 3.15% 1.69% 53.7% 4.45% 1.64% 36.8%
EURJPY 3.51% 4.04% 115.1% 4.89% 6.58% 134.4% 7.13% 6.12% 85.8% 8.88% 2.95% 33.2%
EURNOK 2.03% 1.25% 61.9% 2.83% 1.64% 57.9% 4.15% 1.33% 32.0% 4.80% 1.52% 31.7%
EURPLN 3.03% 2.31% 76.4% 4.27% 3.12% 73.0%
EURUSD 3.09% 3.26% 105.6% 4.38% 4.69% 107.1% 6.05% 3.43% 56.7% 6.70% 2.72% 40.6%
GBPUSD 2.65% 2.52% 94.9% 3.75% 3.36% 89.4% 5.85% 3.13% 53.4% 6.77% 1.55% 22.8%
USDARS 4.73% 0.49% 10.3% 7.98% 0.97% 12.2%
USDBRL 4.30% 2.58% 60.0% 6.37% 2.86% 44.9%
USDCAD 2.53% 1.58% 62.3% 3.61% 1.85% 51.2% 5.96% 1.70% 28.5% 7.26% 0.88% 12.1%
USDCHF 3.11% 2.92% 94.0% 4.37% 3.57% 81.7% 5.87% 1.52% 25.9% 6.43% 0.02% 0.4%
USDCLP 3.57% 2.52% 70.7% 5.16% 2.54% 49.2%
USDCOP 4.27% 2.27% 53.2% 6.54% 1.83% 28.0%
USDCZK 3.86% 3.22% 83.4% 5.44% 3.51% 64.6%
USDDKK 3.19% 2.65% 83.0% 4.56% 2.95% 64.6% 6.14% 2.69% 43.8% 6.70% 2.84% 42.4%
USDHKD 0.32% 0.20% 64.2% 0.63% 0.30% 46.8%
USDIDR 4.14% 2.64% 63.6% 6.47% 3.17% 49.0%
USDILS 2.35% 1.48% 63.1% 3.29% 1.59% 48.4%
USDINR 2.59% 2.29% 88.5% 5.18% 3.58% 69.0%
USDJPY 3.14% 3.65% 116.0% 4.39% 5.20% 118.5% 5.95% 4.24% 71.3% 6.62% 2.89% 43.6%
USDKRW 3.01% 2.20% 73.3% 4.26% 3.24% 76.1%
USDMXN 3.36% 1.78% 53.0% 4.92% 2.25% 45.8%
USDNOK 3.47% 2.39% 68.9% 4.89% 2.78% 56.9% 7.15% 2.31% 32.3% 8.01% 1.45% 18.1%
USDPHP 3.50% 1.31% 37.3% 5.16% 1.78% 34.6%
USDPLN 4.22% 2.55% 60.5% 5.95% 3.17% 53.3%
USDSEK 3.50% 2.92% 83.5% 4.91% 3.90% 79.3% 7.24% 3.46% 47.8% 8.28% 2.74% 33.0%
USDSGD 1.77% 1.02% 57.4% 2.57% 0.96% 37.5%
USDTRY 4.19% 2.48% 59.2% 6.35% 2.66% 41.9%
USDTWD 1.61% 1.73% 108.0% 2.42% 2.45% 101.2%
USDZAR 4.81% 4.10% 85.2% 6.80% 5.73% 84.4%

62
Effect of the carry trade
Historically, the forward rate is a biased indicator
After the start of a contract, the spot rate at the
inception of the deal is the best estimate of the spot
rate at the end of the deal
The shaded area represents, schematically, the
area where the spot rate is most likely to be – ie,
very large moves are unlikely.
The forward rate lies off to the side to the direction
of depreciation of the higher yielding currency and
is a biased predictor
Inception of an option
Spot rates do not tend to move to the forward
Direction of increasing rate
Most likely range
for spot at expiry
Forward rate
Spot rate at
inception

63
Putting in the implied data
History tends to prove the forward rate to be wrong
We have inserted a distribution around the forward
rate, which represents the implied distribution
derived from the option volatility
…but as we know, this is demonstrably not the
case.
The forward rate and the implied distributions are
assumed to be the best estimates of the future
evolution of the deal when the premium of an
option is calculated
Historical vs implied means and distributions
Implied data are not good predictors
Forward rate
Spot rate at
inception
Most likely range
for spot at expiry

64
At the end of the deal
… the mispricings come home
Now we have layered on the payouts to a put and a
call option, and suddenly all becomes clear.
…then it’s very clear that the put option has a good
chance of making money while the call option is
much more likely to lose its premium
If we assume that the most likely scenario is that
the spot rate at expiry lands in the shaded area…
Option payouts
Asymmetry give puts an advantage
Long put
payoff
Long
call payoff
Premium cost
of ATMF option
Forward rate
Spot rate at
inception
Most likely range
for spot at expiry

65
… and the carry trade also becomes clear
In the likely area, the carry trade makes money and it is better to hedge with calls than forwards
We can now add the forward contract payoffs to the
already rather complicated diagram, and we see
the carry trade laid out
These cases would occur for large interest rate
differentials and low premium cost for the option.
The short forward (betting against the forward rate)
makes money, while the long forward loses it, and
can for some cases lose more money than the
option premium.
Forward and option payouts
Rationale behind carry trade is clear
Long put
payoff
Long
call payoff
Premium cost
of ATMF option
Forward rate
Spot rate at
inception
Most likely range
for spot at expiry
Long forward payoff

66
Is it just an Emerging Markets effect?
Is the effect that we see purely caused by the EM elements in the portfolio?
Though the effect is certainly stronger for EM pairs,
it is by no means negligible for G10 pairs.
The effect is not particularly dependent on period
In the 12m tenor, G10 puts tend to pay back about
120% of their premium cost, but G10 calls pay back
only about 80%.
Forward and option payoutsPayout/premium
ratios for ATMF call and put options
Effects stronger for EM pairs, but clear for G10 pairs
0%
20%
40%
60%
80%
100%
120%
140%
1W 1M 3M 6M 12M 2Y 3Y
Payout/Premium Ratio for ATMF Calls and Puts
G10 Calls EM Calls G10 Puts EM Puts

67
7. Conclusions 81

68
Conclusions
As data builds up over the decades, long term anomalies persist
There is a long term tendency for long dated options to deliver very different value than short dated
options
Risk perception in the market leads to interesting correlations
Emerging market hedging can often be done best with options
The effect of carry is critical to FX option value

69
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