it is about derivative contract

1. Derivative Pricing
Zuhair M Ismail

2. INTRODUCTION
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3. Type of Derivatives
 Future Contracts
 Forward contracts
 Options
 Swaps
 Warrants
The above are the common used derivatives.
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4. FORWARD RATE
AGREEMENTS
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5. Parties involved
 A future borrower would be interested in protecting
himself against a rise in interest rates. He will be a buyer
of an FRA
Borrower = Buyer of FRA
 A lender, on the other hand, would wish to guard against
interest rates falling. Effectively he would be the seller of
the FRA
Lender = Seller of FRA
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6.  FRAP=((R−FRA)×NP×P) × ( 1 ​)
Y 1+R x (P/Y)
 FRAP=FRA payment
 FRA=Forward rate agreement rate, or fixed interest
rate that will be paid
 R=Reference, or floating interest rate used in the contract
 NP=Notional principal, or amount of the loan that
interest is applied to
 P=Period, or number of days in the contract period
 Y=Number of days in the year based on the correct day-
count convention for the contract​
Forward Rate Agreement Pricing or
Interest Rate Swap Agreement Pricing

7.  A borrower enters into a forward rate agreement with the goal
of locking in an interest rate if the borrower believes rates
might rise in the future.
 So then a borrower might want to fix their borrowing costs
today by entering into an FRA.
 No Cash is paid at the time of entering into the contract.
 The cash difference between the FRA and the reference rate
or floating rate is settled on the value date or settlement date.
 If the amount is positive then the seller of the contract pays to
the buyer. So effectively Reference rate > FRA rate.
 If the amount is negative then the buyer pays to the seller. So
effectively Reference Rate < FRA rate.
Swap Agreement Pricing Explained
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8.  You buy a 2x5 FRA at a rate of 5.43.
 What is your view of interest rates?
Answer:
You are buying the FRA because you think the settlement
price will be higher and you will make a profit. Therefore
you believe interest rates will rise.
Swap or FRA example
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9.  A currency Forward Agreement is mostly a hedging tool
 This is a binding contract as all forward contracts are.
 The purpose is to lock the exchange rate for the purchase of
or sale of a currency on a future date.
 A currency forward settlement can either be on cash
(difference) or on delivery basis.
 However the same i.e. cash or delivery has to be specified
before hand so that it is mutually known and acceptable to
both parties.
Currency Forward Agreement
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10.  Example
 Importer wants to lock in the exchange rate for 30 days as he has to
make a LC payment.
 Amount of LC payment is USD 1,000,000/-
 Current Exchange rate is PKR 179/ 1 USD
 Days are 30 days
 Libor is being used for this example
 So if 1 month Libor is 2 %
 Then the rate theoretically would be
 179*0.02 = 3.58
 3.58/360 days to make it a 1 day rate = 0.009944
 0.009944 is then multiplied by 30 days = 0.30 approx. (taking 2
decimals)
 Now theoretically any rate that the importer gets on or around 179.30 is
a good rate as he is basing his decision on the interest rate convention
which is a good basis.
Currency Forward Agreement
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11.  Example
 practically however he will negotiate and try and get a best possible
deal.
 Now suppose this is a delivery contract.
 On 30 days, the bank will buy the actual dollars (suppose they have not
hedged the transaction; otherwise they normally would).
 So if rate is 179.10 then the customer has actually paid a higher rate and
looses 0.20 on the transaction. He gets his promised USD 1 M and pays
for the LC.
 If the rate is 179.50 then the Bank actually looses money on the deal as
they have to pay a higher amount on the deal. Again the importer gets
his promised USD 1 M and pays for the LC.
 In case of a ND contract, only differentials are paid; so in case of 179.10
then the importer has to pay PKR 200 K to the Bank and vice versa.
 In this example an ND can only take place if in the middle of the forward
deal, the LC has been cancelled and they just honor the commitment at
the end of the forward agreement to keep the relations smooth on either
side.
Currency Forward Agreement - 2
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12. FORWARD FORWARD RATES
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13.  Example
 So far we have taken into consideration the spot vs forwards.
 However at times, there are instances when the forward / forward
processing of transaction needs to take place.
FORWARD FORWARD INTEREST RATES ARE PRICES WHICH
PERTAIN TODAY TO DEPOSIT PERIODS COMMENCING IN THE
FUTURE
WHAT IS THE RATE?
Borrow Funds for 3 months
Short Funds for 3 months
0 3 6
Lend for 6 months
Forward Forward Rates
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14. The need for forward forward rates
 A lot of transactions are based on the future
 Exporters receiving funds
 Importers have to make maturity payments
 Funds need to be repatriated for entities operating as
subsidiaries, etc.
 Rates need to be fixed in advance to avoid risk
(discussed in the coming slides) and in case of rolling
over credit facilities which is again a form of risk
management.
 Rates would be required in case of mismatches.
Institutions lend / borrow funds at various maturities and
may have a ‘maturity gap’ which is different than a
‘liquidity gap’.
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15. The need for forward forward rates 2
 So a dealer than hedge and cover his positions. This
would be pure risk management techniques and most
widely used to support operations in institutions like
banks.
 A dealer may also intend to ‘offer’ the product as a tool
to earn profits. Not only then would this be a good
market product but also utilized to earn profits. Although
not widely used but in cases of arbitrage an opportunity
arises and profits are made.
 Speculation can be done and based on ‘views’ of dealers
positions may be taken. An example = if dealer think
rates are going to fall then short today and cover when
interest rates are down to make profits. 15

16. Forward Forward Rates 2
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17. Forward Forward Rates example
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18. Forward Forward Rates explained
 The first step is to analyze the fact that lending of funds is to take
place
 Suppose it is USD 1 M
 So the interest will be received in six months time.
interest recv = (USD 1 M * 4% * 180 days = USD 20,000/=)
 Meanwhile since it needs to be squared, we can immediately borrow
funds; the deal available right now is for 3 months.
interest pay = (USD 1 M * 3.5% * 90 days = USD 8,750/-)
 Difference in the rate = USD 11,250/-
 So in order to earn the difference the rate should now compensate
(for now no loss / no profit is being assumed which is the basic need
or better requirement of hedging)
rate = 11,250 / 1,008,750 * 360 / 90 * 100% = 4.461%
 Thereby 4.461% would be the forward forward rate.
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19. Forward Forward Rates Risks
 The rates can change – interest rate risk
 The rate for the gap period or from 3 to 6 months may change at the
3 month time period – reinvestment risk
 Individual risks like Credit Risk of the institutions
 Liquidity risk is also present whereby the liquidity matrix of the
institution can change the ‘gap’ may increase in our example or may
squeeze down.
 There may be market risks including regulatory / policy changes.
 Last but not the least as these are tailor made products (forwards)
there is always counter party risk. The other party may not process
or act the opposite position to yours exposing you to a double loss. 19

20. Forward Forward Rates Risks
 The rates can change – interest rate risk
 The rate for the gap period or from 3 to 6 months may change at the
3 month time period – reinvestment risk
 Individual risks like Credit Risk of the institutions
 Liquidity risk is also present whereby the liquidity matrix of the
institution can change the ‘gap’ may increase in our example or may
squeeze down.
 There may be market risks including regulatory / policy changes.
 Last but not the least as these are tailor made products (forwards)
there is always counter party risk. The other party may not process
or act the opposite position to yours exposing you to a double loss. 20

21. Forward Forward Rates Risks 2
 Any physical cash transaction inflates the balance sheet
• Full capital adequacy requirements apply.
• Full credit line implications apply.
• Cash market spread implications.
• Loss of liquidity.
These considerations can also hamper the deals in the forward
forward markets to be unattractive.
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22. FUTURES
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23. Future Pricing
 The price of a futures is taken in 3 steps:
 Spot price of the underlying asset
 Financing cost (which should include storage and / or insurance
cost of the asset in cases where required)
 Cash flow generated by the underlying asset (if any); this is
because during the time where the contract is being bought the
asset is still in the use of the seller and thereby it is a cost to you
as a buyer.
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24. Future Pricing – an example
 The spot / ready price of oil is USD 95
 The 1 year financing for example is 5.5% p.a.
 Insurance and storage cost is lets say USD 5
 Price of Futures:
 USD 95 + (95 * 0.055) + 5 = 105.225 (1 year future price)
 This is the price where there is no profit or loss.
 Of course in reality 3 possible outcomes as discussed
before can and do take place.
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