This document provides an overview of options, including definitions, concepts, pricing models, risks, and strategies. It defines options, outlines key terms like premium, strike price, and expiration. It explains pricing models including intrinsic value and factors that affect option prices like underlying price, volatility, and time to expiration. Put-call parity and how options can be used to synthesize other positions are also summarized.

1. finlogIQ
Knowledge for financial IQ
STRICTLY PRIVATE AND CONFIDENTIAL
Chapter 8
Options
August 2012

2. Chapter summary and outline
This chapter outlines the definitions, basic concepts and features of
options, as well as pricing and valuation models, risks in trading
options, trading strategies and other types of options in the market.
Chapter outline:
• What is an option?
• Introduction to options trading
• Definitions and basic concepts
• Pricing
• Valuation models
• Risks in trading options (and derivatives in general)
• Option-based strategies
• Market outlook strategies
• Other type of options
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3. What is An Option?
• Option offers a choice or a right.
• Person who owns the option has the right but not the obligation to act on
the option
• It is the underlying asset that determines the value of the options
Introduction to options trading
• Prior to exchange-traded options, calls and puts were traded over-the-
counter (“OTC”).
• The idea of standardization by having fixed strike prices and fixed expiration
dates came from the Chicago Board of Trade (“CBOT”) since futures
contracts had proved to be workable there.
• Options are traded on a range of instruments from currencies, interest
rates, fixed income securities, indices, commodities, and metals to energy.
• There are also options on futures contracts, as well as, options on options,
known as compound options.
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4. Definitions and Basic Concepts
• Premium is the price paid for the call or put option
• European option can be exercised only at expiration.
• American option permits the owner to exercise at any time before or at
expiration
– The American option must be worth at least as much as the European option,
since it can be exercised anytime.
– The American option can be worth more (when it is favorable to exercise earlier)
• Option buyer as known as holder of the option
• Option seller as known as writer of the option
• Buyer has the right to exercise the option
• Seller has the obligation to fulfill the contractual terms should the buyer
exercise the option
• Call option gives the holder the right to buy the underlying from the writer at
the strike price on or before a specified date
• Put option gives the holder the right to receive the strike price upon delivery
of the underlying to the writer on or before a specified date
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5. Definitions and Basic Concepts - 2
• Strike price (also known as the exercise price) is the price paid to acquire
the underlying or price received to sell the underlying
• Depending on the market and type of underlying, the seller usually has one
of 3 delivery options:
– Closeout,
– Settlement by cash or physical delivery and
– Exchange-for-physicals (“EFP”)
• Physical delivery is common when the underlying is a physical commodity
while Cash settlement is common when the underlying is a financial asset
• “Moneyness” refers to the potential profit or loss from the immediate
exercise of an option.
• In-the-money when it yields a positive return when exercised.
– Call option with strike price of $100 when stock price at $110 is $10 in-the-money
• Out-of-the-money when its yields a negative return (thus would not be
exercised).
– The call option would be out-of-the-money if the underlying’s price is $90.
• At-the-money when it neither yields a profit nor a loss (underlying’s price at
$100).
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6. Pricing
Price Components
• The options may be either calls or puts, and the options may be either
European or American.
• Common notation:
– St = price of the underlying stock at time t
– X = the exercise price for the option
– T = the expiration date of the option
– ct = the price of a European call at time t
– Ct = the price of an American call at time t
– pt = the price of a European put at time t
– Pt = the price of an American put at time t
– Rf = risk-free interest rate
• At expiration, both European and American options have exactly the same
exercise rights.
• Therefore, European and American options at expiration have identical
values, assuming the same underlying security and the same exercise
price:-
CT (ST , X, T) = cT (ST , X, T) and PT (ST , X, T) = pT (ST , X, T)
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7. Pricing - 2
Intrinsic Value Formula and Implications for Exercise - Buy or Sell a Call Option
Intrinsic Value of a Call CT = MAX{0, ST - X}
Example
• Consider a call option with an exercise price of $10 and assume that the
underlying stock trades at $9.50.
• At expiration, the call owner may either exercise the option or allow it to
expire worthless.
• In this case, the call owner must allow the option to expire.
• If the owner of the call exercises the option, he pays $10 and receives a
stock that is worth $9.50.
• This gives a loss of $0.50 if exercised, and so it will not make any sense to
do so.
ST - X = $9.50 - $10.00 = -$0.50
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8. Pricing - 3
Intrinsic Value Formula and Implications for Exercise - Buy or Sell a Call Option
(cont)
In the same example, assume that the stock price is $10.50 at expiration.
• The call option with an exercise price of $10.00 now allows the holder to
exercise the option by paying the exercise price.
• Therefore, the owner of the call can acquire the stock worth $10.50 by
paying $10.00.
• This gives an immediate payoff of $0.50 from exercising.
• Using these numbers we find:-
CT = MAX{0, ST - X = MAX{0, $10.50 - $10.00} = MAX{0, $0.50} = $0.50
• Here the value of the call equals the maximum of zero or the stock price
minus the exercise price.
• Theoretically, the value of the call is unlimited as illustrated by the upward
sloping line.
• If the stock price were $100 at expiration, the call would be worth
MAX{0, ST - X } = $90
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9. Pricing - 4
Intrinsic Value Formula and Implications for Exercise - Buy or Sell a Call Option
(cont)
• Dotted line shows the value of a short position in the same call option
• Short position has a zero value for all stock prices equal to or less than the
exercise price.
• If the stock price exceeds the exercise price, the short position is costly.
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10. Pricing - 5
Intrinsic Value Formula and Implications for Exercise - Buy or Sell a Call Option
(cont)
• The profit or loss on the long call position, after considering the option
premium, if held until expiration is:-
CT - Ct = MAX{ 0, ST - X } - Ct
• Seller of a call receives payment when the option first trades.
– Hope for a stock price at expiration that does not exceed the exercise
price.
• The profit or loss on the sale of a call, with the position being held until
expiration, is:-
Ct - CT = Ct - MAX{ 0, ST - X }
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11. Pricing - 6
Intrinsic Value Formula and Implications for Exercise - Buy or Sell a Call Option
(cont)
• Taking into account the initial cost of the option
• Shifts the long call graph down by the $0.50 purchase price and shifts the
short call graph up by the same amount, which is the premium collected for
writing the option.
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12. Pricing - 7
Intrinsic Value Formula and Implications for Exercise - Buy or Sell a Call Option
(cont)
• First, for the call buyer, the worst that can happen is losing the entire
purchase price of the option.
– The potential dollar loss is much greater if we hold the stock rather than the call.
– However, a small drop in the stock price can cause a complete loss of the option
price.
• Second, potential profits from a long position in a call option are
theoretically unlimited.
– The profits depend only on the price of the stock at expiration.
• Third, the holder of a call option will exercise any time the stock price at
expiration exceeds the exercise price.
– The call holder will exercise to reduce a loss or to capture a profit.
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13. Pricing - 8
Intrinsic Value Formula and Implications for Exercise - Buy or Sell a Call Option
(cont)
• Premium paid by the purchaser at the time of the initial trade belongs to the
seller no matter what happens from that point forward.
– The seller attains this maximum profit when the holder of the call cannot exercise
because the call owner will allow the option to expire worthless for any stock
price at expiration at or below the exercise price.
• Call owner can exercise, the seller's profits will be lower and the seller may
incur a loss.
• The potential losses from selling a call are theoretically unlimited.
• Options market is a zero-sum game because the buyer's gains are the
seller's losses, and vice versa.
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14. Pricing - 9
Call options at expiration and arbitrage
• No-arbitrage pricing principle: where prices of various related securities
would be such that there would be no arbitrage opportunities available, to
show that call option prices must obey the formula shown in the slides
before.
• If prices are different from the expected prices based on the principle,
arbitrage opportunities arise.
• Consider a call option with an exercise price of $10. At expiration, with the
stock trading at $10.30, the price of a call option must be $0.30. To see why
the call must trade for at least $0.30, consider the arbitrage opportunity that
arises if the call is only $0.20.
Transaction Cash Flow ($)
Buy 1 call -0.20
Exercise the call -10.00
Sell the share +10.30
Net Cash Flow +0.10 => riskless profit, hence arbitrage possible
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15. Pricing - 10
Buy or sell a put option
• Same notation for an American put, but all of the conclusions hold
identically for European puts.
• Holder of a put either exercises or allows the option to expire worthless.
• If exercises the holder surrenders the stock and receives the exercise price
• The holder of a put will exercise only if the stock price is less than the
exercise price
• The value of a put option at expiration equals zero, or the exercise price
minus the stock price, whichever is higher:
Intrinsic Value of a Put PT = MAX{ 0, X - ST }
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16. Pricing - 11
Buy or sell a put option (cont)
• At expiration, the holder of the put can either exercise or allow the put to
expire worthless.
• With an exercise price of $10 and a stock price of $10.20, the holder cannot
exercise profitably.
• To exercise the put, the trader would surrender the stock worth $10.20 and
receive the exercise price of $10, thereby losing $0.20 on the exercise.
• PT = MAX{0, X - ST }= MAX{0, $10 - $10.20} = MAX{0, - $0.20} = 0
• if the stock price equals or exceeds the exercise price at expiration, the put
is worthless.
• PT = MAX{0, X - ST } = MAX{0, $10 - $9.40} = MAX{0, $0.60} = $0.60
• In the same example, assume the stock trades at $9.40.
– The put is worth $0.60 because it gives its owner the right to receive the $10
exercise price by surrendering a stock worth only $9.40.
– The writer who shorts the put will suffer a loss of $0.60.
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17. Pricing - 12
Buy or sell a put option (cont)
• The graph shows the value of a long position as the solid line and the value
of a short position as the dotted line.
• Figure on the right shows the same graph, after considering option cost
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18. Pricing - 13
Buy or sell a put option (cont)
• Put values parallel our results for call options in several ways:
– the option market is a zero sum game and a short position can never have a
positive value at expiration.
– The seller of a call or put hopes that nothing happens after the initial transaction
when he collects the option price.
– The best outcome for the seller of either a put or a call is that there will be no
exercise and that the option will expire worthless.
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19. Time Value
• Difference between the market price of the option and its intrinsic value is
referred to as time value, or more accurately, speculative value
• At expiration, time value will be zero, and therefore, the market price of the
option approaches its intrinsic value as expiry approaches.
Option Price = Intrinsic Value + Time Value
• Minimum value of an option is its intrinsic value.
– For call option, maximum price is the price of its underlying (ie when strike = 0)
– For put option, maximum price is its strike price (ie when underlying price = 0)
• Time value decreases at an increasing rate as the option approaches
expiration
– Approximately two thirds of the time value is lost in the last one third of the time
to expiration.
– It becomes zero on the expiration date of the option, and the option price will be
the same as its intrinsic value.
• The volatility of the underlying security also has a significant impact on time
value:
– The greater the volatility of the underlying security, the higher the time value, all
other things being equal.
– In addition, time value tends to be at its highest levels when the option is at-the-
money.
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20. Basic Factors Affecting Option Price
• A higher stock price would imply a higher call option price and a lower put
option price.
– Based on the same intrinsic value formula, a higher strike price would imply a
lower call option price and higher put option price.
• Given more time, the time value will be higher.
– As the expiration date approaches, time value declines, thus implying a lower
option price for both calls and puts as the underlying would have more time, thus
opportunity, to move favorably to the option holder’s advantage.
• Cash flows in the form of dividends (expected over the life of the option)
have an impact on option prices.
– The payment of a dividend lowers the ex-dividend stock price.
– Since the strike price of an option is not adjusted for dividends, the payment of
dividends lowers the price of a call option but increases the price of a put option.
– The impact of high dividend payouts is similar to having a lower underlying price.
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21. Basic Factors Affecting Option Price -2
• A change in interest rates results in an opportunity gain or loss when a
warrant is purchased.
– As interest rates go up, the proceeds from the time deposit investment would go
up, making the latter choice more attractive and as such the call option will bid
up and result in higher call prices.
– However, interest rates generally do not have a strong impact on most options,
except for fixed income and interest rate options.
• For both call and put options, higher volatility of the underlying security
means that there is a greater chance for both types of options to be
exercised in the future.
– This would make them more valuable.
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22. Put-Call Parity
• Relationship between put, call, stock and bond prices
• Two assumptions
– it applies only to European-style options
– there are no dividends paid on the underlying stock during the lifetime of the
option.
• Put can be synthesized by buying a call, selling the stock and investing the
proceeds in a risk-free bond.
P0 = C0 – S0 + X/(1 + Rf )T
• Restated, other synthetic securities can be created:-
Synthetic bond X/(1 + Rf )T= S0 + P0 – C0
Synthetic stock S0 = C0 – P0+ X/(1 + Rf)T
• Long the asset = Long call, sell put and lend PV of exercise price
• Long the call = Long the stock, long put and borrow PV of exercise price
• Long the put = Short the stock, long call and lend PV of exercise price
• The put-call parity demonstrates two very important concepts.
– It is always possible to replicate one of the investments with the other three.
– It shows that options can be priced from a relative standpoint.
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23. Synthetic Structures
• Synthetic structures can be constructed from a combination of buying or
selling the underlying and buying or selling options.
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24. Comparison Between Futures and Options
Obligation and Right
• A futures contract is an obligation.
• The user of a futures contract is obligated to accept or deliver the
underlying security.
• In contrast, the user of an option has a right to accept or deliver the
underlying security.
• If he chooses not to do so, he is not liable for anything.
Impact on Returns
• Futures contract has symmetrical returns.
• Upside risks and downside risks are similar magnitude
• Options have asymmetrical returns.
• Downside is limited to the amount of the premium paid while the upside in
unlimited.
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25. Comparison Between Futures and Options - 2
Mark-to-Market
• Futures contract is subject to daily mark-to market based on the daily
settlement price whereas options are not, except for exchange-traded
options contracts.
Valuation and Pricing
• Much easier to price a futures contract, based on observable parameters in
the market (such as term structure of interest rates)
• For options, the most important factor, which is the future volatility, cannot
be determined.
• Volatility is one of the most important elements in evaluating an option,
because it is usually the only valuation variable not known with certainty in
advance.
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26. Valuation Models
• Option can be valued during its lifetime, rather than just on its expiry date.
– Using either Binomial model and Black-Scholes model.
– Models developed since the 1990s, which did away with some of the unrealistic
assumptions of the Black-Scholes model, are currently being used by major
financial institutions.
• For all options, the options price is greater or equal to zero (never negative)
– Options has the possibility of unlimited profits, only liability is option premium
• For all options, options price is less than or equal to the underlying price.
– I.e. for a 3-month option on gold, the actual commodity – gold - can last forever
while the option is only for 3 months.
– Hence, the value of the option can never be greater than the underlying asset
since one will be better off acquiring the commodity than the option
• For American options, the option price is greater or equal to intrinsic value.
− If the option price were less than the intrinsic value, the option buyer could earn
immediate and risk-free profits by purchasing the option, exercising it and
covering the exercised position in the underlying market.
• Hence, option price must be some positive value between the intrinsic value
and the value of the underlying asset.
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27. The Black-Scholes Model
• Assumptions about how markets tend to behave are similar to the random
movement of particles in physics.
– Determines the theoretical value of an option on the basis of a neutral hedge
created with risk offsetting positions in the option and the underlying.
– Spot price of the underlying, strike price of the option, interest rate, time until
option expiration, and volatility of the underlying important.
• Elegance and simplicity of the Black-Scholes model and
– Consistency with the capital asset pricing model of portfolio theory are
responsible for its widespread adoption.
• Weaknesses are its restrictive assumptions:
– European-style exercise feature;
– Underlying asset price is distributed lognormally;
– Interest rate and volatility of the underlying asset are constant;
– Pays no dividends or coupons before expiration of the option;
– Competitive and frictionless markets;
– No counterparty risk;
– Market participants prefer more wealth to less; and
– No arbitrage opportunities.
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28. Parameters for Pricing of Options
Underlying Asset Price
• Price of the underlying asset increase, value of the call option will increase
• Price decrease, the value of the put option will increase
Exercise Price or Strike Price
• Exercise price fluctuates positively with value of the put options but
inversely with the value of the call options.
• For an in-the-money call, the lower the exercise price, the higher will be the
intrinsic value.
• For an out-of -the money call, the lower the exercise price the higher the
probability that the call can be exercised at a profit.
Time to Expiry
• The longer the time to expiry, the higher is the probability that it can be
exercised at a profit.
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29. Parameters for Pricing of Options - 2
Variability of the Price of the Underlying Asset (Volatility)
• Volatility refers to the degree of movement of the underlying asset price and
is measured by the standard deviation.
• Three measures of volatility
– Future volatility is what best describes the future distribution of prices for an
underlying asset.
– Historical volatility is a statistical measure of how fast the underlying security has
been changing in price.
– Implied volatility is the volatility that is being traded in the marketplace.
Interest rates
• Risk-free interest rate rises, the value of the call option increases.
• A call option gives the buyer a right to buy the asset without having to pay
for the full cost immediately.
• If the interest rates are high, the amount of money you have to put aside
now to buy the asset eventually will be less.
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30. Price Sensitivity and Inputs to Valuation Models
• The underlying price, the exercise price, the risk-free rate, the time to
expiration and the volatility.
• Relationship between the variables and the option price are usually called
the option Greeks
Delta
• Major sensitivity among the 5 Greeks
• The first-order relationship between the option price and the underlying
price
Delta = Change in option price/Change in underlying price
Δ = δV/δS
where V is the option price and S is the underlying price
• The delta of the Call option is a value between 0 to 1
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31. Price Sensitivity and Inputs to Valuation Models
-2
Delta (cont)
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32. Price Sensitivity and Inputs to Valuation Models
-3
Delta (cont)
• Traders and dealers in options use delta to construct hedges to offset the
risk assumed by buying and selling options.
• If the dealer is short 1,000 call options, he must buy a certain number of the
underlying asset to hedge against an increase in the price of the underlying
asset and that amount to buy is largely determined by delta.
– This process is known as delta hedging.
• As the underlying asset price changes, delta changes.
• Similarly, as time to expiry declines, delta changes as well.
• Since delta constantly changes, delta hedging is a dynamic process and
hence is commonly referred to as dynamic hedging.
• The deltas of Put options are negative and have values between -1 to 0.
• An increase in the underlying asset price results in a decrease in the value
of the Put option.
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33. Price Sensitivity and Inputs to Valuation Models
-4
Gamma
• Sensitivity of delta to changes in the underlying asset price.
• Second-order relationship between option price and its underlying asset
price.
Gamma = δ2V/δS2
• When gamma is large, delta changes rapidly
• Does not provide a good estimation of sensitivity to the underlying asset
price changes.
• Gamma tends to be large when the option is at-the-money and close to
expiration
• Hence it is under these circumstances that the delta hedge would work
poorly.
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34. Price Sensitivity and Inputs to Valuation Models
-5
Gamma (cont)
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35. Price Sensitivity and Inputs to Valuation Models
-6
Vega
• Relationship or sensitivity of the option price to volatility.
• Volatility is defined as the standard deviation of the continuously
compounded return on the underlying.
• Vega is larger as the option is closer to being at-the-money.
– Option price becomes most sensitive to volatility when the option is at-the-
money.
• Vega for both call and put options are positive – increased volatility leads to
higher option prices.
• Vega is the only variable that cannot be easily obtained because it pertains
to the volatility over the life of the option, and not past or current volatility.
• Current estimate of volatility
– implied volatility : is the market’s consensus estimate of the underlying’s rate of
return volatility.
– “worked-backwards”: replacing the Black-Scholes price with the market price to
obtain volatility
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36. Price Sensitivity and Inputs to Valuation Models
-7
Theta
• Sensitivity of the option price to the time to expiration.
• Rate of time value decay is known as the option’s theta.
• Call options, theta is negative.
• Most of the time, the theta of put options are negative as well.
Rho
• Sensitivity of the option price to the risk free rate.
• Is the continuously compounding rate of return on the risk-free security
whose maturity corresponds to the option’s life.
• Call option price has a positive correlation with the risk-free rate,
• Put option price has a negative correlation.
• Both types of options are not sensitive to this variable, especially European-
style options.
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37. Risk in trading options (and derivatives)
• Time risk – options have finite life, and its price decreases as time passes
• Liquidity risk – risk that option holder cannot close his position due to
insufficient bids or offers in the market
• Credit risk – risk of counterparty defaulting on its obligation
• Operational risk – likelihood of errors occurring during trading due to
systems
• Model risk – risk associated with choice and use of financial/valuation
models
• Settlement risk – risk that a counterparty does not deliver a security or its
value in cash as per the agreement
• Regulatory risk – the risk of changes in regulations
• Tax risk – risk from uncertainty on taxation of derivatives
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38. Option based strategies
• Uncovered or naked position (open option position without combining it with
an offsetting position in other securities)
Call buying strategies
• Uncovered long position in call options is an alternative to buying the
underlying, with a limited downside (value of the option, which is at a
fraction of the purchase price of the underlying).
• Can also be used as part of a cash extraction strategy, when the investor
who has the underlying asset and needs cash, sells it and buys call options
to maintain upside exposure to the underlying asset.
• Equity calls can also be combined with non-equity underlying securities.
– Long call option position + fixed income instrument = Equity Linked Note (“ELN”)
which has the downside protection of the fixed income and upside participation
of the call option on an underlying equity security.
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39. Option based strategies - 2
Call buying strategies (cont)
• Call can be used to hedge a short position in the underlying asset.
– Breakeven point is the purchase price of the underlying less the premium.
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40. Option based strategies - 3
Call writing strategies
• Writing a call (uncovered) would merely be extracting the option premium,
and risking an unlimited loss should the underlying asset’s price moves up
strongly and continually during the life of the option.
• A simultaneous purchase of the underlying asset with the sale of a call
option is known as a covered call position.
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41. Option based strategies - 4
Put buying strategies
• Buying an uncovered put = alternative to shorting the underlying asset
• Long put with a long position in the underlying asset is known as a
protective put strategy (aka portfolio insurance)
– Limits the downside of portfolio while still being able to enjoy the upside afforded
by an increase in the underlying asset by paying a fixed premium for the put.
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42. Option based strategies - 5
Put writing strategies
• Increases income by the amount of premium collected.
– But the downside can be considerable => downside volatility of the underlying
• Put writing, when combined with a purchase of the fixed rate note,
enhances the yield of the note.
– I.e. a bull equity linked note, which is part of the ELN classification of products
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43. Market outlook strategies
• Neutral
– covered call writing (strike price at the market), straddle writing, straddle
purchase (if high volatility of the underlying asset is expected), combination
writing (collar).
• Bullish
– covered call writing (strike price above the market), uncovered put writing, call
purchase, bull spread.
• Bearish:
– covered call writing (strike price below the market), uncovered call
writing, covered put writing, put purchase, bear spread.
• May not be suitable in the structured warrants market
• Investors and traders cannot write the warrants (warrants are only written by
designated issuers)
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44. Straddle, strangle
Straddle
• A straddle consists of a long call
and long put with the same
underlying asset, expiration date
and strike price
– At expiration, if the asset price =
strike price, then the option expires
worthless.
– A straddle is rather expensive, as
investor buys both a call and a put
option.
– Only when you think the volatility is
rising would you buy straddle.
– The theta for a straddle is
negative, thereby reducing the
value of the portfolio as it
approaches maturity.
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45. Straddle, strangle
Strangle
• Strangle is similar to the straddle
except that the strike prices for the
call and put are different.
– Strike price of the call is higher
than the strike price of the put
option.
– Less costly than the straddle.
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46. Spreads
• Vertical Spread
– Created by options with different strike prices by same expiry date.
• Bull Spread/ Bear Spread
– Bull spread is used to express a somewhat bullish view on the market by buying
a call with a lower strike price and selling a call with a higher strike price.
– Investor pays a premium for the spread => this is called a debit spread.
– Buying a lower strike put and selling a higher strike put can also create a bull
spread.
– We would have created a positive cash flow since a put with a higher strike price
is more expensive than one with a lower strike price =>credit spread
• payoff for a debit spread will obviously be more than that of a credit spread
– Bear spread => buy a call/put with a higher strike and sell another with a lower
strike
– The view is that the market will trade lower but not lower than your lower strike
price.
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47. Spreads - 2
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48. Spreads - 3
• Butterfly Spread
– Non-aggressive spread, view that the market will be trading in a range
– Created by buying an option with a low strike S1 and selling two options at a
higher strike S2 and finally buying another option at an even higher strike S3.
• Condor Spread
– variation of butterfly spread with wider range (4 options)
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49. Spreads - 4
• Ratio Spread
– Transact option contracts in specified ratios.
– Bearish on the market we can express it by buying one call at a low strike and
selling two or more at a higher strike.
– Limited profit and unlimited loss potential.
– Sell a put with a higher strike and buy two or more puts at a lower strike.
– Unlimited profit and limited loss potential.
• Calendar Spread
– Options having the same strike price but different expiry dates are called
calendar spreads.
– It can be selling short-dated option and buying a long-dated one expressing a
view that the volatility may increase or vice-versa
• Diagonal Spread
– Vertical spreads are formed by options with different strike prices but the same
expiry dates while calendar spreads are created by options having similar strike
prices but different expiry dates.
– Diagonal spread is a combination of vertical and calendar spreads.
– Spread where both the strike prices and expiration dates are different.
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50. Trading with options
• Short options are vehicles to profit from stable prices, time decay and falling
volatility.
• Long options will bring profits when prices trend heavily over a short time
period and volatility rises.
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51. Hedging with options
• Enables market participants to transfer part or all of the risk associated with
holding a position in the underlying instrument from one party to another.
• Options act like a traditional insurance policy
• Hedgers
– Either have a natural long or short position, OR
– Others have voluntarily chosen to take long or short positions and now wish to
lay off part or all of the risk
• There is a cost associated to hedging
– May be immediately apparent because it involves an initial cash outlay or subtler
either in terms of lost profit opportunity or additional risk under some
circumstances.
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52. Hedging with options - 2
• Buying Options for Protection
– The easiest way to hedge an underlying position using options is to purchase
either a call to protect a short position or a put to protect a long position
• Writing Covered Options
– Purchase of an option offers limited and known risk, a hedger might be willing to
accept more risk in return for some other advantage
– Instead of purchasing an option to protect an existing position, a hedger might
consider selling an option against his position
– Does not offer the limited risk afforded by the purchase of an option but results in
a cash credit rather than debit
• Zero Cost Options
– Hedger desires the limited risk afforded by the purchase of an option, but also
wants to avoid cash outlay associated with such a strategy
– He can simultaneously combine the purchase of an option with the sale of
another
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53. Other Types of Options
Index Options
• Allow investors to trade on general stock market (index) movements the
same way as they can trade equity options.
• Unlike some stock options which require the physical delivery of the
underlying stock upon exercise, the exercise of index options is settled in
cash.
– The amount of cash settlement is equal to the difference between the closing
price of the index (on settlement date) and the strike price of the option multiplied
by a predetermined multiplier
Interest Rate Options
• Written on fixed-income securities (options on physicals) or interest rates
futures contracts (options on futures).
• Attractive because the trader’s risk is limited to the option premium, but the
profit potential is unlimited, within the life of the option.
• Their prices are quoted as a percentage of the principal amount of the
underlying debt security.
– For example, a trader who thinks long term interest rates will rise can speculate
by buying put options on Treasury bonds.
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54. Other Types of Options - 2
Currency Options
• A foreign exchange or currency option is a contract which allows for the sale
and purchase of a pre-determined amount of foreign currency at a fixed
exchange rate on or before a specified date.
• Currency options can be used for speculative purposes or to hedge an
existing currency exposure.
• Structurally similar to currency futures contracts.
• Currency call option is similar to a long position in currency futures,
• Currency put is similar to a short position in currency futures.
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55. Other Types of Options - 3
Options on Futures
• Options can be priced off cash instruments as well as futures contracts.
– Options on cash instruments => exercised to obtain a position in a cash asset
– Options on futures => exercised to obtain a futures position.
• Options on futures tend to enjoy greater liquidity than those that call for the
actual delivery of a cash instrument.
– For institutions undertaking cross-hedging, this is important.
• Option contracts on SGX are futures options and are American-style
options.
– These option contracts can be exercised anytime prior to expiry.
– It is the policy of SGX to exercise any in-the-money options at maturity unless
there are specific instructions to the contrary.
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