Chapter 3- Insurance, Collars and Other Strategies.ppt

Chapter 3Insurance, Collars, and Other Strategies

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Basic Insurance StrategiesOptions can be Used to insure long positions (floors)Used to insure short positions (caps)Written against asset positions (selling insurance)


Insuring a Long Position: FloorsA put option is combined with a position in the underlying assetGoal: to insure against a fall in the price of the underlying assetExample: Buying a 1000- strike put with 6 months to expiration, in conjunction with holding an index position with a current value of $1,000. 1000-strike price put option has a value of $74.201. Risk free rate is 2% for 6 months.


Insuring a Long Position: Floors

Payoff at expirationS&R IndexS&R PutPayoff(Cost + Interest)Profit9001001000-1095.68-95.68950501000-1095.68-95.68100001000-1095.68-95.68105001050-1095.68-45.68110001100-1095.684.32115001150-1095.6854.32120001200-1095.68104.32


Insuring a Long Position: Floors (contd)Example: S&R index and an S&R put option with a strike price of $1,000 togetherBuying an asset and a put generates a position that looks like a call!


Insuring a Short Position: CapsA call option is combined with a short position on the underlying assetWhen you short sell an asset, you need to buy back that asset to cover your position in the future. However, you will suffer a loss if the price increase.Goal: to insure against an increase in the price of the underlying asset (when one has a short position in that asset)


Insuring a Short Position: CapsGiven risk free- rate is 2%You short sell S&R index at $1,000.After 6 months, you need to buy back S&R index to cover your short position.You scare that S&R will increase in price after 6 months => you buy a call option with a strike price of 1000 at a premium of $93.809 to hedge this risk.Profit calculation for the combined position:Initially, you receive $1,000 from short sell S&R and pay $93.809 for call => Net cash inflow = 1000 93.809 . Afterward, you can use this money to invest this money at risk free rate to receive (1000 93.809) 1.02 = 924.32 after 6 months.If after six months, S&R index is 1000 => the payoff for your short position is -1000 => your profit = -1000 + 924.32 = -75.68.


Insuring a Short Position: Caps


Insuring a Short Position: Caps (contd)Example: short-selling the S&R index and holding a S&R call option with a strike price of $1,000An insured short position looks like a put!


Selling InsuranceFor every insurance buyer there must be an insurance sellerStrategies used to sell insuranceCovered call (can also be called option overwriting or covered writing) is writing an call option when there is a corresponding long position in the underlying asset is called covered writingNaked writing is writing an option when the writer does not have a position in the asset


Covered Writing: Covered CallsIf you own the S&R index and simultaneously sell a call option => you have written a covered call.For example, you buy the S&R index at the price of $1,000, risk- free rate is 2%.You also sell a call option with a strike price of $1,000 for a premium of $93.809. If the S&R price at expiration is $1,100. Calculate the profit for the combined position (covered call position) ?Profit = 1100 (1000 1.02) + (93.809 1.02) 100 = 75.68


Covered Writing: Covered Calls


Covered Writing: Covered CallsExample: holding the S&R index and writing a S&R call option with a strike price of $1,000Writing a covered call generates the same profit as selling a put!


Covered Writing: Covered PutsCovered put = writing a put option + short position on underlying asset.Example: You sell a put option on S&R index with a strike price of $1,000, the premium is $74.201. You scare that the S&R index will decrease below $1,000=> short a put option will suffer a loss. You short sell S&R index to be able have gain on this short position when index fall. The gain from short position will offset the loss from written put.


Covered Writing: Covered PutsExample: shorting the S&R index and writing a S&R put option with a strike price of $1,000Writing a covered put generates the same profit as writing a call!


Synthetic ForwardsA synthetic long forward contractBuying a call and selling a put on the same underlying asset, with each option having the same strike price and time to expirationExample: buy the $1,000- strike S&R call and sell the $1,000-strike S&R put, each with 6 months to expiration. Call premium :93.81Put premium: 74.2.


Synthetic Forwards (contd)(Long call + short put) at the same strike price of $1,000 will create the same position of long forward with strike price of $1,020. This means that both positions will produce the same profit.Differences between a synthetic long forward contract and the actual forwardThe forward contract has a zero premium, while the synthetic forward requires that we pay the net option premiumWith the forward contract, we pay the forward price, while with the synthetic forward we pay the strike price


Put-Call ParityThe net cost of buying the index using options must equal the net cost of buying the index using a forward contractCall (K, t) Put (K, t) = PV (F0,t K)Call (K, t) and Put (K, t) denote the premiums of options with strike price K and time t until expiration, and PV (F0,t ) is the present value of the forward priceThis is one of the most important relationships in derivatives!


Put-Call ParityExample: Consider buying the 6-month 1000- strike S&R call for a premium of $93.809 and selling the 6-month 1000-strike put for a premium $74.201. These transactions create a synthetic forward permitting us to buy the index in 6 months for $1,000.Because the actual forward price is $1020, this synthetic forward permits us to buy the index at a bargain of $20, the present value of which is $20/1.02 = $19.61. The difference is option premium is also $19.61.This result in exactly what the put-call parity equation state: $93.809


Spreads and CollarsAn option spread is a position consisting of only calls or only puts, in which some options are purchased and some writtenExamples: bull spread, bear spread, box spreadA collar is the purchase of a put option and the sale of a call option with a higher strike price, with both options having the same underlying asset and having the same expiration dateCollar = long put + short call with higher strike price.Example: zero-cost collar


SpreadsA bull spread is a position, in which you buy a call and sell an otherwise identical call with a higher strike priceIt is a bet that the price of the underlying asset will increaseBull spreads can also be constructed using puts


Spreads (contd)A bear spread is a position in which one sells a call and buys an otherwise identical call with a higher strike priceA box spread is accomplished by using options to create a synthetic long forward at one price and a synthetic short forward at a different priceA box spread is a means of borrowing or lending money: It has no stock price riskA ratio spread is constructed by buying m calls at one strike and selling n calls at a different strike, with all options having the same time to maturity and same underlying assetRatio spreads can also be constructed using puts


CollarsA collar represents a bet that the price of the underlying asset will decrease and resembles a short forwardA zero-cost collar can be created when the premiums of the call and put exactly offset one another


SummaryCollar = long put + short call at higher strike price.Expectation => investor expects price will decrease.Bull spread = long call + short call at a higher strike price.Expectation => investor expects price will increase. Bear spread = short call + long call at a higher strike price.Expectation => investor expects price will decrease.Box spread = ( synthetic long forward by calls at one price) + (synthetic short forward by calls at different price)Motivation => a means for borrowing or lending money.Ratio spread = Buying m calls at one strike + selling n calls at different strike.Motivation => create a spread with zero premium.Remember => all options have: same time to maturity + same underlying asset.Remember: the general motivation of all spread is that the initial premium is reduced.


Speculating on VolatilityOptions can be used to create positions that are nondirectional with respect to the underlying assetExamplesStraddlesStranglesButterfly spreadsWho would use nondirectional positions?Investors who do not care whether the stock goes up or down, but only how much it moves, i.e., who speculate on volatility


StraddlesBuying a call and a put with the same strike price and time to expiration

A straddle is a bet that volatility will be high relative to the markets assessment


StranglesBuying an out-of- the-money call and put with the same time to expiration

A strangle can be used to reduce the high premium cost, associated with a straddle


Written StraddlesSelling a call and put with the same strike price and time to maturity

Unlike a purchased straddle, a written straddle is a bet that volatility will be low relative to the markets assessment


Butterfly SpreadsWrite a straddle + add a strangle = insured written straddle

A butterfly spread insures against large losses on a straddle


Asymmetric Butterfly Spreads


Summary of Various Strategies Different positions, same outcomeStrategies driven by the view of the markets direction











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Chapter 3- Insurance, Collars and Other Strategies.ppt