FEC Financial Engineering Club

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FEC Financial Engineering Club. More On Options. Agenda. Put-Call Parity Combination of options. Review. - PowerPoint PPT Presentation



FEC Financial Engineering Club

More On OptionsAgendaPut-Call ParityCombination of optionsReviewOption - a contract sold by one party (option writer) to another party (option holder). The contract offers the buyer the right, but not the obligation, to buy (call) or sell (put) a security or other financial asset at an agreed-upon price (the strike price) during a certain period of time or on a specific date (exercise date).

Call options give the option to buy at certain price, so the buyer would want the stock to go up.Ex: Groupon

Put options give the option to sell at a certain price, so the buyer would want the stock to go down.Ex: Auto Insurance PolicyWhy use Options?VersatilityMake profit when market goes up or downHedgingLimit any losses in your investments

Different types of PurchasesOn the left is a table where the net cost at time 0. The cash flows occur only at time 0 and time T.Note that all of those three portfolios end up giving you a share of stock at time TIf you just rearrange the variables, you will get the same formula every time.Portfolios 1 and 2Portfolios 2 and 3Analysis of Portfolio 2 and 3Portfolios 1 and 3The Put-Call ParityWhats so important about it?A static price relationship between the prices of European put and call options of the same class.These option and stock positions must all have the same return or else an arbitrage opportunity would be available to traders. Any option pricing model that produces put and call prices that don't satisfy put-call parity should be rejected as unsound because arbitrage opportunities exist.

All the sameIn summary, the equation provides a simple test for various option pricing models. If you cannot produce the put-call parity equation, then the option model presented is flawed.Put-call Parity exampleGiven the following information:Forward price = $163.13150-strike European call premium = $23.86150-strike European put premium = $11.79The risk-free annual effective rate of interest is X. Determine X.

Combining optionsPayoff graphs for four basic positions

PriceProfitExplain how to come up with these graphsput the forward-strike formula under the graphs15StraddleFavor both sides of an issue at onceCombination of an at-the-money put and an at-the-money call


WrittenStrangleSimilar as straddle, but at lower financing costCombination of an out-of-the-money put and an out-of-the-money call

Butterfly spreadCombination of a written straddle (a short call + a short put) and an out-of-the-money long put + an out-of-the-money long call (i.e. a strangle)Make a profit if the price doesnt change very muchProvide insurance for big price changes

Asymmetric butterfly spreadThe weights of the long put and the long call are determined by the location of the peakExample:A 105-strike written callBuy 0.25 units of a 90-strike call and 0.75 units of a 110-strike call for each unit of the 105-strike call that you write


90-105-110 asymmetric butterfly spreadBull spreadBuy a call and sell it at a higher price, or but a put and sell it at a higher priceYou think the price will increase

Bear spreadWe think the price will declineA mirror image of bull spread

100-strike short call100

100110100-110 bear spreadBox spread

A box spread with a guaranteed payoff of $10.00

A long 100-strike call and a short 110-strike callA short 100-strike put and a long 110-strike putThe strategy is to receive a guaranteed payoff, regardless of changes in the market priceRatio spreadAn unequal number of options at different strike prices are bought and soldThe strategy is that the price wont change very much, but the investors wants insurance in case the price declines

CollarCombination of a long put and short call at a higher priceThe investor wants a constant payoff for a range of spot prices, and an increasing payoff as the spot price decreases

Collard stockCombination of owning the stock and buying a collar with the stock

Combination of options

(1) A 100-110 bull spread using call optionsNet Premium = 15.79 11.33 = 4.46Current spot price of $100Combination of options

(2) A 100-120 box spreadNet Premium = 15.79 7.96 + 18.55 7.95 = 18.43

120Current spot price of $100Combination of options

(3) An 80-120 strangleNet Premium = 2.07 + 7.95 = 10.02

Current spot price of $100Combination of options

(4) A straddle using at-the-money optionsNet Premium = 15.79 + 7.96 = 23.75

Current spot price of $100Combination of options

(5) A collar with a width of $10 using 90-strike and 100-strike options

Net Premium = 4.41 -15.97 = -11.38

Current spot price of $100Combination of options

Current spot price of $100(6) A ratio spread using 90-strike and 110-strike options, with a payoff of 20 at a spot price at expiration = 110, and a payoff of 0 at a spot price at expiration = 120

Buy one 90-strike call, and write three 110-strike callNet Premium = 21.46 3 * 11.33 = -12.53

Combination of options

(7) A butterfly spread with a straddle using at-the-money options and with insurance using options that are out-of-the money by $10Net Premium = -15.79 7.96 + 4.41 + 11.33 = -8.01

Current spot price of $100