2. (5 points) European style options can only be exercised at maturity. A trader tells you that buying a 3-month European put with strike price $100 and selling a 3-month European call with strike price $100 simultaneously is equivalent to taking a 3-month short forward position with delivery price S100. Determine whether this is corect by comparingf f the two positions

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Option is a financial derivative which is based on underlying assets and it provide its buyer a right to buy or sell the underlying assets at predefined price on maturity. Option doesn't put any obligation to its buyer. However, option writer has obligation to transact if buyer of option exercise the option. There are two types of Options Call option - give right to Buy Put option - give right to sale Forward is a contract between two parties to transact underlying assets at predefined price on delivery date. It contains obligation to parties. Following are payoff of the Call option, Put option and Forward Call option = Max((Sale Price of Stock - Strike Price),0) Put option = Max((Strike Price-Sale of stock Price),0) Short Forward = Delivery Price - Stock Price Further, Option payoff for option seller is exact opposite to the Payoff of option buyer , which means Payoff for short call = - Max((Sale Price of Stock - Strike Price),0) In above case, the delivery Price of Forward and Strike Price of Option is same i.e $ 100 In Position-1 buy 3-month European put & sale 3-month European call option Assuming both option has same premium and Buy Put and Short Call nullify the Premium. As option provide right, so option is exercised only if it provide profit to its buyer. In case of Put option - Put option exercised only if Stock price is below to strike price on maturity. In case of Call option Call option exercised only if stock price is above to strike price on maturity. Thus in our case, if stock price goes up put option exercise or if it goes down then buyer of call exercise it. If price goes below to strike price, then payoff of Position-1 Strike Price - Stock Price = Positive of difference between Strike Price ans Stock Price If price goes above to strike price, then payoff of Position-1 - (Stock Price - Strike Price) = Negative of difference between strike Price and Stock Price Payoff of forward contract - Position-2 If price goes below delivery price Delivery Price - Stock Price = Positive of difference between Delivery Price and Stock Price If price goes above delivery price Delivery Price - Stock Price = Negative of difference between Delivery Price and Stock Price Please note- The delivery Price and Strike is same $ 100. Thus, whether goes up or down the payoff would be same for both positions. Please refer to below spreadsheet for plot of Payoff of Position-1 and Position-2 vs.Stock price for better understanding. Thus, It is correct that Both position have same payoff for any price of stock on maturity..

2. (5 points) European style options can only be exer…

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1 Forsame underlying stock Stock Price If Put option excercised If Call option excercised Total Pa Strike Price (K) Premuim Buy 3-month European Put $ Sell 3-month European Call 100.00 P 100.00 P MAX(K-S,0) MAX(0,(S-K (S-K) Deli Price (X X-S Short 3-month Forward 100.00 X-S 10 Short Call Total Payoff Position-1 Stock Price on Maturity Long Put Payoff Total Payoff Position-2 30.00 20.00 10.00 Pay off 30.00 $ 20.00 $ 10.00 $ 12 13 14 15 16 17 18 30.00 20.00 $ 10.00 $ 100 110 120 130 (10.0ol S $ (20.00) $ 30.00 10.00) $ (20.00) $ 10.00 20 30.00 20 21 23 70 25 26 27 S(40.00) $30.00) $20.00) (10.00) S- $10.00 $20.00 $30.00 $40.00 Total Pay off Position-1 Total Payoff Position-2

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2. (5 points) European style options can only be exercised at maturity. A trader tells you...

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