IEOR 4700 Compute the price of an American call option with strike

1. Compute the price of an American call option with strike K=110 and maturity T=.25years.2.Compute the price of an American put option with strikeK=110 and maturityT=.25years.3. Is it ever optimal to early exercise the put option of Question 2? YES OR NO4.If your answer to Question 3 is “Yes”, when is the earliest period at which itmightbe optimal to early exercise? (If your answer to Question 3 is “No”, then you shouldsubmit an answer of 15 since exercising after 15 periods is not an early exercise.5. Do the call and put option prices of Questions 1 and 2 satisfy put-call parity?YesNo6. Compute the fair value of an American call option with strikeK=110 and maturityn=10 periods where the option is written on a futures contract that expires after15 periods. The futures contract is on the same underlying security of the previousquestions.7. What is the earliest time period in which youmight want to exercise the Americanfutures option of Question 6?8. Compute the fair value of achooser option which expires aftern=10 periods. Atexpiration the owner of the chooser gets to choose (at no cost) a European call optionor a European put option. The call and put each have strike K=100 and they mature5 periods later, i.e. at n=15.

 

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