A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1.50. The table below lists the prices of some barrier option on the same stock with a maturity of 1 year and strike of USD 100. Assuming a continuously compounded risk-free rate of 5% per year what is the price of a European put option on the stock with a strike of USD 100.
　　Option                                                                          Price
　　Up-and-in barrier call, barrier USD 95                          USD 5.33
　　Up-and-out barrier call, barrier USD 95                       USD 1.78
　　Down-and-in barrier put, barrier USD 80                     USD 3.5
　　Up-and-in barrier put, barrier USD 80                          USD 1.27
　　A.     USD  3.27
　　B.     USD  5.36
　　C.     USD  5.61
　　D.     USD  3.78
　　        Answer: C
　　The sum of the price of up-and-in barrier call and up-and-out barrier call is the price of an otherwise the same European call. The price of the European call is therefore USD 5.33 + USD1.78 = USD 7.11
　　The put-call parity relation gives Call – put = Forward (with same strikes and maturities)
　　Thus, 7.11 – put = 1.50. Thus put = 7.11 – 1.50 = 5.61
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