A 1-year call option with a strike price of $80 cost $20. A share costs $70....

A 1-year call option with a strike price of $80 cost $20. A share costs $70. The interest rate is 10% per year. Find the cost of a 1-year put option with a strike price of $80 and explain your result.

Expert Solution

The equation expressing put-call parity is:

C + PV(x) = P + S

Where
C=Price of call option
PV (x) = Present valueof strike price
P=Price of put option
S=spot price of share

20+(80/1.1) =P+70
20+72.73=P+70
92.73-70=P
P=22.73

Cost of 1 year put option =$22.73


Put Call Parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to (and hence has the same value as) a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract

jeff jeffy answered 1 year ago

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