Assume that there are no arbitrage opportunities. Is there enough information to determine which option has the higher market value? If so, which option, the call or the put, has higher market value?
Given the fact above, Is a six-month call with an exercise price of $60 more or less valuable than a similar six-month put? Show your work.
Call Put Parity equation should hold true.
C - P ==> S0 - PV(K)
RHS ==> S0 - PV (K) = 120 - 124 / (1 + 3%)2 = 3.12 > 0
==>C - P > 0
==>C > P
Three months Call Put option are of same value. Hence, C - P ==> 0.
C - P = S0 - PV(K) = 0
S0 - 60 / (1 + r)3/12 = 0
S0 = 60 / (1 + r)0.25
Apply the call put parity to 6 months option:
C - P = S0 - PV(K) = S0 - 60 / (1 + r)6/12 = S0 - 60 / (1 + r)0.5
S0 = 60 / (1 + r)0.25
C - P = S0 = 60 / (1 + r)0.25 - 60 / (1 + r)0.5 > 0
C > P
6 month call option will be more valuable than put option.
C - P = S0 - PV(K)
Or, 25 - 8 = 17 = S0 - 100 / (1 + r)3/12
S0 is not given explicity in this question. Assuming this XYZ stock is same as the one mentioned in part (a), S0 = 120
Hence, 17 = 120 - 100 / (1 + r)3/12 = 120 - 100 / (1 + r)0.25
Hence, 100 / (1 + r)0.25 = 120 - 17 = 103
Price of a three month Zero Coupon Bond of face value 100 = FV / (1 + r)t = 100 / (1 + r)0.25 = 103
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