Consider two \"corresponding\" options, consisting of a call and a put with the
ID: 2790449 • Letter: C
Question
Consider two "corresponding" options, consisting of a call and a put with the exact same parameter values. For this pair, the current price of the underlying asset is $93, the options have an exercise price of $83 and they expire in 6 months. Additionally, the risk-free rate is 5% p.a. What is the difference between the premium of the put option, P, and the premium of the call option, C; that is, what is the value of P - C? Write the answer with two decimals; e.g., 3.24. Do NOT use the $ symbol in your answer; just write a numerical value. Of course, include the negative sign if the answer is negative; but do not include the positive sign if the answer is positive. NOTE: Use the continuous time version of the Put-Call Parity equation
Explanation / Answer
Using the put call parity equation,
C + X/(1+r)t = S0 + P
P - C = X/(1+r)t - S0
Here S0 = 93, X = 83, r = 5%, t = 0.5
Hence,
P - C = 83/(1.05)0.5 - 93 = -12.00