The following futures options prices appear in the Wall Street Journal on 18/1/9
ID: 2663697 • Letter: T
Question
The following futures options prices appear in the Wall Street Journal on 18/1/95.They refer to options on the DM future, to mature in April. The current futures price
is 65.39. Assume that these options mature on 18/4/95, so that the time to maturity
is 0.25 years, and the current US$ interest rate for this maturity is 5%, continuously
compounded.
Strike Call Put
64.50 1.41 0.53
65.00 1.11 0.72
65.50 0.85 0.96
66.00 0.66 1.27
66.50 0.49 –
67.00 0.37 1.97
Check whether put-call parity holds for these prices. (Assume these options are European - they are actually American, but the early exercise premium is very small.)
Explanation / Answer
The trick here is to remember one implication from Put Call Parity: Denote P as the Price of a put C is the price of the call F is the price of forward contract (you have written Forward but I don't see how that was related) K is the strike price r is the interest rate (compounded continuously) We get C-P = e^(-rt)[F-K] in your case, t = 0.25, r = 0.05 For example, for the first one, you want to check if: 1.41 - 0.53 = e^(-0.25*.05)[65.39-64.50] 0.88 = 0.8789 which is which is correct after rounding I was able to vefity that this equality holds after rounding for all of the Strike/Call/Put sets you gave, with the exception of Strike = 66.50, for which you have not given a put price. Hope this helps
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