 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2011/b/4/d/solution

For matching European strike and expiry with no dividends, put-call parity gives

C_{0} - P_{0} = S_{0} - K e^{- 2 r}

. Using the rate and put price from part (c),

C_{0} = \frac{800}{121} + 100 - \frac{11700}{121} = \frac{1200}{121} pounds \approx 9.9174.

As a check, only the

uu

call payoff is positive, at

27

. Its risk-neutral expectation is

27 (2/3)^{2} = 12

1. 1^{2}

gives the same value.

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