Past exam of the mathematical models of financial derivatives course of the University of Oxford / 2015 / 1 / c

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- Solution c

Solution

The risk-neutral probability obeys

R = q u + (1 - q) d

. Thus

R = \frac{2}{3} \frac{4}{3} + \frac{1}{3} \frac{2}{3} = \frac{10}{9}, R^{- 1} = \frac{9}{10} .

Substitution into the risk-neutral pricing recursion gives

V_{t} = \frac{9}{10} (\frac{2}{3} V_{t + 1}^{u} + \frac{1}{3} V_{t + 1}^{d}) = \frac{3}{10} (2 V_{t + 1}^{u} + V_{t + 1}^{d}) .

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