Question

Consid er an asset whose stochastic differential equation is A derivative on that asset, VtS.). has a payoff at expiry of PayfS)-5-s 2 S 0 elsewhere The risk free rate of return is r = 0.1. The volatility is σ = 0.5. 1. Write the PDE to solve for V(S.d); that is the Black Scholes like equation. 2. Write the equation that expresses the unknown x - S,t) as a function of the known VTs-h,t+ d).vS,t+ d, VS+ h,t+ dt) that would be used in an explicit scheme 3. Write the equation that expresses the known X- V(S,t + dt) as a function of known VtS- h)V(S,o.Vts+ h,) that would be used in an implicit scheme.

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Answer 1

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