You are given that the fair price to pay at time for a derivative paying X...

  

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You are given that the fair price to pay at time for a derivative paying X at time T is V = e)E[X|F], where Q is the risk-neutral probability measure and F, is the filtration with respect to the underlying process. The price movements of a non- dividend-paying share are governed by the stochastic differential equation dS, =S, (udt+odB,), where B, is standard Brownian motion under the risk-neutral probability measure. Solve the above stochastic differential equation. Determine the probability distribution of Sr|S,. Hence show that the fair price to pay at time for a forward on this share, with forward price K and time to expiry T-1.is: V=S-Ke-(T-1) (i) (ii) (iii) [4] [2] [4] You are given that the fair price to pay at time for a derivative paying X at time T is V = e)E[X|F], where Q is the risk-neutral probability measure and F, is the filtration with respect to the underlying process. The price movements of a non- dividend-paying share are governed by the stochastic differential equation dS, =S, (udt+odB,), where B, is standard Brownian motion under the risk-neutral probability measure. Solve the above stochastic differential equation. Determine the probability distribution of Sr|S,. Hence show that the fair price to pay at time for a forward on this share, with forward price K and time to expiry T-1.is: V=S-Ke-(T-1) (i) (ii) (iii) [4] [2] [4]

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i Given the SDE dSt Stdt dBt We can solve this using It... View the full answer