Question 1 - Black-Scholes-Merton PDE Proof (5 Marks) An investment firm is developing a new Exotic...

 

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Question 1 - Black-Scholes-Merton PDE Proof (5 Marks) An investment firm is developing a new Exotic Derivative Contract. This contract will pay off stock price at expiry squared, S,², given stock price is less than the strike price, K. That is defined by the following function: S Payoff (G)= [ST ≤ K STK 0 $7 Given that the underlying stock is assumed to follow Geometric Brownian Motion; dS = μSdt+oSdz (A) Use Risk-Neutral Valuation to derive the fair price of the security at time t in terms of the stock price, S, at time t. This will be referred to as G. (2 Marks) (HINT: You will first need to derive the stochastic process that is followed by Y,= S₂², Your derivation in (a) should show that Y, also follows a GBM) Question 1 - Black-Scholes-Merton PDE Proof (5 Marks) An investment firm is developing a new Exotic Derivative Contract. This contract will pay off stock price at expiry squared, S,², given stock price is less than the strike price, K. That is defined by the following function: S Payoff (G)= [ST ≤ K STK 0 $7 Given that the underlying stock is assumed to follow Geometric Brownian Motion; dS = μSdt+oSdz (A) Use Risk-Neutral Valuation to derive the fair price of the security at time t in terms of the stock price, S, at time t. This will be referred to as G. (2 Marks) (HINT: You will first need to derive the stochastic process that is followed by Y,= S₂², Your derivation in (a) should show that Y, also follows a GBM)

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