5. Suppose the Black-Scholes framework holds. A non-dividend-paying stock is now selling for x >...

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5. Suppose the Black-Scholes framework holds. • A non-dividend-paying stock is now selling for x > 0. • The volatility of the stock is o per annum. The interest rate is r per annum with continuous compounding. The payoff function of a T-year European option written on the stock is f(S) = (In(S³) - K)†, where K> 0 is a constant. (a) Write down the stochastic differential equation that the stock price follows in the risk-neutral world. [3 marks] (b) Use the risk-neutral valuation or other method to find the price of the option at time t. Express your result in terms of N(x) = ² -y² dy. [9 marks] ∞ (c) Determine the Delta A of the option at time t. [2 marks] /2πT 5. Suppose the Black-Scholes framework holds. • A non-dividend-paying stock is now selling for x > 0. • The volatility of the stock is o per annum. The interest rate is r per annum with continuous compounding. The payoff function of a T-year European option written on the stock is f(S) = (In(S³) - K)†, where K> 0 is a constant. (a) Write down the stochastic differential equation that the stock price follows in the risk-neutral world. [3 marks] (b) Use the risk-neutral valuation or other method to find the price of the option at time t. Express your result in terms of N(x) = ² -y² dy. [9 marks] ∞ (c) Determine the Delta A of the option at time t. [2 marks] /2πT

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a The stochastic differential equation that the stock price follows in the riskneutral world is dSS ... View the full answer