Assume the Black-Scholes framework holds. The price of a stock is governed by a stochastic differential equation dSt = S dt+oStdBt, B: denotes a standard Brownian motion. where {Bt, t > 0} is a standard Brownian motion, 1, 0, and So are given positive constants. Let r denote the interest rate per annum with continuous compounding. The payoff function of a forward contract for the long position is f(S) = ln(S) - K where K is a positive constant. The delivery date of the contract is T. (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 method to determine the value of the contract at time 0. [20 marks] (c) Determine the Greek letters A and V for the contract at time 0. [7 marks] Assume the Black-Scholes framework holds. The price of a stock is governed by a stochastic differential equation dSt = S dt+oStdBt, B: denotes a standard Brownian motion. where {Bt, t > 0} is a standard Brownian motion, 1, 0, and So are given positive constants. Let r denote the interest rate per annum with continuous compounding. The payoff function of a forward contract for the long position is f(S) = ln(S) - K where K is a positive constant. The delivery date of the contract is T. (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 method to determine the value of the contract at time 0. [20 marks] (c) Determine the Greek letters A and V for the contract at time 0. [7 marks]