Determine the stock price distribution at time t

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Reference no: EM131240912

At time 0 the price of a non-dividend-paying stock is S0. Suppose that the time interval between 0 and T is divided into two subintervals of length t₁ and t₂. During the first subinterval, the risk-free interest rate and volatility are r₁ and σ₁, respectively. During the second subinterval, they are r₂ and σ₂, respectively. Assume that the world is risk neutral.

(a) Use the results in Chapter 14 to determine the stock price distribution at time T in terms of

(b) Suppose that is the average interest rate between time zero and T and that V is the average variance rate between times zero and T. What is the stock price distribution as a function of T in terms of

(c) What are the results corresponding to (a) and (b) when there are three subintervals with different interest rates and volatilities?

(d) Show that if the risk-free rate, r, and the volatility, α, are known functions of time, the stock price distribution at time T in a risk-neutral world is

where is the average value of r, is equal to the average value of σ² , and S₀ is the stock price today and ?(m, v) is a normal distribution with mean m and variance v.

Reference no: EM131240912

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