PDF MATH4143: Numerical Methods in Finance Assignment 2 Due on ...

MATH4143: Numerical Methods in Finance Assignment 2

Due on Monday, March 10 (in-class)

1. Suppose that a stock price has an expected return of 16% per annum and a volatility of 30% per annum. When the stock price at the end of a certain day is $50, calculate the following: a) The expected stock price at the end of the next day. b) The standard deviation of the stock price at the end of the next day.

2. Suppose that a stock price S follows geometric Brownian motion dS = ?S dt + S dz ,

what is the process followed by the variable y = er(T -t) . S

3. Write computer programs to value the European up-and-out option using Monte Carlo simulations. a) Consider a European up-and-out option with strike price K = $6, the annual risk-free interest rate r = 5%, initial asset price S0= $5, and volatility = 30%, the expiry date of one year (i.e., T = 1) and barrier B = 8. b) Compute the 95% confidence intervals for the total number N of time steps N = 102 , 103 ,and 104 , and the number M of discrete sample paths M = 102 , 103 , 104 and 105. Do these confidence intervals always contain the exact value $0.0983 given by Black-Scholes formula? Explain why.

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