pure discount bond

1. Simulate 1,000 paths of the Brownian motion W on the time interval [0, 1], using 25 time periods. Estimate the mean and the variance of W(1). Draw a graph of one of the paths.
2. The one-year spot rate is 6%. According to your model of the term structure, you simulate the values of the one-year spot interest rate that could prevail in the market one year from now. You do only five simulations and get 6%, 6.52%, 6.32%, 5.93%, and 6.41%. Compute, using Monte Carlo, the rough approximation of the price of a one-year European call on the two-year pure discount bond with strike price 94.

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