(Solution) - Consider the following SDE for the spot rate drt -(2025 Original AI-Free Solution)

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Consider the following SDE for the spot rate: drt = ?rtdWt.
(a) Write a program that simulates a path for rt by simulating dWt. Assume r0 = 0.01, T = 2.0 and ? = 0.05. Calculate the expectation of the terminal spot rate, rT.
(b) Solve the given SDE and repeat the above simulation by simulating a single Wt along each path. As above, calculate the expectation of the terminal spot rate, rT.
(c) Show empirically that these two simulation methods converge as the number of draws increases and comment on their relative efficiency.