# Question

Use Itˆo’s Lemma to evaluate d(√S).

For the following four problems, use Itˆo’s Lemma to determine the process followed by the specified equation, assuming that S(t) follows

(a) Arithmetic Brownian motion, equation (20.8);

(b) A mean reverting process, equation (20.9); and

(c) Geometric Brownian motion, equation (20.11).

For the following four problems, use Itˆo’s Lemma to determine the process followed by the specified equation, assuming that S(t) follows

(a) Arithmetic Brownian motion, equation (20.8);

(b) A mean reverting process, equation (20.9); and

(c) Geometric Brownian motion, equation (20.11).

## Answer to relevant Questions

Suppose that S follows equation (20.36) and Q follows equation (20.37). Use Itˆo’s Lemma to find the process followed by S2Q0.5. Verify that equation (21.12) satisfies the Black-Scholes equation. What is the boundary condition for which this is a solution? Use the Black-Scholes equation to verify the solution in Chapter 20, given by Proposition 20.3, for the value of a claim paying Sa. Repeat the previous problem assuming that δ1= 0.05 and δ2 = 0.12. Verify that both procedures give a price of approximately $15.850. Under the same assumptions as the previous problem, show that the value of a claim paying S2(T ) if S1(T) > KS2(T ) is where σ2, δ1, and δ2 are defined as in the previous problem. In the next set of problems you will use ...Post your question

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