# Question

Suppose that on any given day the annualized continuously compounded stock return has a volatility of either 15%, with a probability of 80%, or 30%, with a probability of 20%. This is a mixture of normals model. Simulate the daily stock return and construct a histogram and normal plot. What happens to the normal plot as you vary the probability of the high volatility distribution?

## Answer to relevant Questions

Use Itˆo’s Lemma to evaluate d[ln(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 ...Assume that one stock follows the process dS/S = αdt + σdZ (20.44) Another stock follows the process dQ/Q = αQdt + σdZ + dq1+ dq2 (20.45) a. If there were no jump terms (i.e., λ1 = λ2 = 0), what would be the relation ...Suppose that ln(S) and ln(Q) have correlation ρ =−0.3 and that S(0) = $100, Q(0) = $100, r = 0.06, σS = 0.4, and σQ = 0.2. Neither stock pays dividends. Use equation (20.38) to find the price today of claims that pay a. ...Verify that ASaeγ t satisfies the Black-Scholes PDE for Repeat the previous problem assuming that δ1= 0.05 and δ2 = 0.12. Verify that both procedures give a price of approximately $15.850.Post your question

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