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.
Answer to relevant QuestionsSuppose that S follows equation (20.36) and Q follows equation (20.37). Use Itˆo’s Lemma to find the process followed by ln(SQ). Suppose that a derivative claim makes continuous payments at the rate _. Show that the Black-Scholes equation becomes Assuming that the stock price satisfies equation (20.20), verify that Ke−r(T−t) + S(t)e−δ(T−t) satisfies the Black-Scholes equation, where K is a constant. What is the boundary condition for which this is a ...Suppose there are 1-, 2-, and 3-year zero-coupon bonds, with prices given by P1, P2, and P3. The implied forward interest rate from year 1 to 2 is r0(1, 2) = P1/P2 − 1, and from year 2 to 3 is r0(2, 3) = P2/P3 − 1. ...In this problem we will use Monte Carlo to simulate the behavior of the martingale St/Pt , with Pt as numeraire. Let x0 = S0/P0(0, T ). Simulate the process xt+h= (1+ σ√ hZt+h)xt Let h be approximately 1 day. a. Evaluate ...
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