Use the answers to the previous two problems to verify that the Black-Scholes formula, equation (12.1), satisfies the Black-Scholes equation. Verify that the boundary condition V [S(T), T ]= max[0, S(T ) − K] is satisfied.
Answer to relevant QuestionsConsider Joe and Sarah’s bet in Examples 21.2 and 21.3. a. In this bet, note that $106.184 is the forward price. A bet paying $1 if the share price is above the forward price is worth less than a bet paying $1 if the share ...Assume the same bonds and numeraire as in the previous question. Suppose that P1/P3 is a martingale following a geometric Brownian process with annual standard deviation σ1= 0.10, and that P2/P3 is a martingale following a ...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 ...Covered call writers often plan to buy back the written call if the stock price drops sufficiently. The logic is that the written call at that point has little “upside,” and, if the stock recovers, the position could ...Assume that S = $45, K = $40, r = 0.05, δ = 0.02, and σ = 0.30. Using the up rebate formula (equation (23.21)), find the value of H that maximizes (H − K) × UR(S, σ, r , T , δ), for T = 1, 10, 100, 1000, and 10,000. ...
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