Suppose that S1 and S2 follow geometric Brownian motion and pay continuous proportional dividends at the rates δ1 and δ2. Use the martingale argument to show that the value of a claim paying S1(T ) if S1(T) > KS2(T ) is
where σ2 = σ2 1 + σ2 2 − 2ρ1, 2σ1σ2 and δ1 and δ2 are the dividend yields on the two stocks.
Answer to relevant QuestionsUnder 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 ...A collect-on-delivery call (COD) costs zero initially, with the payoff at expiration being 0 if S Consider the Level 3 outperformance option with a multiplier, discussed in Section 16.2. This can be valued binomially using the single state variable SLevel 3/SS&P, and multiplying the resulting value by SS&P. a. Compute ...The quanto forward price can be computed using the risk-neutral distribution as E(Yx−1). Use Proposition 20.4 to derive the quanto forward price given by equation (23.30). Using the Merton jump formula, generate an implied volatility plot for K = 50, 55, . . . 150. a. How is the implied volatility plot affected by changing αJ to−0.40 or−0.10? b. How is the implied volatility plot affected ...
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