Question
Consider the case of the put option derived above. We assume a Black-Scholes world where S 1 and S 2 have geometric Brownian motion dynamics
Consider the case of the put option derived above. We assume a Black-Scholes world where S1 and S2 have geometric Brownian motion dynamics as follow:
dS1t/S1t= 1dt + 1dz1t
dS2t/S2t= 2dt + 2dz2t
where 1 and 2 are respectively the expected return of the S&P 500 and the FTSE indices, 1 and 2 their respective volatility, and z1t and z2t are correlated Brownian motions in the sense that dz1.dz2 = dt. Moreover, you may assume that there is a money market account denotes Bt and paying a risk-free rate r: dBt/Bt= rdt
1. Using risk-neutral pricing, derive an analytical formula for the price of the option.
2. What do you observe in this formula regarding the risk-free rate ? Can you explain your observation ?
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Business Forecasting
Authors: John E. Hanke, Dean Wichern
9th edition
132301202, 978-0132301206
