Consider a Black-Scholes world where the interest rate is the constant r and where there are two stocks with prices SA a
Posted: Wed May 04, 2022 1:35 pm
- Consider A Black Scholes World Where The Interest Rate Is The Constant R And Where There Are Two Stocks With Prices Sa A 1 (296.35 KiB) Viewed 44 times
Consider a Black-Scholes world where the interest rate is the constant r and where there are two stocks with prices SA and S that satisfy the SDES dSA = SA (µ^dt + o^dB₁) and dSB = S² (u³dt + g³dB₁). where the two Brownian motions are independent. Think of yourself as the owner of one A share. Some guy proposes to write you an option that will give you the right, but not the obligation, to exchange your one A for one B share at time T. What is the time t arbitrage free price of this option. You should work this out as completely as you can. In particular, you should get a formula that looks like the Black-Scholes formula. Explain how you would replicate such na option.