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Unformatted text preview: by trading in the three calls. Exercise 2: Consider the market model with constant interest rate r and risk-neutral price process given by geometric Brownian motion S with volatility , i.e., dS t = S t ( r dt + d f W t ). Let v ( S ,r, ) denote the corresponding Black-Scholes price of a call option ( S T K ) + at time 0 and investigate the limit lim v ( S ,r, ) . Exercise 3: Let v ( T,S ,r, ) be as in Exercise 2 and prove the following formulas for the two Greeks Rho and Vega, % = r v ( S ,r, ) = KT e rT N d and V = v ( S ,r, ) = S T N d + . Exercise 4: Exercise 6.10 on page 293 in Shreves book. 1...
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- Spring '08