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 σ , i.e., dS t = S t ( r dt + σ d f W t ). Let v ( S ,r,σ ) denote the corresponding Black-Scholes price of a call option ( S T − K ) + at time 0 and investigate the limit lim σ ↑∞ v ( S ,r,σ ) . Exercise 3: Let v ( T,S ,r,σ ) be as in Exercise 2 and prove the following formulas for the two Greeks Rho and Vega, % = ∂ ∂r v ( S ,r,σ ) = KT e − rT N ° d − ¢ and V = ∂ ∂σ v ( S ,r,σ ) = S √ T N ° d + ¢ . Exercise 4: Exercise 6.10 on page 293 in Shreve’s book. 1...
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- Spring '08
- Brownian Motion, arbitrage opportunity, Upson