| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 100 === The Black-Scholes formula was the widely-used model for option pricing, this formula can be use to calculate the price of option by using current underlying asset prices, strike price, expiration time, volatility and interest rates. The European call option price from the model is a convex and increasing with respect to the initial underlying asset price. Assume underlying asset prices follow a generalized geometric Brownian motion, it is true that option prices increasing with respect to the constant interest rate and volatility, so that the volatility can be a very important factor in pricing option, if the volatility process σ (t) is constant (with σ (t) =σ for any t ) satisfying σ _1 ≤ σ (t) ≤ σ_2 for some constants σ_1 and σ_ 2 such that 0 ≤ σ_ 1 ≤ σ_ 2. Let C_i(t, S_t) be the price of the call at time t corresponding to the constant volatility σ_ i (i = 1,2), we will derive that the price of call option at time 0 in the model with varying volatility belongs to the interval [C_1(0, S_0),C_2(0, S_0)].
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