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- iwanttobelieve
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Qualitative finance
Let B be the contigent claim:with K1<K2, S the underlying and T the expiry date.You want to compare qualitatively the price of this option in 2 models.a. Black-Scholes, sigma = sigma_0 is constantb. Local vol, sigma = sigma(S) is smiled, e.g. a parabole that is centered in K the mean of K1,K2 and say, below sigma_0 on [K1,K2] and above outside.The question reads:Can you possibly compare the two prices.
Qualitative finance
2 is more expensive.Let's consider case, when both processes goes above K_2 at some t<T. Process 2 has higher probability to return back to the interval [K_1,K_2], volatility is more than sigma_0.At any place in the interval [K_1,K_2] the process 2 has less probability than process 1 to go out of [K_1,K_2] interval, volatility is less than sigma_0.So, probability that process 2 ends up in the interval [K_1,K-2] is higher.