Wichita State University
We study the problem of reconstruction of the asset price dependent local volatility from market prices of options with different strikes. For the general diffusion process we apply the linearization technique and derive that the option price can be obtained as a sum of the Black-Scholes formula and an explicit functional which is linear in volatility. We obtain an integral equation for this functional and show that under certain natural conditions it can be inverted for volatility. We demonstrate the stability of the linearized problem, and show that the numerical algorithm is accurate for volatility functions with various properties.
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Fall 2001]