Identifying the volatility of underlying assets from option prices (Q2709875)

The authors study the problem of determination of the option value and volatility function satisfying a boundary value problem for the Black-Scholes equation by using the current market prices of options with different strike and fixed maturity values. This inverse problem is reduced to an inverse parabolic problem with terminal observation. The volatility of the underlying asset is defined then on the base of optimal control approach. A necessary optimality condition is derived. The convergence of approximate optimal solutions is shown. The uniqueness of the optimal control (which is still an open problem) is discussed.