Articlebronze2001

Identifying the volatility of underlying assets from option prices

116 citations0/0 files storedInverse Problems

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Stochastic processes and financial applications Differential Equations and Boundary Problems Numerical methods in inverse problems

Abstract

In this paper, we use an optimal control framework to determine implied volatility and make a rigorous mathematical analysis of this inverse problem. We also prove the approximate optimal solutions converge to the appropriate solutions for the original problem. Being different from ordinary parameter identification problems, our problem is to identify the coefficient of the second-order partial derivative in the equation with the PDE being non-divergent.

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References

1994Implied Binomial Trees 1998Derivatives: The Theory and Practice of Financial Engineering 1996Implied Trinomial Tress of the Volatility Smile 1997A technique for calibrating derivative security pricing models: numerical solution of an inverse problem 1997The inverse problem of option pricing

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2003A new well-posed algorithm to recover implied local volatility 2007An inverse problem of determining the implied volatility in option pricing 2006On decoupling of volatility smile and term structure in inverse option pricing

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