Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/7360
 Title: Reconstructing the unknown volatility function Authors: Coleman, Thomas FLi, YuyingVerma, Arun Keywords: computer sciencetechnical report Issue Date: Sep-1998 Publisher: Cornell University Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR98-1706 Abstract: Using market European option prices, a method for computing a {\em smooth} local volatility function in a 1-factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of the true local volatility function from a finite set of observation data. It is emphasized that accurately approximating the true local volatility function is crucial in hedging even simple European options, and pricing exotic options. A spline functional approach is used: the local volatility function is represented by a spline whose values at chosen knots are determined by solving a constrained nonlinear optimization problem. The optimization formulation is amenable to various option evaluation methods; a partial differential equation implementation is discussed. Using a synthetic European call option example, we illustrate the capability of the proposed method in reconstructing the unknown local volatility function. Accuracy of pricing and hedging is also illustrated. Moreover, it is demonstrated that, using a different constant implied volatility for an option with different strike/maturity can produce erroneous hedge factors. In addition, real market European call option data on the S and P 500 stock index is used to compute the local volatility function; stability of the approach is demonstrated. URI: http://hdl.handle.net/1813/7360 Appears in Collections: Computer Science Technical Reports

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