Calibrating Volatility Surfaces via Relative-Entropy Minimization

38 Pages Posted: 1 Feb 1997  

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Craig A. Friedman

TIAA-CREF

Richard Holmes

New York University (NYU) - Courant Institute of Mathematical Sciences

Dominick J. Samperi

Decision Synergy

Date Written: December 12, 1996

Abstract

We present a framework for calibrating a pricing model to a prescribed set of option prices quoted in the market. Our algorithm yields an arbitrage-free diffusion process that minimizes the relative entropy distance to a prior diffusion. We solve a constrained (minimax) optimal control problem using a finite-difference scheme for a Bellman parabolic equation combined with a gradient-based optimization routine. The number of unknowns in the optimization step is equal to the number of option prices that need to be matched, and is independent of the mesh-size used for the scheme. This results in an efficient, non- parametric calibration method that can match an arbitrary number of option prices to any desired degree of accuracy. The algorithm can be used to interpolate, both in strike and expiration date, between implied volatilities of traded options and to price exotics. The stability and qualitative properties of the computed volatility surface are discussed, including the effect of the Bayesian prior on the shape of the surface and on the implied volatility smile/skew. The method is illustrated by calibrating to market prices of Dollar-Deutschemark over-the-counter options and computing interpolated implied-volatility curves.

JEL Classification: G13

Suggested Citation

Avellaneda, Marco and Friedman, Craig A. and Holmes, Richard and Samperi, Dominick J., Calibrating Volatility Surfaces via Relative-Entropy Minimization (December 12, 1996). Available at SSRN: https://ssrn.com/abstract=648 or http://dx.doi.org/10.2139/ssrn.648

Marco Avellaneda (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

251 Mercer Street
New York, NY 10012
United States
212-998-3129 (Phone)
212-995-4121 (Fax)

Finance Concepts LLC ( email )

590 Madison Avenue
21st Floor
New York, NY 10022
United States

HOME PAGE: http://www.finance-concepts.com

Craig A. Friedman

TIAA-CREF ( email )

730 3rd Ave
New York, NY 10017
United States

Richard Holmes

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

Dominick J. Samperi

Decision Synergy ( email )

375 South End Ave., Suite 8J
New York, NY 10280
United States

HOME PAGE: http://www.decisionsynergy.com

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