Semi-Parametric Estimation of American Option Prices

63 Pages Posted: 12 Jan 2011

See all articles by Patrick Gagliardini

Patrick Gagliardini

USI Università della Svizzera italiana; Swiss Finance Institute

Diego Ronchetti

University of Groningen - SOM Research School

Date Written: December 1, 2010

Abstract

We introduce a novel semi-parametric estimator of the price of American options in a discrete time, Markovian framework. The estimator is based on a parametric specification of the stochasticdiscount factor and is non-parametric w.r.t. the historical dynamics of the state variables. The estimation method exploits the no-arbitrage conditions for the short-term risk-free bond, the underlying asset and a cross-section of observed prices of American options written on it. We use the dynamic programming representation of American option prices to make explicit the nonlinear restrictions on the model parameters coming from option data. We obtain an estimator of the transition density of the state variables process by minimizing a statistical measure based on the Kullback-Leibler divergence from a kernel-based transition density, subject to the no-arbitrage restrictions. We use the estimator to compute the price of American options not traded in the market by recursive valuation. Other functionals of the transition density interesting for financial applications can be estimated in a similar way.

Keywords: American option, kernel estimator, semi-parametric estimation, dynamic programming, recursive valuation, Fréchet derivative, nonlinear functional

JEL Classification: C14, G13, C60

Suggested Citation

Gagliardini, Patrick and Ronchetti, Diego, Semi-Parametric Estimation of American Option Prices (December 1, 2010). Swiss Finance Institute Research Paper No. 10-57. Available at SSRN: https://ssrn.com/abstract=1738219 or http://dx.doi.org/10.2139/ssrn.1738219

Patrick Gagliardini (Contact Author)

USI Università della Svizzera italiana ( email )

Via Buffi 13
Lugano, TN 6900
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Diego Ronchetti

University of Groningen - SOM Research School ( email )

P.O. Box 800
9700 AV Groningen
Netherlands
+31 50 363 3460 (Phone)
+31 50 363 7337 (Fax)

HOME PAGE: http://www.rug.nl/staff/d.ronchetti/

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