Valuing American Options Using Fast Recursive Projections

67 Pages Posted: 2 Jun 2016

See all articles by Antonio Cosma

Antonio Cosma

Université du Luxembourg

Stefano Galluccio

BNP Paribas Fixed Income

Paola Pederzoli

University of Houston - C.T. Bauer College of Business

O. Scaillet

University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics

Date Written: June 1, 2016

Abstract

We introduce a fast and widely applicable numerical pricing method that uses recursive projections. The method is based on a simple grid sampling of value functions and state-price densities. Numerical illustrations with different American and Bermudan payoffs with dividend paying stocks in the Black Scholes and Heston models show that the method is fast, accurate, and general.

We find that the early exercise boundary of an American call option on a discrete dividend paying stock is higher under the Merton and Heston models than under the Black-Scholes model, as opposed to the continuous dividend case. A large database of call options on stocks with quarterly dividends shows that adding stochastic volatility and jumps to the Black-Scholes benchmark reduces the amount foregone by call holders failing to optimally exercise by 25%. Transaction fees cannot fully explain the suboptimal behavior.

Keywords: Option pricing, American option, Bermudan option, discrete transform, discrete dividend paying stock, suboptimal non-exercise, numerical techniques

JEL Classification: G13, C63

Suggested Citation

Cosma, Antonio and Galluccio, Stefano and Pederzoli, Paola and Scaillet, Olivier, Valuing American Options Using Fast Recursive Projections (June 1, 2016). Paris December 2016 Finance Meeting EUROFIDAI - AFFI, Available at SSRN: https://ssrn.com/abstract=2788072 or http://dx.doi.org/10.2139/ssrn.2788072

Antonio Cosma (Contact Author)

Université du Luxembourg ( email )

162a, avenue de la Faïencerie
Luxembourg, L-1511
Luxembourg
+352 46 66 44 6763 (Phone)
+352 46 66 44 6835 (Fax)

Stefano Galluccio

BNP Paribas Fixed Income ( email )

10, Harewood Avenue
NW1 6AA London
United Kingdom

Paola Pederzoli

University of Houston - C.T. Bauer College of Business ( email )

Houston, TX 77204-6021
United States

Olivier Scaillet

University of Geneva GSEM and GFRI ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland
+ 41 22 379 88 16 (Phone)
+41 22 389 81 04 (Fax)

HOME PAGE: http://www.scaillet.ch

Swiss Finance Institute

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

University of Geneva - Research Center for Statistics

Geneva
Switzerland

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