Approximating payoffs and pricing formulas

Laurent, Jean-Paul; Darolles, Serge

Laurent, Jean-Paul; Darolles, Serge (2000), Approximating payoffs and pricing formulas, Journal of Economic Dynamics and Control, 24, 11-12, p. 1721–1746. http://dx.doi.org/10.1016/S0165-1889(99)00092-5

Type

Article accepté pour publication ou publié

Date

2000-10

Nom de la revue

Journal of Economic Dynamics and Control

Volume

Numéro

11-12

Éditeur

Elsevier

Pages

1721–1746

Résumé (EN)

We use the ideas developed by Madan and Milne (1994. Mathematical Finance 3, 223–245), Lacoste (1996. Mathematical Finance 6, 197–213) to explore the optimality of polynomial approximations in pricing securities. In particular, we look at the approximations for security payoffs as well as the associated pricing formula in a L2 framework. We apply these ideas to two examples, one where the state variable follows an Ornstein–Uhlenbeck process and one based on Brownian motion with reflecting barriers, to illustrate the strengths and weaknesses of the approach.

Mots-clés

Infinitesimal generator; Markov process; Spectral analysis; Payoff approximation; Pricing formula

JEL

C10 - General
C63 - Computational Techniques; Simulation Modeling
G12 - Asset Pricing; Trading Volume; Bond Interest Rates