Approximating payoffs and pricing formulas

Serge Darolles (1) , Jean-Paul Laurent (2, 3)

1 DRM-Finance
2 Financial models, Group ALM
3 SAF - Laboratoire de Sciences Actuarielle et Financière

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

Domaines: Economies et finances

Serge Darolles, Jean-Paul Laurent. Approximating payoffs and pricing formulas. Journal of Economic Dynamics and Control, 2000, 24 (11-12), pp.1721-1746. ⟨10.1016/S0165-1889(99)00092-5⟩. ⟨halshs-00678228⟩