Pricing Exotic Derivatives Exploiting Structure

Debora Sesana
debora.sesana@eco.unipmn.it
Dipartimento S.E.I., UniversitÓ del Piemonte Orientale A. Avogadro, via Perrone 18, I-28100 Novara, Italy

Daniele Marazzina
daniele.marazzina@polimi.it
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

Gianluca Fusai
gianluca.fusai@eco.unipmn.it
Dipartimento S.E.I., UniversitÓ del Piemonte Orientale A. Avogadro, via Perrone 18, I-28100 Novara, Italy
Faculty of Finance, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ, UK

 

ABSTRACT: In this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring occurs, and the underlying evolves according to a Markov one-dimensional stochastic processes. The approach exploits the structure of the matrix arising from the numerical quadrature of the pricing backward formulas to devise a convenient factorization that helps greatly in the speed-up of the recursion.  The algorithm is general and is examined in detail with reference to the CEV (Constant Elasticity of Variance) process for pricing different exotic derivatives, such as Asian, barrier, Bermudan, lookback and step options for which up to date no efficient procedures are available. Extensive numerical experiments confirm the theoretical results.

 

MATLAB CODE for pricing a Down&Out barrier call option: CEV_DownOutCall.m

Matlab codes for other contracts will be provided upon request.