Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks

Article type: Research Article

Authors: Capriotti, Luca^{; *}

Affiliations: Quantitative Strategies, Investment Banking Division, Credit Suisse Group, One Cabot Square, London E14 4QJ, United Kingdom

Correspondence: [*] Corresponding author: Luca Capriotti, Quantitative Strategies, Investment Banking Division, Credit Suisse Group, One Cabot Square, London E14 4QJ, United Kingdom. E-mail: [email protected]

Abstract: We show how Adjoint Algorithmic Differentiation can be combined with the so-called Pathwise Derivative and Likelihood Ratio Method to construct efficient Monte Carlo estimators of second order price sensitivities of derivative portfolios. We demonstrate with a numerical example how the proposed technique can be straightforwardly implemented to greatly reduce the computation time of second order risk.

Keywords: Adjoint Algorithmic Differentiation, Monte Carlo, derivatives securities, risk management

DOI: 10.3233/AF-150045

Journal: Algorithmic Finance, vol. 4, no. 1-2, pp. 81-87, 2015