Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models

CREATES Research Paper 2009-14

35 Pages Posted: 7 Apr 2009

See all articles by Dennis Kristensen

Dennis Kristensen

University College London; Aarhus University - CREATES; Cemmap (Centre for Microdata Methods and Practice)

Antonio Mele

University of Lugano; Swiss Finance Institute; Centre for Economic Policy Research (CEPR)

Date Written: April 7, 2009

Abstract

This paper develops a new systematic approach to implement approximate solutions to asset pricing models within multi-factor diffusion environments. For any model lacking a closed-form solution, we provide a solution obtained by expanding the analytically intractable model around a known auxiliary pricing function. We derive power series expansions, which provide increasingly improved refinements to the initial mispricing arising from the use of the auxiliary model. In practice, the expansions can be truncated to include only a few terms to generate extremely accurate approximations. We illustrate our methodology in a variety of contexts, including option pricing with stochastic volatility, volatility contracts and the term-structure of interest rates.

Keywords: Asset pricing, stochastic volatility, the term-structure of interest rates, closed-form

JEL Classification: G12, G13

Suggested Citation

Kristensen, Dennis and Kristensen, Dennis and Mele, Antonio, Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models (April 7, 2009). CREATES Research Paper 2009-14, Available at SSRN: https://ssrn.com/abstract=1374212 or http://dx.doi.org/10.2139/ssrn.1374212

Dennis Kristensen (Contact Author)

University College London ( email )

Gower Street
London WC1E 6BT, WC1E 6BT
United Kingdom
+44 (0)20 7679 5846 (Phone)

HOME PAGE: http://www.ucl.ac.uk/economics/

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Cemmap (Centre for Microdata Methods and Practice) ( email )

7 Ridgmount Street
London WC1E 7AE, WC1E 7 AE
United Kingdom

Antonio Mele

University of Lugano ( email )

Via Buffi 13
Lugano, 6900
Switzerland

HOME PAGE: http://antoniomele.org

Swiss Finance Institute

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

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom