Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models

• 成果类型: Article
• 署名作者: Kristensen, Dennis; Mele, Antonio
• 署名单位: University of London; London School Economics & Political Science; Columbia University
• 刊物名称: JOURNAL OF FINANCIAL ECONOMICS
• ISSN/ISSBN: 0304-405X
• DOI: 10.1016/j.jfineco.2011.05.007
• 发表日期: 2011
• 页码: 390-415
• 关键词: Continuous-time models; Option pricing theory; stochastic volatility; Closed-form approximations

摘要

We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a closed-form approximate solution, which relies on the expansion of the intractable model around an auxiliary one. We derive an expression for the difference between the true (but unknown) price and the auxiliary one, which we approximate in closed-form, and use to create increasingly improved refinements to the initial mispricing induced by the auxiliary model. The approach is intuitive, simple to implement, and leads to fast and extremely accurate approximations. We illustrate this method in a variety of contexts including option pricing with stochastic volatility, computation of Greeks, and the term structure of interest rates. (C) 2011 Elsevier B.V. All rights reserved.