A FAMILY OF DENSITY EXPANSIONS FOR LEVY-TYPE PROCESSES

• 成果类型: Article
• 署名作者: Lorig, Matthew; Pagliarani, Stefano; Pascucci, Andrea
• 署名单位: Princeton University; Institut Polytechnique de Paris; Ecole Polytechnique; University of Bologna
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP994
• 发表日期: 2015
• 页码: 235-267
• 关键词: jump

摘要

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci and Riga [SIAM J. Financial Math. 4 (2013) 265-296], we derive a family of asymptotic expansions for the transition density of the underlying as well as for European-style option prices and defaultable bond prices. For the density expansion, we also provide error bounds for the truncated asymptotic series. Our method is numerically efficient; approximate transition densities and European option prices are computed via Fourier transforms; approximate bond prices are computed as finite series. Additionally, as in Pagliarani, Pascucci and Riga (2013), for models with Gaussian-type jumps, approximate option prices can be computed in closed form. Sample Mathematica code is provided.