The Density Process of the Minimal Entropy Martingale Measure in a Stochastic Volatility Model with Jumps (Reprint)

Benth, Fred Espen and Meyer-Brandis, Thilo (2010): The Density Process of the Minimal Entropy Martingale Measure in a Stochastic Volatility Model with Jumps (Reprint). In: Lee, Cheng-Few; Lee, Alice C. and Lee, John (eds.) : Handbook of Quantitative Finance and Risk Management. Boston, MA: Springer. pp. 1567-1575

Abstract

We derive the density process of the minimal entropy martingale measure in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard (Journal of the Royal Statistical Society, Series B 63:167–241, 2001). The density is represented by the logarithm of the value function for an investor with exponential utility and no claim issued, and a Feynman–Kac representation of this function is provided. The dynamics of the processes determining the price and volatility are explicitly given under the minimal entropy martingale measure, and we derive a Black and Scholes equation with integral term for the price dynamics of derivatives. It turns out that the price is the solution of a coupled system of two integro-partial differential equations.

• Item Type: Book Section
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISBN: 978-0-387-77117-5 ; 978-0-387-77116-8
• Place of Publication: Boston, MA
• Language: English