Small-time expansions of the distributions, densities, and option prices of stochastic volatility models with L茅vy jumps

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• 作者：José ; E. Figueroa-Ló ; pez^a ; ^{figueroa@purdue.edu} ; Ruoting Gong^b ; ^{rgong@math.gatech.edu} ; Christian Houdré ; ^b ; ^{houdre@math.gatech.edu}
• 关键词：60G51 ; 60F99 ; 91G20 ; 91G60
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：April, 2012
• 卷：122
• 期：4
• 页码：1808-1839
• 文件大小：339 K

摘要

We consider a stochastic volatility model with L茅vy jumps for a log-return process of the form , where is a classical stochastic volatility process and is an independent L茅vy process with absolutely continuous L茅vy measure . Small-time expansions, of arbitrary polynomial order, in time-, are obtained for the tails , , and for the call-option prices , , assuming smoothness conditions on the density of away from the origin and a small-time large deviation principle on . Our approach allows for a unified treatment of general payoff functions of the form for smooth functions and . As a consequence of our tail expansions, the polynomial expansions in of the transition densities are also obtained under mild conditions.