Pricing Options on Assets with Jump Diffusion and Uncertain Volatility

Mathematical Finance/Financial Engineering Seminar
Tuesday, September 22, 2009 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 269
Gunter Meyer – School of Mathematics, Georgia Tech
Liang Peng
When the asset price follows geometric Brownian motion but allows random Poisson jumps (called jump diffusion) then the standard Black Scholes partial differential for the option price becomes a partial-integro differential equation (PIDE). If, in addition, the volatility of the diffusion is assumed to lie between given upper and lower bounds but otherwise not known then sharp upper and lower bounds on the option price can be found from the Black Scholes Barenblatt equation associated with the jump diffusion PIDE. In this talk I will introduce the model equations and then discuss the computational issues which arise when the Black Scholes Barenblatt PIDE for jump diffusion is to be solved numerically.