Development of computational algorithms for evaluating option prices associated with square-root volatility processes (Q1041306)

The purpose of this paper is to develop computational algorithms for evaluating the prices of such exotic options based on a bivariate birth-death approximation approach. Given the underlying price process \(S_{t}\), the logarithmic process \(U_{t} = \log S_{t}\) is first approximated by a birth-death process \(B^U_t\) via moment matching. A second birth-death process \(B^V_t \) is then constructed for approximating the stochastic volatility process \(V _{t }\) through infinitesimal generator matching. Efficient numerical procedures are developed for capturing the dynamic behavior of \(\{ B^U_t , B^V_t \} \). Consequently, the prices of any exotic options based on the Heston model can be computed as long as such prices are expressed in terms of the joint distribution of \(\{ S _{t } ,V _{t } \}\) and the associated first passage times.