We reduce a problem of pricing continuously monitored defaultable securities (barrier options, corporate debts) in a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. In the case when the interest rate is governed by a linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also find an estimation of the rate of convergence of the suggested approximation and illustrate results by numerical examples.
|Title of host publication||Mathematical Control Theory and Finance|
|Editors||Andrey Sarychev, Albert Shiryaev, Manuel Guerra, Maria do Rosário Grossinho|
|Place of Publication||Berlin; London|
|Publisher||Springer, Springer Nature|
|Number of pages||13|
|Publication status||Published - 2008|