On contingent-claim valuation in continuous-time for volatility models of Ornstein–Uhlenbeck type

摘要

The paper addresses the valuation of contingent claims in stochastic volatility models of Ornstein–Uhlenbeck type, stressing the situation when volatility is driven by purely-discontinuous Lévy processes. A reduction series methodology is developed for this purpose which also provides a way for the numerical study of the value-functionals. The methodology is illustrated in the options case and in models based on GIG-distributions; numerical examples are provided. These examples show how the series enable computation accuracies of some three decimal places with just a single digit number of terms.