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

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.