Pricing inflation products with stochastic volatility and stochastic interest rates

► We consider a Heston type inflation model in combination with a Hull-White model for nominal and real interest rates, in which all the correlations can be non-zero. ► We derive an efficient approximate semi-closed pricing formula for two types of inflation dependent options: index and year-on-year inflation options. ► The approach is illustrated using a real-life pension fund example, where the Heston Hull-White model is used to determine the value of conditional future indexations.