Less Expensive Pricing and Hedging of Long-Dated Equity Index Options When Interest Rates are Stochastic

Many providers of variable annuities such as pension funds and life insurers seek to hedge their exposure to embedded guarantees using longdated derivatives. This paper extends the benchmark approach to price and hedge long-dated equity index options using a combination of cash, bonds and equities under a variety of market models. The results show that when the discounted index is modelled as a squared Bessel process, as in Platen's minimal market model, less expensive hedging is achieved irrespective of the short rate model.