Taking a portfolio perspective on option pricing and hedging, we show that within the standard Black-Scholes-Merton framework large portfolios of options can be hedged without risk in discrete time. The nature of the hedge portfolio in the limit of large portfolio size is substantially different...

In this paper we derive a market value for Guaranteed Annuity Optionusing martingale modeling techniques. Furthermore, we show how to construct a static replicating portfolio of vanillainterest rate swaptions that replicates the Guaranteed Annuity Option. Finally, we illustrate with historical...