The pricing and hedging of rate of return guarantees

The basis for this chapter is the pricing and hedging of multi-period rate of return guarantees. We find closed form expressions for the market value of multi-period rate of return guarantees, and we also show that the market value of these guarantees can be hedged by self- financing trading strategies. We show expressions for these trading strategies both when interest rates are deterministic and when they are stochastic. We consider the return on two underlying assets, a stock and a money market account. The functions describing the number of units of the assets in the hedge portfolio for a European option are continuous functions. We show that for multi-period rate of return guarantees, these functions are discontinuous. We also show that by introducing stochastic interest rates, the hedging strategies changes quite considerably, in that one needs to use more assets to get a per- fect hedge.