Analytical Valuation of Barrier Interest Rate Options Under Market Models

Abstract

Barrier caps, floors, and swaptions are priced in a closed form via the time-changed technique under the market models. The parameters of the resulting formulas can be easily extracted from market data. This makes the pricing formulas more easily implemented in practice. In addition, the monitoring of the barrier crossing is based on the observable forward LIBOR and swap rates, which helps hedging operations.