Fast Calibration of Interest Rate Claims in the Quadratic Gaussian Model : 2 the Swaptions

In the second part of a series of articles on the pricing of interest rate contingent claims in the multifactor Quadratic Gaussian model, we concentrate on the pricing of swaptions. Assuming the zero-coupon bond volatility to be a deterministic function of some Markov processes, we derive the true volatility of the coupon-bond as a weighted sum of some zero-coupon bond volatility with different maturities. Bounding the stochastic weights such that the misspecified volatility dominates the true one, we obtain bounds and hedges to the true price which are solved with approximate solutions of the Black type to the prices of call option and binary option when volatility, rates and dividends are function of the Markov processes.