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The market model of interest rate dynamics. (English) Zbl 0884.90008
Summary: A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.

MSC:
91B28Finance etc. (MSC2000)
91B26Market models (auctions, bargaining, bidding, selling, etc.)
91B84Economic time series analysis
60H15Stochastic partial differential equations