Generic market models
The authors introduce generic market models featuring forward rates that span periods other than the classical LIBOR and swap periods. The main outset of the paper is that a model is deemed proper for a certain interest rate derivative if the volatility of a rate that appears in the contract payoff has been calibrated correctly to the market volatility. The new angle of this paper is that no-arbitrage is considered in the market spanned at a given time point by the various forward swap rates in a generic market model. The conditions are provided that guarantee the absence of arbitrage in these static forward agreement markets for the generic setting. The necessary and sufficient conditions are derived for the structure of the forward rates to span an arbitrage-free economy in terms of relative discount bond prices, at all times. Generic expressions are developed for the drift terms occurring in the stochastic differential equation driving the forward rates under a single pricing measure. There is demonstrated how the instantaneous correlation of the generic forward rates can be calculated from the instantaneous correlation of forward LIBOR rates. The efficiency of drift calculations is discussed.
scientific article; zbMATH DE number 5158698