The Normal Class Of Arbitrage-free Spot-rate Models

In this paper we first show how to determine the T-forward adjusted risk-measure using the concept of fundamental solution to linear PDE’s. After that, relying on Fourier transformation we derive bond-and bond-option prices for the Extended Vasicek model from Hull and White (1990) and the Quadratic Interest Rate model. With respect to the Quadratic Interest Rate model we succeed in carrying the analysis much further than Jamshidian (1996). A special discrete time model – which in some cases is appropriate for the Quadratic Interest Rate model – is also derived.

The last part of the paper analyse Monte Carlo techniques in connection with spot-rate models with a time-dependent drift. We also introduce a method – using the concept of forward induction – that constrain the Monte Carlo simulated spot-rate process for the matching of the initial yield-curve. For the pricing of path-dependent contingent claim, we deduce that, even though Monte Carlo is the natural method to use, it might not be the most efficient one – at least not when the spot-rate is Markovian.

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