In the "positive interest" models of Flesaker and Hughston , the nominal discount bond system is determined by the specification of a one-parameter family of positive martingales. In the present paper we extend this analysis to include a variety of distributions for the martingale family, parameterised by a function that determines the behaviour of the market risk premium. These distributions include jump and diffusion characteristics that generate various interesting properties for discount bond returns. For example, one can generate skewness and excess kurtosis in the bond returns by choosing the martingale family to be given by (a) exponential gamma processes, or (b) exponential variance gamma processes. The models are "rational" in the sense that the discount bond price is given by the ratio of a pair of weighted sums of positive martingales. Our findings lead to semi-analytical formulae for the prices of European options on discount bonds  .
In the "positive interest" models of Flesaker-Hughston , the nominal discount bond system is determined by a one-parameter family of positive martingales. In the present paper we extend this analysis to include a variety of distributions for the martingale family, parameterised by a function that determines the behaviour of the market risk premium. These distributions include jump and diffusion characteristics that generate various properties for discount bond returns. For example, one can generate skewness and excess kurtosis in the bond returns by choosing the martingale family to be given by (a) exponential gamma processes, or (b) exponential variance gamma processes. The models are "rational" in the sense that the discount bond price is given by a ratio of weighted sums of positive martingales. Our findings lead to semi-analytical formulae for the prices of options on discount bonds . A number of general results concerning L\'evy interest rate models are presented as well .
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Flesaker and Hughston
Flesaker-Hughston
D
the specification of
D
interesting
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the ratio of a pair of
a ratio of
D
European
A
. A number of general results concerning L\'evy interest rate models are presented as well