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By taking the relevant expectations, the model yields a complete initial term structure for the continuum of maturities, endogenously interpolating between the observed data. Thus it is more parsimonious in its assumptions in the sense that there is no need for an exogenous interpolation rule and the interpolation is consistent with the assumed short rate dynamics. Furthermore, unlike Jamshidian (1995) and Scott (1995), their model retains the flexibility to fit an initial term structure of volatility by choosing the volatility parameters on the intervals accordingly. Having constructed the model in a single and a multifactor version, they provide solutions for options on zero coupon bonds and other fixed income derivatives, such as spread options. In addition, they characterize how the model interpolates interest rates, fitting it to actual swap market data. When considering a market where data is available for only a small number of maturities, such as the swap market, calculations remain simple enough to justify the label "closed form". For a very large number of initial data points their approach can be interpreted as a fast forward induction algorithm, and in contrast to other numerical methods such as Hull and White (1993), which also input only discrete points on the initial term structure, their method fits the inputs exactly, without numerical error.
π SIMILAR VOLUMES
In this article, the authors discuss mixed exponential distributions and, more generally, scale mixtures with specific consideration the purpose of insurance modeling. Results are derived for equilibrium distributions (defined via stop-loss transforms) of mixed distributions. Some recursive relation
Yushkevich can also be applied to certain models where control of the flow is possible. The method consists in a transformation to a model without control of the flow by a kind of time change.