Coupon Bond Valuation with a Non-Affine Discount Yield Model
I report a closed form for the Laplace transform of the Ahn Gao (RFS, 1999) discount function and show how this can be used for pricing non-zero coupon bond prices, including hybrid fixed/variable rate instruments. In contrast, numerical techniques have to be used to analyse these prices for the standard affine yield specifications. I find that many of the characteristics of the Cox Ingersoll and Ross (JF, 1980) solutions extend to this more general non-affine specification. The allowance for mean reversion in the Ahn-Gao specification means that the solutions are hypergeometric rather than power functions, but the properties of these functions are nicely established, facilitating qualitative analysis. The prices of interest rate options can be backed out of these formulae by Laplace inversion, overcoming a major problem with the original Ahn and Gao (1999) valuation approach.
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