By Detlef Repplinger
RWT Award 2008!
For his first-class monograph, Detlef Repplinger received the RWT Reutlinger Wirtschaftstreuhand GMBH award in June 2008.
A significant subject matter of this ebook is the advance of a constant unified version framework for the overview of bond concepts. ordinarily strategies on 0 bonds (e.g. caps) and suggestions on coupon bearing bonds (e.g. swaptions) are associated by way of no-arbitrage relatives throughout the correlation constitution of rates of interest. as a result, unspanned stochastic volatility (USV) in addition to Random box (RF) types are used to version the dynamics of complete yield curves. The USV versions postulate a correlation among the bond expense dynamics and the subordinated stochastic volatility method, while Random box types enable for a deterministic correlation constitution among bond costs of other phrases. Then the pricing of bond suggestions is finished both via working a Fractional Fourier remodel or by means of employing the built-in Edgeworth enlargement method. The latter is a brand new extension of a generalized sequence enlargement of the (log) attribute functionality, specially tailored for the computation of workout probabilities.
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Additional resources for Pricing of Bond Options: Unspanned Stochastic Volatility and Random Field Models
1)) is exact in the sense that the Taylor expansion is valid for inﬁnity terms. Hence, the generalized EE is an equivalent expression for the pdf (cdf). 3 The approximation of a lognormal-pdf 25 2 -pdf Fig. 3 Approximation error running an EE of a χ30 ing an EE for the approximation of a lognormal-like pdf requires that the single terms of the series expansion converges. Hence, in comparison to the approximation of the χv2 -pdf we have to overcome an additional constraint. Unfortunately, as we have seen in the last section, the accuracy of the approximation mainly depends on the number of terms M used for the series expansion.
2 Pricing of zero-coupon bond options 45 ϒt (z) = EtT0 ezX(T0 ,T1 ) . 11) Hence, the ability to derive a closed-form of Θt (z) crucially depends on the ability to ﬁnd a solution for the transform ϒt (z). 1 The closed-form solution Now, by applying the Fourier inversion technique we derive the well known formula for the price of an option on a discount bond. 12) = ezX(t)+A(t,z) given the new random variable X(t) = log P (t, T1 ) . 9) we obtain the dynamics of the new variable X(t) as follows d X(t) = dX (t, T1 ) − dX (t, T0 ) =− 1 N ∑ σ0i − σ1i 2 i=1 2 N dt + ∑ σ0i − σ1i dwTi 0 .
Lim b→∞ 0 z∗2 2 dz∗ . g. Abramowitz and Stegun , p. 787 l (n + 2l)!. 32 4 The Integrated Edgeworth Expansion This implies that the above integral equation is well-deﬁned. Furthermore, we can rewrite the integral over the Hermite polynomial Hn+2l (z∗ ) as follows s ∗2 e−z Hn+2l (z∗) dz∗ = Hn+2l−1 (0) − e−s Hn+2l−1 (s) , 2 0 and hereby obtain a closed-form solution for the integral √b 2 √b 2 ∗2 ∗2 e−z Hn+2l (z∗ ) dz∗ = lim lim b→∞ K √ 2 ∗2 e−z Hn+2l (z∗ ) dz∗ − e−z Hn+2l (z∗ ) dz∗ b→∞ 0 K √ 2 0 K2 = e− 2 Hn+2l−1 K √ .
Pricing of Bond Options: Unspanned Stochastic Volatility and Random Field Models by Detlef Repplinger