By Detlef Repplinger

ISBN-10: 3540707212

ISBN-13: 9783540707219

**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**

**Example text**

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 [1], 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

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