Options bonds

Exo-nido metallacarbaborane complexes are at present comparatively rare, but are nevertheless a clear bonding option by which a number of metal-ligand fragments may interact with a C2B9 cage system. However, the species 62 are singled out from all other known examples by having... 

The last bond network in Figure 3.7 illustrates the only localized bond option open to a tervalent atom required to bond to six neighbors, which it can do only by use of three 3c-2e bonds. Not surprisingly, carbon atoms are not normally found in connectivity six sites in carboranes. The only such site among infraicosahedral closo dicarbaboranes, the unique site in C2B9H11, is... 

A single bond is the basic bond created by DRAW, RING (and the item GROUP not yet considered). The BOND option allows the user to select a bond type from the BOND sub-menu and change the nature of any explicit, non-aromatic bond in the structure to the selected type. The endpoints of the bond to be altered are accessed by the mouse after a bond type has been selected. A dotted bond type can be used for limited description of stereo arrangement. A bond-erase feature is built into the sub-menu and is obtained by selecting bond-type zero. Examples of the different bond-types appear in Figure 1. 

Cox, Ingersoll and Ross [22] and Jamshidian [42] demonstrate that closed-form solutions for zero-coupon bond options can be derived for single-factor square root and Gaussian models. More generally, Duffie, Pan and Singleton... 

We overcome this inconsistency, by deriving a unified framework that directly leads to consistent cap/floor and swaption prices. Thus, in general we start from a HJM-like framework. This framework includes the traditional HIM model as well as an extended approach, where the forward rates are driven by multiple Random Fields. Furthermore, even in the case of a multifactor unspanned stochastic volatility (USV) model we are able to compute the bond option prices very accurately. First, we make an exponential affine guess for the solution of an expectation, which is comparable to the solu-... 

In chapter (2), we derive a unified framework for the computation of the price of an option on a zero-coupon bond and a coupon bond by applying the well known Fourier inversion scheme. Therefore, we introduce the transform t (z), which later on can be seen as a characteristic function. In case of zero-coupon bond options we are able to find a closed-form solution for the transform t z) and apply standard Fourier inversion techniques. Unfortunately, assuming a multi-factor framework there exists no closed-form solution of the characteristic function Et z) given a coupon bond option. Hence, in this case Fourier inversion techniques fail. 

In chapter (6), we extend the traditional HJM approach, by assuming that the sources of uncertainty are driven by Random Fields. For that reason, we introduce a non-differentiable Random Field (RF) and an equivalent T-differentiable counterpart. Given the particular Random Field, we derive the corresponding short rate model and show in contrast to Santa-Clara and Sor-nette [67] and Goldstein [33] that only a T-differentiable RF leads to admissible well-defined short rate dynamics". Santa-Clara and Sornette [67] argue that there is no empirical evidence for a T-differentiable RF. We conclude that the existence of some pre-defined short rate dynamics enforces the usage of a r-differentiable RF. Furthermore, we compute bond option prices when... 

Eberlein and Kluge [29] find a closed-form solution for swaptions using a L6vy term stnicture model. A solution for bond options assuming a one-factor model has been derived by Jamishidian [42]. 

Furthermore, we want to be consistent with our lEE approach, where the price of the coupon-bond options can only be computed by summing over the single exercise probabilities Up [AT]... 

In the following we use the term swaption and option on a coupon bond option interchangeably. Nevertheless, keeping in mind that a swaption is only one special case of an option on a coupon bond. 

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