BICs 4 Derivatives

Vol II: Applications

Summary:

Volume II is also subdivided into 5 modules and 12 chapters with a section of appendices.

Module I, Chapters I-V describe in detail the BICs derived pricing algorithms for a variety of Derivatives contracts of interest to the Professional and Academic community. Indeed the unique appeal of these algorithms is their model independent nature. Chapter II is particularly interesting as it deals with the pricing of CMOs that caused quite some stir in the Financial Derivatives community when it was learned that Columbia University patented a Sobol Low Discrepancy sequence to price them, patents US 5,940,810 and US 6,058,377. Our analysis shows how the BICs approach allows faster, easier and more flexible algorithms without any low discrepancy analysis. Chapter III provides a treatment of American options and Hawaiian options that does not depend on the choice of model assumptions. We show how the optimal exercise conditions derived for these contracts and for the generalized passport option in chapter IV are robust to model specification using elementary mathematics. In chapter V, we provide a detailed treatment of moments based derivatives. This generic term comprises but is not limited to volatility/variance swaps and options. It also comprises skew/kurtosis swaps and options as well as correlation swaps and options. The development of such algorithms offers a unique opportunity for the rapid expansion of contracts taking advantage of empirically documented features of these moments.

In Module II, we develop in chapter VI an independent theory of interpolation. This may constitute a separate mathematical subject on its own. We view it as a critical general mathematical innovation. It is linked to this module mainly because in many derivatives calibration problems, the first step is interpolation or as one leading practitioner puts it: "Options theory is an ingenious but glorified method of interpolation"

In chapter VII, we study in the context of BICs, the classical Dupire-Derman-Rubinstein problem of deriving local volatilities under the historical assumptions. We see how we can rigorously obtain the local volatilities can in the discrete time/space framework without resorting to the Fokker Plank equations or any other theorem. In the same spirit, we show how to derive the local volatilities also in an Andersen-like calibration framework with jumps. From there we see how to generalize to other relevant yet non- classical scenarios.

In Chapter VIII, we study the case where we do not have BICs prices constituting a BIC basis available, but a collection of related derivatives contracts. We show how one optimally derives hedges under such conditions using the available instruments. We also develop metrics for measuring the effectiveness of a hedge and obtain relevant critical general formulas.

In chapter IX, we establish new closed form portfolio allocations with mean variance data and constrained allocations requirements. Despite these problems having been specified for over 50 years now, this is, to the best of our knowledge, the first closed form solutions proposed. The BICs framework further allows us to use these results for derivatives portfolio optimization in the most general sense quite easily.

Chapter X further shows the applicability of the earlier results for general risk management and in particular coherent VAR analysis, portfolio optimization under VAR constraints, while showing via BICs how one can appraise VAR defects.

In chapter XI, we review FAS 133, its extensions and the international correspondent IAS 39 and show the metrics of chapter VIII are particularly well suited for transparent compliance.

In chapter XII, we review the emerging systems architectures the advent of BICs is likely to facilitate. We look in detail at pricing or decision systems, risk management systems and exchange or trading systems.