BICs 4 Derivatives

Vol I: Theory

Summary:

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

Chapter I provides in plain English a multi-disciplinary and financial derivatives perspective on the case for BICs. Chapter II further sets the case for BICs and gets into more technical mathematical details of the prior art and reviews very specifically the related derivatives literature starting from Arrow Debreu through the Black Scholes analysis, the Harison-Kreps-Pliska fundamental theorems and the recent literature on derivatives spanning. It reviews the treatment of market microstructure, hedging practices with Greeks and the incomplete market hedging approach via error minimization and their shortcomings. This allows us to expose further the context of practical issues dealt with in volume II: portfolio hedging, Risk management, VAR, Derivatives accounting.

Chapter III reviews the previous attempts at defining derivatives and their shortcomings and proposes the new definition that will provide effective in our subsequent treatment. It also proposes the algebraic lexicon for their treatment. We provide numerous pedagogical examples to illustrate our description.

Chapter IV defines BICs in detail. BICs formats, Arrow Debreu BICs, Options BICs, and Fourier BICs enter into our language. We show how to decompose Derivatives into BICs. We redefine Arbitrage and Completeness. In Chapter V, we establish how all this works in a multi-period market, either for derivatives decomposition or pricing.

Chapter VI starts our market microstructure investigation by first considering the case of a price taker that sees a bid and offer prices for all derivatives contract. Properties of the bid and offer are established. We prove a fundamental theorem of asset pricing (FTAP) in this context. We establish a very important "Coase" type theorem that shows the dependence of Derivatives prices on the composing BIC basis. We further establish very important quantitative estimates.

Chapter VII continues our market microstructure investigation by now considering the position of a single market maker that must quote arbitrage free BICs. We establish another FTAP in this context. Then we look at the case of multiple market makers quoting BICs and establish another set of results.

In Chapter VIII, we round the set of practical issues to one must take into account including counterparty credit risk, and other legal and operational issues.

Module III should be of very important interest to transaction cost economists and the New Institutional Economics School .

Chapter IX looks at a surprising theoretical application that essentially makes the use of copulas for distributional linkage redundant and limited in scope. This is a very important mathematical result on its own. Chapter X shows how Levy processes are particularly well suited for derivatives pricing using the Fourier BIC set format introduced in chapter IV.

Chapter XI and XII deal at a theoretical level with the computational issues associated with the use of BICs. We describe the tools with which a priori complexity becomes actually very tractable.