Entropía relativa y cobertura de derivados

Abstract

The goal of this thesis is to analyze and apply the concept of Entropy to the valuation and hedging of derivative financial instruments issued on equities. More specifically, it develops a methodology based on the lowest relative Entropy to solve the problem of valuation and, above all, hedging of a type of exotic equity option called Cliquets. In an informal manner, financial valuation target is to obtain the value in monetary units of assets whose purpose is the investment or the financing. These assets are defined as financial instruments, and the locations and mechanisms by which are exchanged is called financial markets. On the other hand, a financial derivative are those instruments whose price depends on, this is, it derives of another variable, this variable is called the underlying, and can be very diverse nature and typology, the vast majority belong to the financial sphere. By way of illustration, we can make a small classification, according to Hull (2003), with the main categories of underlying: i. Financial Assets equity shares of companies, stock indices, etc. ii. Exchange Rate iii. Commodities: oil gas, copper, etc. iv. Financial assets in fixed income: bonds, deposits, etc. v. Other: credit, temperature, sports betting, … The valuation of financial instruments is done via two methodologies: i. Absolute Valuation ii. Relative Valuation In a simplified manner, absolute valuation is based on taking into consideration all the cash flows associated with the instrument...