An Arrow Debreu implementation of the recovery theorem
KeywordsArrow - Debreu model ; Risks ; Arbitrage free ; Transition independence ; MATLAB ; Markov processes
Ross recovery is an option pricing model. The recovery theorem is a tool developed by Ross to determine the predictive content of market prices. It is an option pricing method similar but different to Black - Scholes. Ross recovery enables the investors to disentangle the future return distribution and pricing kernel from option prices which are in the Arrow Debreu environment and thus, option prices become state prices. Moreover, Arrow and Debreu model is the central model of General Equilibrium Theory where state prices use the sense of numeraire. The combination of these two models occurs under specific assumptions. More specifically, under the existence of a Markov process, a transition independence, an irreducible pricing matrix, no arbitrage, complete markets and discrete time. In this thesis, firstly we present a historical review of the Arrow & Debreu model and its connections with the asset pricing theory. Secondly, we also present a historical review of the recovery theorem by Ross and criticize its extensions. As an empirical formulation of this theorem, we construct the transition state price matrix through a snapshot of option prices on the stock index FTSE/JSE Top 40, using least–squared minimization techniques subject to constraints in Matlab programming. According to Ross recovery theorem this matrix entails the knowledge of the real world probabilities matrix.