Temporary Stabilization and the Real Option of Waiting when Consumption can be Delayed: an Extreme Value Approach

This paper develops, in a small open economy framework, a stochastic model of exchange-rate-based inflation stabilization that is expected to be temporary. Agents have expectations of devaluation driven by a mixed diffusion-jump process where the expected size of a possible devaluation is supposed to have an extreme value distribution of the Fréchet type; as the stylized facts from the Mexican's 1994 and Argentinean's 2001 cases have show n. Consumption and wealth equilibrium dynamics are examined when a stabilization plan is implemented. The case of a stochastic stabilization horizon guided by an exponential distribution is studied. Moreover, this paper also deals with pricing the real option of waiting for postponing consumption when a stabilization plan is about to be abandoned; a claim on a non-traded asset. We also assess the effects of exogenous shocks on consumption and economic welfare. Finally, we use the proposed model to carry out simulation experiments that reproduces the booms of private consumption in the Mexican case of 1989-1994 and the Argentinean case of 2001-2003, which resulted in extreme devaluations.Inflation stabilization, Contingent claims, Extreme values

On Consumption, Investment and Risk

The Mexican episode of 1992-1994 was characterized by a steep rise in consumption accompanied by a sharp fall in investment. This paper provides an explanation of the negative response of investment to political risk, as occurred in Mexico between 1992 and 1994. It is assumed that, inside an adjustable band, the expected rate of depreciation is driven by a mixed diffusion-jump process and the expected real rate of return on an international bond is governed by a diffusion process, both processes being correlated. This paper analyzes a small open stochastic economy. Two cases are considered: i) a cash-in-advance, Ramsey-type economy, and ii) a Sidrauski-type economy.

Pricing Derivatives Securities with Prior Information on Long- Memory Volatility

This paper investigates the existence of long memory in the volatility of the Mexican stock market. We use a stochastic volatility (SV) model to derive statistical test for changes in volatility. In this case, estimation is carried out through the Kalman filter (KF) and the improved quasi-maximum likelihood (IQML). We also test for both persistence and long memory by using a long-memory stochastic volatility (LMSV) model, constructed by including an autoregressive fractionally integrated moving average (ARFIMA) process in a stochastic volatility scheme. Under this framework, we work up maximum likelihood spectral estimators and bootstraped confidence intervals. In the light of the empirical findings, we develop a Bayesian model for pricing derivative securities with prior information on long-memory volatility.contingent pricing, econometric modeling

Política fiscal, estabilización de precios y mercado incompletos

This paper develops a stochastic model of temporary stabilization of prices with the exchange rate acting as a nominal anchor of inflation. The model presents imperfect credibility, and explicitly recognizes the uncertainty in the dynamics of the exchange rate and in the expected behaviour of fiscal policy. It is assumed that a mixed diffusion-jump stochastic process drives the exchange rate. Also, the model supposes that the tax rate on wealth follows a geometric Brownian motion. Under this framework, it is assumed that a derivatives market to hedge against future devaluation does not exist, that is, financial markets are incomplete. Consumption and portfolio decisions of a representative consumer, in equilibrium, are examined when the stabilization plan is implemented and fiscal policy is uncertain. Finally, the effects of exogenous shocks in the exchange-rate policy and economic welfare are assessed.

Opciones, cobertura y procesos de difusión con saltos: Una aplicación a los títulos de Gcarso

We present two models for hedging European options on an underlying asset driven by a mixed diffusion-jump process. The first model, values the option as the average of option prices hedging sequential jumps. In the second model, the option price is determined by minimizing the variance of the portfolio value. In particular, we develop hedging strategies for the case of GCARSO shares

Cobertura de flujos financieros con instrumentos de renta fija

In this paper, we develop a stochastic model to hedge the present value of cash flows against interest-rate risk with fixed-income products, in particular, with zero coupon bonds. In our approach, the dynamics of the interest rate is driven by a mean-reverting stochastic diffusion process. The model stresses the concepts of money duration and money convexity in interest-rate risk management. An application is addressed, by way of illustration, to generate hedging strategies with zero coupon bonds when the term structure of the interest rate is driven by the Vasicek's (1977) model.

The Valuation of Mortgage Backed Securities with Stochastic Probabilities of Default and Prepayment

The aim of this paper is to provide a new approach to project the Mortgage Backed Securities (MBS) cash flows in emerging markets where collateral information is limited, wrong or scarce. Under this framework, we use the Cox Process to model stochastic probabilities of prepayment and default. The model deals with general intensity dynamics and is applied to the starting MBS Mexican market.Mortgage valuation, MBS prepayment, MBS default, MBS curtailment, Cox Process.

El modelo de Vasicek y la integral de trayectoria de Feynman

The aim of this paper is to show the convenience of using mathematical tools from quantum mechanics to solve some financial problems. In particular, the Vasicek short-rate model in continuous time is discussed in the framework of the Feynman path integral. To do this, the Lagrangian of the system is obtained from the Hamiltonian associate to the backward Fokker-Planck equation. Subsequently, the action is calculated to obtain the price of a zero-coupon bond and its forward rate. In conclusion, the paper attempts to show that quantum mechanics is an effective alternative in solving some complex problems that arise in pricing derivatives.Productos derivados

Sobre la convergencia del modelo GARCH(1,1)-M al movimiento geométrico browniano con reversión a la media

This paper shows, under certain conditions, the convergence of the GARCH (1.1)-M model to the geometric Brownian motion with mean reversion (diffusion GARCH process). The importance from this result is that the problem of inference on the parameters of the valuation models of options with stochastic volatility can be reduced by estimating the model GARCH (1.1)-M. It is also carried out a discussion on the assumptions that ensure the existence and uniqueness of the limit process. Finally, it is provided a quick demonstration of the convergence, which is less formal, but more intuitive and easy to remember.Convergencia de procesos estocásticos, valuación de derivados, volatilidad estocástica

Valuación de opciones arcoíris sobre canastas de activos bajo procesos de difusión con saltos

ResumenEn este trabajo se estudia la valuación de opciones sobre el máximo o el mínimo (precio o rendimiento) de 2 activos riesgosos, conocidas como opciones arcoíris. Se extiende la valuación de estos contratos al caso en que los activos presentan difusiones combinadas con saltos. Los parámetros de los procesos de saltos son estocásticos, y específicamente el tamaño del salto sigue una distribución normal, lo cual hace necesario recurrir a los procesos de Lévy. Se desarrolla una metodología numérica con MATLAB para valuar una opción cesta (o canasta) de venta, y un put sobre el máximo y en el mínimo de 2 activos riesgosos; los resultados se pueden extender para el caso de n activos.AbstractThis paper studies the pricing of options on the maximum or minimum (price or return) of two risky assets, known as rainbow options. It extends the valuation of these contracts to the case where assets are driven by diffusions combined with jumps. The parameters of the jump process are stochastic, specifically the jump size follows a Normal distribution, making it necessary to resort to Lévy processes. A numerical methodology is developed with MATLAB to provided the price of a basket sale option, and put on the maximum and the minimum of two risky assets; the results can be extended to the case of n assets