Patricia Saavedra, Begoña Fernández
The Banxico Option was created by the Central Bank of Mexico to increase its international reserves without affecting its exchange rate. This option has the following characteristics: i). The option is sold through a public auction among the Mexican banks the last day of each month. ii). The option gives the right to the banks to sell a fixed amount of dollars in one or several transactions in any trading day of the following month. iii) The strike price is the fix price of the dollar the day before the date of exercise. The fix price is determined by the market and is published once a day by the Central Bank. iv) In order to buy dollars when the market is offering the Central bank imposes an additional restriction for exercise: The strike price must be less or equal than the average price of the fix during the last twenty days before the date of exercise.
This is an exotic option whose strike price is stochastic and depends on the path of the fix price.
The purpose of the poster is to present the results we obtained in the study of the valuation and the optimal time of exercise of the Banxico Option with and without the iv restriction. The binomial and the Black-Scholes models are considered. We apply the poinbt of view of the Dynamical Programming Principle and the Optimal Stopping Time Theorem. With these results we propose a rule of exercise for the Banxico option that let us valuate the option via a Monte-Carlo method. Numerical results are presented.