Relative Value in Clear Present Danger

Abstract

In this paper, we propose two simple models to price options on a pegged currency such as Argentine Peso (ARG) whose time evolution is almost exclusively a discrete jump process. The first model is a one-step binomial tree model which expresses any vanilla option as a linear combination of an at the money forward (ATMF) option, a cash position, as well as a bond denominated in local currency. As a result, any mis-pricing of the option on a relative basis can be arbitraged readily. In the second model, we extend the one-step binomial tree to a multi-step binomial tree and derive a pricing equation in the continuous time limit based on risk-neutral assumptions. In both models, we point out the existence of a crucial relation between the jump related parameters and the spread between the domestic and foreign interest rates as a consequence of no-arbitrage pricing.