Finding the option-implied country risk of Brazil

Pinto, Afonso de Campos
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The theoretical models for option pricing need the assumption that the volatility for the underlying security is constant for a specific tenor. But, in the market, we see a different implied volatility for each Strike in the same tenor, forming what is called a Smile. The fact that the volatility is curved, instead of a straight line, shows that the market assumes a credit risk in the underlying security. In this way, this work tries to extract the credit risk in a volatility Smile of a FX rate. So, the credit risk is actually the country risk. Using the article Option Pricing When Underlying Stock Returns Are Discontinuous, from Merton (1976), we adapted the model for the FX Rate instead of a stock. Also, we are interested in a specific case of discontinuous returns, the Jump to Default model, in which the underlying security value goes to zero (a negative return of 100%). If a currency has such a negative return, it means a default of the country that issues that currency.

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