A Discrete Monitoring Method for Pricing Asian Interest Rate Options

Allan Silva, Jack Baczynskiy and José Vicente

No 409, Working Papers Series from Central Bank of Brazil, Research Department

Abstract: As determined by the BM&FBovespa standards, the ID index is built up discretely according to overnight DI rate. We addressed the IDI Call Option Pricing problem using this discretely compounded hypothesis in lieu of the continuous updated case found in the literature. Our method converges to the benchmark (which refers to the exact price considering the discretely compounded hypothesis). This is not possible for any short rate modeling framework which adopts IDI continuously compounded hypothesis. It is noteworthy that the benchmark prices as well as the prices under the discretely compounded hypothesis with a reasonable number of mesh points are always cheaper than those of the continuously compounded case. In addition, we introduced a general purpose version of a classical finite difference scheme which provides an spurious oscillation free solution of the PDE to obtain an approximate price of the option.

Date: 2015-11
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