A Benchmark Approach of Counterparty Credit Exposure of Bermudan Option under Lévy Process: The Monte Carlo-COS Method

Abstract

An advanced method, which we call Monte Carlo-COS method, is proposed for computing the counterparty credit exposure profile of Bermudan options under Lévy process. The different exposure profiles and exercise intensity under different mea- sures, P and Q, are discussed. Since the COS method [1] delivers accurate Bermudan prices, and no change of measure [2] needed to get the P-probability distribution, the exposure profile produced by the Monte Carlo-COS algorithm can be used as a benchmark result, E.g., to analyse the reliability of the popular American Monte Carlo method [3], [4], [5]. The efficient calculation of expected exposure (EE) [6] can be further applied to the computation of credit value adjustment (CVA) [6].