Pricing TARNs Using a Finite Difference Method

Abstract

Target accumulation redemption notes (TARNs) are a popular product with Asian foreign exchange investors. They have a number of variations, but their main feature is that option-like payoffs occur on a set of future dates, depending on whether the underlying exchange rate is above or below a specified strike level. The total payout is capped and the contract expires when the cap is reached. The standard valuation technique for this path-dependent payoff is Monte Carlo simulation. In this article, Luo and Shevchenko develop an efficient finite-difference approximation that accommodates path dependence and even non-diffusive jumps in the exchange rate. In a comparison simulation against Monte Carlo, the new technique achieves much better accuracy in less execution time.