PRICES AND SENSITIVITIES OF BARRIER AND FIRST-TOUCHDIGITAL OPTIONS IN LEVY-DRIVEN MODELS

摘要

We present a fast and accurate FFT-based method of computing the prices and sensitiv-ities of barrier options and first-touch digital options on stocks whose log-price follows aLevy process. The numerical results obtained via our approach are demonstrated to bein good agreement with the results obtained using other (sometimes fundamentally dif-ferent) approaches that exist in the literature. However, our method is computationallymuch faster (often, dozens of times faster). Moreover, our technique has the advantagethat its application does not entail a detailed analysis of the underlying Levy process: oneonly needs an explicit analytic formula for the characteristic exponent of the process.Thus our algorithm is very easy to implement in practice. Finally, our method yieldsaccurate results for a wide range of values of the spot price, including those that arevery close to the barrier, regardless of whether the maturity period of the option is longor short.