APPLYING THE WIENER-HOPF MONTE CARLO SIMULATION TECHNIQUE FOR LEVY PROCESSES TO PATH FUNCTIONALS

作者：Frreiro Castilla Albert^*; Van Schaik Kees

来源：Journal of Applied Probability, 2015, 52(1): 129-148.

DOI：10.1239/jap/1429282611

• Wiener-Hopf decomposition
• Monte Carlo simulation
• multilevel Monte Carlo
• Levy process
• exotic option pricing
• first passage time
• overshoot
• insurance risk process

In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Levy processes from Kuznetsov et al. (2011) to path functionals; in particular, first passage times, overshoots, undershoots, and the last maximum before the passage time. Such functionals have many applications, for instance, in finance (the pricing of exotic options in a Levy model) and insurance (ruin time, debt at ruin, and related quantities for a Levy insurance risk process). The technique works for any Levy process whose running infimum and supremum evaluated at an independent exponential time can be sampled from. This includes classic examples such as stable processes, subclasses of spectrally one-sided Levy processes, and large new families such as meromorphic Levy processes. Finally, we present some examples. A particular aspect that is illustrated is that the Wiener-Hopf Monte Carlo simulation technique (provided that it applies) performs much better at approximating first passage times than a 'plain' Monte Carlo simulation technique based on sampling increments of the Levy process.

• 出版日期2015-3