Estimators of sensitivities of an Asian option: numerical analysis

Abstract

In this paper, we investigate three methods for computing price sensitivities (or greeks) of an Asian option, namely, finite difference methods, a likelihood ratio method, and a pathwise method and we analyze the outputs. The efficiency of results is evaluated by means of Monte Carlo with and without, variance reduction technique.

Sensitivities of Asian options in the Black-Scholes model

“…Numerical tests. We compare in this Section the analytical approximations for the Greeks of the Asian options against numerical results obtained using alternative implementations from Moussi et al (2014); Chatterjee et al (2017); Boyle & Potapchik (2008).…”

“…Scenario 1. One first scenario was considered by Moussi et al (2014), see Table 3 in this paper. These authors use the following scenario (32) r = 0.1 , K = 100 , σ = 0.25 , T = 0.5 .…”

“…(2014) using three different methods: finite differences (FD), pathwise (PW) and likelihood method (Lkhd). For each sensitivity we show the three results from Table 3 of Moussi et al (2014), and the short maturity approximations given above.…”

“…Numerical results for the Greeks of a call Asian option under the scenario (32) and the shown values of S 0 , from Table3ofMoussi et al (2014). The first three rows give the finite difference (FD), pathwise (PW) and likelihood (Lkhd) methods ofMoussi et al (2014). The last rows give the short maturity approximations for the sensitivities of this paper.…”