Stratified Sampling for Monte Carlo Asian Option Pricing

Summary

The document asks how to apply stratified sampling, a variance reduction technique, when pricing Asian options by Monte Carlo simulation. It contrasts stratifying the terminal Brownian motion value for a European option with stratifying the average of Brownian motion values at the Asian option’s observation times.

It gives no proposed algorithm, derivation, simulation results, or resource that resolves the question. The key methodological issue is how to construct strata for a path-dependent average rather than a single terminal value. Any implementation would need to account for the dependence among observations along the Brownian path; the document itself does not explain how to do so.

Key ideas

• Stratified sampling is raised as a variance reduction method for Monte Carlo pricing.
• The question concerns adapting a terminal-value method for European options to an average used in Asian options.
• The sampled Brownian motion values at different observation times are dependent.
• The document does not provide an implementation, evidence, or a solution.

Tags

# Stratified sampling in asian options


# Stratified sampling in asian options












I am using the procedure of stratified sampling for variance reduction. In the Glasserman book the algorithm for stratified the terminal value of the Brownian motion is given for european options. For asian options he has written to stratify the average of brownian motions : $ W(t_1), W(t_2) ... W(t_m) $

But i cannot figure out how to exactly go about doing this. Any resource for this specific problem would be highly helpful.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.