# Monte Carlo Option Pricing: Averaging Price Per Path

In Glasserman's book, he computes the price of an option by first computing the average price over each simulated price path. Once all the paths have been simulated, the average of all the payoffs is computed using the average price of each simulated path.

In the finance courses I have taken, the algorithm I have been taught is to compute all the simulated price paths, work out the payoff of each path and then take the average payoff which is then discounted.

Glasserman's algorithm involves more computation steps since for each price path I have to compute this average price. Why does Glasserman take this approach? Also if there is anybody working in the industry, what algorithm is actually taken to pricing vanilla options i.e. does industry follow the textbook approach or do they apply any other optimisation techniques?

• I don't remember this part of the book explicitly but isn't it to avoid memory issues? When you incrementally compute the average payoff each time you simulate a new path, you can free the memory after each step, while the second approach requires storing each path and computing the average only after each one has been simulated. In other words, Glasserman's approach can work with thousands of millions of simulations, while on most work stations the second method would fail (not enough memory). – Quantuple Mar 29 '16 at 9:17
• @Quantuple, fair point - Glasserman's method does have that advantage. – user16556 Mar 29 '16 at 9:23
• @Quantuple I think Quantuple has answer it perfectly. His comment should be an answer. – SmallChess Mar 29 '16 at 11:55
• @Student T I have reformulated my comment as an answer. Thanks – Quantuple Mar 29 '16 at 12:35