We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.
Physica A Statistical Mechanics and its Applications
- Pub Date:
- February 2010
- Quantitative Finance - Pricing of Securities;
- Quantitative Finance - Computational Finance
- 13 pages, 3 figures, updated version has added references to path integral literature