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Regression methods for pricing complex American-style options
1Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
IEEE Transactions on Neural Networks
|February 6, 2008
Summary
This study presents a simulation-based dynamic programming method for pricing complex American-style options. Choosing representative states via risk-neutral simulation bounds approximation error, unlike arbitrary state selection.
Area of Science:
- Quantitative Finance
- Computational Finance
- Numerical Methods
Background:
- Pricing complex American-style options is challenging due to high-dimensional state spaces.
- Approximate dynamic programming offers a potential solution for such complex financial instruments.
Purpose of the Study:
- To introduce and analyze a novel simulation-based approximate dynamic programming method for pricing American-style options.
- To investigate the impact of state space dimensionality and representative state selection on approximation error.
Main Methods:
- Developed a simulation-based approximate dynamic programming approach within a finitely parameterized family of value functions.
- Introduced a variant of value iteration adapted for parametric settings and a single time-state pair value function.
- Evaluated value functions using finite sets of representative state space elements.
Main Results:
- Arbitrary selection of representative states can lead to exponentially growing approximation errors with the time horizon.
- Simulating the state process using risk-neutral probability distributions to select representative states bounds the approximation error.
Conclusions:
- The proposed simulation-based approximate dynamic programming method provides a viable approach for pricing complex American-style options.
- Risk-neutral simulation for representative state selection is crucial for controlling approximation error in high-dimensional settings.
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