Abstract
The recently proposed canonical least-squares Monte Carlo (CLM) method is extended by incorporating uniquely a variance constraint in the derivation of the equivalent martingale measure used by CLM. This derivation can be viewed as a change of measure numerically by modifying both the drift term and the volatility term of the underlying stochastic process, for which the analytic form is not explicitly given or assumed. The extended method will be called the variance-constrained CLM (vCLM). In practice, the forward variance used in the pricing of an option is set to be the square of the volatility implied by vCLM at the market price of the option from a previous trading day. With a data set of 16419 put prices for the American-style S&P 100 Index options, vCLM is found to produce an average absolute pricing error of only 5.95%, easily outperforming many competing approaches.
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