*Article* **Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options**

**R. Mark Reesor 1,\* and T. James Marshall 2**


Received: 31 August 2019; Accepted: 3 May 2020; Published: 13 May 2020

**Abstract:** We present the Forest of Stochastic Trees (FOST) method for pricing multiple exercise options by simulation. The proposed method uses stochastic trees in place of binomial trees in the Forest of Trees algorithm originally proposed to value swing options, hence extending that method to allow for a multi-dimensional underlying process. The FOST can also be viewed as extending the stochastic tree method for valuing (single exercise) American-style options to multiple exercise options. The proposed valuation method results in positively- and negatively-biased estimators for the true option value. We prove the sign of the estimator bias and show that these estimators are consistent for the true option value. This method is of particular use in cases where there is potentially a large number of assets underlying the contract and/or the underlying price process depends on multiple risk factors. Numerical results are presented to illustrate the method.

**Keywords:** Monte Carlo; multiple exercise options; dynamic programming; stochastic optimal control
