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

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.

Computational Finance

“…The authors find conditions for well-defined changes of measure and develop closed form expressions for two key characteristic functions, which allow for fast and efficient calculation of derivatives prices and risk measures and exposures, and they demonstrate numerically the significant impact of their model, both with respect to changes on the implied volatility surface and on two standard risk measures. Reesor and Marshall (2020) present a new numerical technique for pricing multiple exercise options by simulation referred to as the Forest of Stochastic Trees (FOST) method. The proposed method uses stochastic trees in place of binomial trees in the Forest of Trees algorithm originally proposed to value swing options and extends this algorithm to allow for a multi-dimensional underlying process.…”

“…This volume includes a wide variety of theoretical and empirical contributions that address a wide range of issues and topics related to computational finance. The published papers consider asset pricing in general with applications to bond pricing, see Dunne (2019), commodity modelling, see Cheng et al (2019), and derivatives pricing, see Létourneau and Stentoft (2019), Reesor and Marshall (2020) and Stentoft (2019); uses calibration techniques, see Van Dijk et al (2018); and considers issues related to hedging, see Dunne (2019). The published papers develop new multivariate models, see Cheng et al (2019), considers option pricing in this challenging setting, see Reesor and Marshall (2020), and addresses issues related to risk management, see Cheng et al (2019), Forsyth andVetzal (2019), andVan Dijk et al (2018).…”

“…The published papers consider asset pricing in general with applications to bond pricing, see Dunne (2019), commodity modelling, see Cheng et al (2019), and derivatives pricing, see Létourneau and Stentoft (2019), Reesor and Marshall (2020) and Stentoft (2019); uses calibration techniques, see Van Dijk et al (2018); and considers issues related to hedging, see Dunne (2019). The published papers develop new multivariate models, see Cheng et al (2019), considers option pricing in this challenging setting, see Reesor and Marshall (2020), and addresses issues related to risk management, see Cheng et al (2019), Forsyth andVetzal (2019), andVan Dijk et al (2018). The volume contains several papers that use simulation, see Dunne (2019), Létourneau and Stentoft (2019), Mukerji et al (2019), andStentoft (2019), and papers that provide new ways to model volatility, see Cheng et al (2019), and for estimating this, see Petrov et al (2019).…”