### Introduction

NAG together with Prof. Oosterlee and an MSc student from TU Delft are investigating the recent Stochastic Grid Bundling Method (SGBM) [1,2]. The objective is to compare the performance of SGBM to the well-known Longstaff-Schwartz (least squares method or LSM) in a non-academic setting, i.e. on the pricing of a Bermudan option, with underlying asset(s) driven by a realistic process such as Heston or LMM. We are looking for an interesting case to test these two methods. This includes the type of option, the underlying processes and any other important features or details.### Outline

The well known LSM by Longstaff-Schwartz[3] is the industry standard for pricing multi-dimensional Bermudan options by*simulation and regression*. LSM is based on the

*regression now*principle, whereas the Stochastic Grid Bundling Method (SGBM) by Jain and Oosterlee applies

*regression later*in order to get more accurate approximations. However, this limits us to apply SGBM to processes where an analytical or approximate expression of the discounted moments are available.

Another advantage of SGBM is its regression on

*bundles*instead of the whole data set in a further attempt to decrease the regression error, and SGBM allows the computation of the Greeks at almost no extra cost.

Numerical results show that, compared to LSM, a higher accuracy can be obtained at comparable computational time. However, these tests were performed on

*academic*problems, using geometric Brownian motion for the underlying assets.

Very recent research (Feng and Oosterlee, Sept 2014) extended SGBM for stochastic volatility and stochastic interest rate dynamics (Heston-Hull-White). This led to the possibility of comparing the performance of SGBM in a non-academic setting and is the cause for our research. We therefore wish to compare LSM and SGBM on a problem which is interesting and relevant to industry. Realistically, handling all the complexities of traded products will probably require more time than we have (around two months), so ideally we seek a problem which captures all the salient features and allowing us to see whether SGBM outperforms LSM.

### Industry Involvement

We would like some advice in defining the product to be valued, especially regarding dimensionality, process, correlation structure, payoff and exercise features. Any additional industry involvement will be light: perhaps a few emails to clarify details, a conf call or face to face meeting.For correspondence or further details please email support@nag.co.uk

#### References

[1] S. Jain and C. W. Oosterlee, "The Stochastic Grid Bundling Method: Efficient Pricing of Bermudan Options and their Greeks,'' papers, SSRN, Sept. 2013.[2] S. Jain and C. W. Oosterlee, "Pricing high-dimensional Bermudan options using the stochastic grid method,'' International Journal of Computer Mathematics, 89(9):1186-1211, 2012.

[3] F. Longstaff and E. Schwartz, "Valuing American Options by Simulation: a Simple Least-squares Approach,'' Review of Financial Studies, vol. 14, no. 1, pp. 113-147, 2001.