SumBSM-R

The set of R codes used for the numerical examples of the "Sum of all Black-Scholes-Merton models" paper by Jaehyuk Choi (@jaehyukchoi).

Paper Information

Title

Sum of all Black-Scholes-Merton models: An efficient pricing method for spread, basket, and Asian options

Abstract

Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the basket, spread, and Asian options. The option price is expressed as a quadrature integration of analytic multi-asset BSM prices under a single Brownian motion. Then the state space is rotated in such a way that the quadrature requires much coarser nodes than it would otherwise or low varying dimensions are reduced. The accuracy and efficiency of the method is illustrated through various numerical experiments.

Links

DOI | arXiv | SSRN. (arXiv is recommended for free download of the latest version.)

Files

• SumBSM/blksmd.R: Functions for pricing. Two main interface functions are
  • blksmd_basket: basket or spread options
  • blksmd_asian: Asian options
• SumBSM/Table_04.R: Table 4. Parmeter set S1 (spread option)
• SumBSM/Table_05.R: Table 5. Parmeter set S2 (spread option)
• SumBSM/Table_06_07_08.R: Table 6~8. Parmeter set B1 (basket option)
• SumBSM/Table_09.R: Table 9. Parmeter set B2 (basket option)
• SumBSM/Table_10.R: Table 10. Parmeter set A1 (discretely monitored Asian option)
• SumBSM/Table_11.R: Table 11. Parmeter set A2 (discretely monitored Asian option)
• SumBSM/Table_12.R: Table 12. Parmeter set A3 (continuously monitored Asian option)

Citation

Choi, J. (2018). Sum of all Black-Scholes-Merton models: An efficient pricing method for spread, basket, and Asian options. Journal of Futures Markets, 38(6), 627–644. https://doi.org/10.1002/fut.21909