Option pricing and Greeks via a moving least square meshfree method

Abstract

We apply a meshfree method using the fast moving least squares approximation to option pricing, particularly for the purpose of obtaining high-order Greeks. The method is shown to be accurate and efficient in obtaining prices and Greeks of European, Asian and Barrier options. We also include a complicated Equity Linked Security (ELS) from the Korean OTC market, as a real-world example.

Keywords:

• Asian option
• Barrier option
• Black–Scholes equation
• ELS
• FMLS
• European option
• Greeks
• meshfree method
• MPCM

JEL Classification:

• C63
• G12

Acknowledgments

The authors thank the referees for careful reading and helpful comments. This research was supported by World Class University programme through the National Research Foundation(NRF) of Korea funded by the Ministry of Education, Science and Technology (R31-2009-000-20007-0), and Ajou University Research Fellowship of 2007–2009. The first author was supported by (NRF-2011-0011855).

Notes

¹It is possible to obtain Asian option prices by the finite difference method using the model of Vecer (2001). However, we study the Rogers–Shi model which allows distinction between our MPCM and the finite difference method.