# Stochastic Modeling for SET50 Index in Thailand Using the Black-Scholes Model with A Time-Dependent Drift Parameter and Its Application to SET50 Futures Pricing

## Authors

• Sanae Rujivan School of Science, Walailak University
• Parawee Hongsai Department of Mathematics, Faculty of Science, Kasetsart University
• Montri Maleewong Department of Mathematics, Faculty of Science, Kasetsart University
• Udomsak Rakwongwan Department of Mathematics, Faculty of Science, Kasetsart University
• Chayaphon Boonchot Division of Mathematics and Statistics, School of Science, Walailak University

## Keywords:

SET50 Index, Black-Scholes Model with Time-Dependent Parameters, PDE, Futures Prices;

## Abstract

In this paper we adopt the Black-Scholes model with a time-dependent drift parameter to describe the SET50 index which is a market-cap weighted index composed of the biggest 50 stocks traded in the Stock Exchange of Thailand (SET). An analytical formula for pricing futures contracts written on the SET50 index is derived by solving a partial differential equation (PDE) formulated for the futures contract pricing. Furthermore, we derive some interesting properties of the futures prices using our formula. Finally, we develop a method to estimate the model parameters by using the market data of SET50 and display an evolution of futures prices over the lifetime of the futures contract with several maturity times.

## References

The Stock Exchange of Thailand, “ดัชนีราคาหุ้น,”Available:https://www.set.or.th/th/products/indvex/files/SET_Index_Methodology_Sep2019_TH.pdf. [Accessed 15September2020].

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