Stochastic pricing formulation for hybrid equity warrants

Teh Raihana Nazirah Roslan; Sharmila Karim; Siti Zulaiha Ibrahim; Ali Fareed Jameel; Zainor Ridzuan Yahya; Teh Raihana Nazirah Roslan; Sharmila Karim; Siti Zulaiha Ibrahim; Ali Fareed Jameel; Zainor Ridzuan Yahya

doi:10.3934/math.2022027

AIMS Mathematics

2022, Volume 7, Issue 1: 398-424. doi: 10.3934/math.2022027

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Research article

Stochastic pricing formulation for hybrid equity warrants

1.
Othman Yeop Abdullah Graduate School of Business, Universiti Utara Malaysia, 50300 Kuala Lumpur, Malaysia
2.
Institute of Strategic Industrial Decision Modelling (ISIDM), Universiti Utara Malaysia, UUM Sintok, 06010 Kedah, Malaysia
3.
School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia
4.
Institute of Engineering Mathematics, Faculty of Applied Sciences and Humanities, Pauh Putra Campus, Universiti Malaysia Perlis (UniMAP), 02600 Arau, Perlis, Malaysia

Received: 19 July 2021 Accepted: 22 September 2021 Published: 13 October 2021
MSC : 91B70, 91G20, 91G39

A warrant is a financial agreement that gives the right but not the responsibility, to buy or sell a security at a specific price prior to expiration. Many researchers inadvertently utilize call option pricing models to price equity warrants, such as the Black Scholes model which had been found to hold many shortcomings. This paper investigates the pricing of equity warrants under a hybrid model of Heston stochastic volatility together with stochastic interest rates from Cox-Ingersoll-Ross model. This work contributes to exploration of the combined effects of stochastic volatility and stochastic interest rates on pricing equity warrants which fills the gap in the current literature. Analytical pricing formulas for hybrid equity warrants are firstly derived using partial differential equation approaches. Further, to implement the pricing formula to realistic contexts, a calibration procedure is performed using local optimization method to estimate all parameters involved. We then conducted an empirical application of our pricing formula, the Black Scholes model, and the Noreen Wolfson model against the real market data. The comparison between these models is presented along with the investigation of the models' accuracy using statistical error measurements. The outcomes revealed that our proposed model gives the best performance which highlights the crucial elements of both stochastic volatility and stochastic interest rates in valuation of equity warrants. We also examine the warrants' moneyness and found that 96.875% of the warrants are in-the-money which gives positive returns to investors. Thus, it is beneficial for warrant holders concerned in purchasing warrants to elect the best warrant with the most profitable and more benefits at a future date.
- equity warrants,
- stochastic interest rate,
- stochastic volatility,
- Heston-CIR model,
- hybrid model
Citation: Teh Raihana Nazirah Roslan, Sharmila Karim, Siti Zulaiha Ibrahim, Ali Fareed Jameel, Zainor Ridzuan Yahya. Stochastic pricing formulation for hybrid equity warrants[J]. AIMS Mathematics, 2022, 7(1): 398-424. doi: 10.3934/math.2022027

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Abstract

A warrant is a financial agreement that gives the right but not the responsibility, to buy or sell a security at a specific price prior to expiration. Many researchers inadvertently utilize call option pricing models to price equity warrants, such as the Black Scholes model which had been found to hold many shortcomings. This paper investigates the pricing of equity warrants under a hybrid model of Heston stochastic volatility together with stochastic interest rates from Cox-Ingersoll-Ross model. This work contributes to exploration of the combined effects of stochastic volatility and stochastic interest rates on pricing equity warrants which fills the gap in the current literature. Analytical pricing formulas for hybrid equity warrants are firstly derived using partial differential equation approaches. Further, to implement the pricing formula to realistic contexts, a calibration procedure is performed using local optimization method to estimate all parameters involved. We then conducted an empirical application of our pricing formula, the Black Scholes model, and the Noreen Wolfson model against the real market data. The comparison between these models is presented along with the investigation of the models' accuracy using statistical error measurements. The outcomes revealed that our proposed model gives the best performance which highlights the crucial elements of both stochastic volatility and stochastic interest rates in valuation of equity warrants. We also examine the warrants' moneyness and found that 96.875% of the warrants are in-the-money which gives positive returns to investors. Thus, it is beneficial for warrant holders concerned in purchasing warrants to elect the best warrant with the most profitable and more benefits at a future date.

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