Hybrid equity warrants pricing formulation under stochastic dynamics

—A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study

Pricing equity warrants under the sub-mixed fractional Brownian motion regime with stochastic interest rate

This paper proposes a pricing model for equity warrants under the sub-mixed fractional Brownian motion regime with the interest rate following the Merton short rate model. By using the delta hedging strategy, the corresponding partial differential equations for equity warrants are obtained. Moreover, the explicit pricing formula for equity warrants and some numerical results are given

A closed-form pricing formula for European options under the Heston model with stochastic interest rate

In this paper, a closed-form pricing formula for European options in the form of an infinite series is derived under the Heston model with the interest rate being another random variable following the CIR (Cox-Ingersoll-Ross) model. One of the main advantages for the newly derived series solution is that we can provide a radius of convergence, which is complemented by some numerical experiments demonstrating its speed of convergence. To further verify our formula, option prices calculated through our formula are also compared with those obtained from Monte Carlo simulations. Finally, a set of pricing formulae are derived with the series expanded at different points so that the entire time horizon can be covered by converged solutions

Dynamic hybrid pricing formulation for equity warrants

Equity warrants are instruments issued by a company that give the stockholder the privilege of buying a stock at a certain strike price within a particular timeframe. Motivated by empirical studies, the Black-Scholes option pricing model is not suitable to price a warrant since both assumptions of constant volatility and constant interest rates in the model are incompatible. This study proposed the Heston-Cox-Ingersoll- Ross (Heston-CIR) hybrid model to identify the effects of stochastic volatility and stochastic interest rates in pricing equity warrants. The study constructed new analytical pricing formulas for equity warrants by using Cauchy transformation and partial differential equation approaches. The local optimization method is employed to obtain the estimated parameter values by calibrating the Heston-CIR model. The effectiveness of the proposed model is investigated through the empirical study using the data from Bursa Malaysia. The proposed model shows significant improvement on the computation time in estimating nine model parameters, ranging from 38.12 to 62.62 seconds compared to the existing models. Moreover, the empirical study suggested that the proposed model is accurate when compared to the real market over five years period. This model also produced smallest pricing errors among the existing models. The finding also suggested equity warrants in moneyness opportunity, 88.75% of the warrants are profitable. In conclusion, the proposed model performs the best in identifying the effects of stochastic volatility and stochastic interest rates in pricing equity warrants