Revisiting the Classical Models: Black-Scholes and Heston With Stochastic Interest Rates and Term Structure of Volatilities

2018 ◽  
Author(s):  
Alberto Bueno-Guerrero
Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 59
Author(s):  
Francesco Rotondi

I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression is ill-posed, the procedure might deliver biased results. The price of the American option might even fall below the price of its European counterpart. For call options, this is likely to occur when the dividend yield of the underlying is high. This distortion is documented within the standard Black–Scholes–Merton model as well as within its most common extensions (the jump-diffusion, the stochastic volatility and the stochastic interest rates models). Finally, I propose two easy and effective workarounds that fix this distortion.


2021 ◽  
Vol 7 (1) ◽  
pp. 398-424
Author(s):  
Teh Raihana Nazirah Roslan ◽  
◽  
Sharmila Karim ◽  
Siti Zulaiha Ibrahim ◽  
Ali Fareed Jameel ◽  
...  

<abstract> <p>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.</p> </abstract>


2012 ◽  
Author(s):  
Jan F. Baldeaux ◽  
Man Chung Fung ◽  
Katja Ignatieva ◽  
Eckhard Platen

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