Option Prices with Stochastic Interest Rates - Black/Scholes and Ho/Lee Unified

This paper extends the Wiener–Itô chaos expansion approach proposed by Funahashi & Kijima (2015) to an equity-interest-rate hybrid model for the pricing of European contingent claims with special emphasis on calibration to the option markets. Our model can capture the volatility skew and smile of option markets, as well as the stochastic nature of interest rates. Further, the proposed method is applicable to widely used option pricing models such as local volatility models (LVM), stochastic volatility models (SVM), and their combinations with the stochastic nature of interest rates; hence, it is suitable for practical purposes. Through numerical examples, we show that our approximation is quite accurate even for long-maturity and/or high-volatility cases.

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American Options on High Dividend Securities: A Numerical Investigation

Risks ◽

10.3390/risks7020059 ◽

2019 ◽

Vol 7 (2) ◽

pp. 59

Author(s):

Francesco Rotondi

Keyword(s):

Interest Rates ◽

American Options ◽

Least Square Method ◽

American Option ◽

Least Square ◽

Stochastic Interest Rates ◽

Stochastic Interest ◽

Black Scholes ◽

Ill Posed ◽

European Counterpart

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.

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Stochastic pricing formulation for hybrid equity warrants

AIMS Mathematics ◽

10.3934/math.2022027 ◽

2021 ◽

Vol 7 (1) ◽

pp. 398-424

Author(s):

Teh Raihana Nazirah Roslan ◽

◽

Sharmila Karim ◽

Siti Zulaiha Ibrahim ◽

Ali Fareed Jameel ◽

...

Keyword(s):

Interest Rates ◽

Stochastic Volatility ◽

Statistical Error ◽

Optimization Method ◽

Calibration Procedure ◽

Stochastic Interest Rates ◽

Black Scholes Model ◽

Stochastic Interest ◽

Black Scholes ◽

Pricing Formula

<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>

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EFFECTS OF RETURN PREDICTABILITY ON OPTION PRICES WITH STOCHASTIC VOLATILITY FOR THE MARKET PORTFOLIO

Annals of Financial Economics ◽

10.1142/s2010495205500053 ◽

2005 ◽

Vol 01 (01) ◽

pp. 0550005

Author(s):

MELANIE CAO

Keyword(s):

Option Pricing ◽

Interest Rates ◽

Stochastic Volatility ◽

Return Predictability ◽

Option Prices ◽

Pricing Model ◽

Stochastic Interest Rates ◽

Market Portfolio ◽

Stochastic Interest ◽

Option Pricing Model

I examine the effects of return predictability on option prices for the market portfolio in the presence of stochastic volatility and/or stochastic interest rates. The analysis is implemented in an equilibrium framework where a consistent option pricing model is derived with the return predictability and stochastic volatility and the precise link between the actual and the risk neutral measures is endogenized. The equilibrium analysis indicates that the return predictability is induced by the mean-reverting and heteroskedastic features of aggregate dividends. It is shown that risk-neutral option pricing model with the stochastic volatility and/or stochastic interest rates can be consistent with return predictability. Numerical results suggest that (i) models with either perfect predictability or no predictability will significantly overprice long-term options across different strike prices when the return of the underlying exhibits modest predictability; (ii) the stochastic volatility does not affect option prices in a significant way when asset return predictability is properly reflected in the actual stock price process; (iii) when return predictability is correctly specified, the effects of stochastic interest rates are not uniform.

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