Option pricing for a stochastic volatility Lévy model with stochastic interest rates

We present option pricing under the double stochastic volatility model with stochastic interest rates and double exponential jumps with stochastic intensity in this article. We make two contributions based on the existing literature. First, we add double stochastic volatility to the option pricing model combining stochastic interest rates and jumps with stochastic intensity, and we are the first to fill this gap. Second, the stochastic interest rate process is presented in the Hull–White model. Some authors have concentrated on hybrid models based on various asset classes in recent years. Therefore, we build a multifactor model with the term structure of stochastic interest rates. We also approximated the pricing formula for European call options by applying the COS method and fast Fourier transform (FFT). Numerical results display that FFT and the COS method are much faster than the numerical integration approach used for obtaining the semi-closed form prices. The COS method shows higher accuracy, efficiency, and stability than FFT. Therefore, we use the COS method to investigate the impact of the parameters in the stochastic jump intensity process and the existence of the process on the call option prices. We also use it to examine the impact of the parameters in the interest rate process on the call option prices.

Download Full-text

Comment on ‘Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates’

Review of Finance ◽

10.1023/a:1009868019690 ◽

1999 ◽

Vol 3 (3) ◽

pp. 311-317

Author(s):

Bent Jesper Christensen

Keyword(s):

Option Pricing ◽

Interest Rates ◽

Stochastic Volatility ◽

Pricing Models ◽

Stochastic Interest Rates ◽

Stochastic Interest ◽

Index Option

Download Full-text

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.

Download Full-text