Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

2021 ◽  
pp. 1-20
Author(s):  
Y. HAN ◽  
Z. LI ◽  
C. LIU
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

Abstract We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

STOCHASTIC VOLATILITY AND JUMP-DIFFUSION — IMPLICATIONS ON OPTION PRICING

1999 ◽  
Vol 02 (04) ◽  
pp. 409-440 ◽  
Author(s):  
GEORGE J. JIANG
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Dynamic Properties ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
Pricing Errors ◽  
Volatility Model ◽  
Random Jump

This paper conducts a thorough and detailed investigation on the implications of stochastic volatility and random jump on option prices. Both stochastic volatility and jump-diffusion processes admit asymmetric and fat-tailed distribution of asset returns and thus have similar impact on option prices compared to the Black–Scholes model. While the dynamic properties of stochastic volatility model are shown to have more impact on long-term options, the random jump is shown to have relatively larger impact on short-term near-the-money options. The misspecification risk of stochastic volatility as jump is minimal in terms of option pricing errors only when both the level of kurtosis of the underlying asset return distribution and the level of volatility persistence are low. While both asymmetric volatility and asymmetric jump can induce distortion of option pricing errors, the skewness of jump offers better explanations to empirical findings on implied volatility curves.

scholarly journals Option Pricing under Double Stochastic Volatility Model with Stochastic Interest Rates and Double Exponential Jumps with Stochastic Intensity

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Ying Chang ◽  
Yiming Wang
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stochastic Interest Rates ◽  
Stochastic Intensity ◽  
Volatility Model ◽  
Double Exponential ◽  
Stochastic Interest ◽  
The Impact

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.

GENERALIZED BN–S STOCHASTIC VOLATILITY MODEL FOR OPTION PRICING

2016 ◽  
Vol 19 (02) ◽  
pp. 1650014 ◽  
Author(s):  
INDRANIL SENGUPTA
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Gaussian Distribution ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Inverse Gaussian ◽  
Martingale Measures ◽  
Structure Preserving ◽  
Volatility Model ◽  
Equivalent Martingale

In this paper, a class of generalized Barndorff-Nielsen and Shephard (BN–S) models is investigated from the viewpoint of derivative asset analysis. Incompleteness of this type of markets is studied in terms of equivalent martingale measures (EMM). Variance process is studied in details for the case of Inverse-Gaussian distribution. Various structure preserving subclasses of EMMs are derived. The model is then effectively used for pricing European style options and fitting implied volatility smiles.

scholarly journals A Stochastic Volatility Model With Realized Measures for Option Pricing

2019 ◽  
Vol 38 (4) ◽  
pp. 856-871 ◽  
Author(s):  
Giacomo Bormetti ◽  
Roberto Casarin ◽  
Fulvio Corsi ◽  
Giulia Livieri
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model
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