The Impact of Overnight Periods on Option Pricing

AbstractThis paper investigates the effect of closed overnight exchanges on option prices. During the trading day, asset prices follow the literature's standard affine model that allows for stochastic volatility and random jumps. Independently, the overnight asset price process is modeled by a single jump. We find that the overnight component reduces the variation in the random jump process significantly. However, neither the random jumps nor the overnight jumps alone are able to empirically describe all features of option prices. We conclude that both random jumps during the day and overnight jumps are important in explaining option prices, where the latter account for about one quarter of total jump risk.

Download Full-text

Option pricing under the fractional stochastic volatility model

ANZIAM Journal ◽

10.21914/anziamj.v63.15204 ◽

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

Download Full-text

ANALYSIS OF MARKET VOLATILITY VIA A DYNAMICALLY PURIFIED OPTION PRICE PROCESS

Annals of Financial Economics ◽

10.1142/s2010495214500067 ◽

2014 ◽

Vol 09 (03) ◽

pp. 1450006 ◽

Cited By ~ 1

Author(s):

CHUONG LUONG ◽

NIKOLAI DOKUCHAEV

Keyword(s):

Stock Price ◽

Implied Volatility ◽

Financial Time Series ◽

Option Price ◽

Option Prices ◽

Price Process ◽

Volatility Index ◽

Quadratic Interpolation ◽

Dynamic Estimation ◽

The Impact

The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial "dynamically purified" price process that in theory allows to eliminate the impact of the stock price movements. The complete elimination would be possible if the option prices were available for continuous sets of strike prices and expiration times. In practice, we have to use only finite sets of available prices. We discuss the construction of this process from the available option prices using different methods. In order to overcome the incompleteness of the available option prices, we suggests several interpolation approaches, including the first order Taylor series extrapolation and quadratic interpolation. We examine the potential of the implied volatility derived from this proposed process for forecasting of the future volatility, in comparison with the traditional implied volatility process such as the volatility index VIX.

Download Full-text

NUMERICAL STABILITY OF A HYBRID METHOD FOR PRICING OPTIONS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024919500365 ◽

2019 ◽

Vol 22 (07) ◽

pp. 1950036

Author(s):

MAYA BRIANI ◽

LUCIA CARAMELLINO ◽

GIULIA TERENZI ◽

ANTONINO ZANETTE

Keyword(s):

Interest Rate ◽

Asset Price ◽

Option Prices ◽

Underlying Asset ◽

Binomial Tree ◽

Price Process ◽

Pricing Options ◽

Model Following ◽

Jump Model ◽

The Interest Rate

We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propose hybrid simulations for the model, following a binomial tree in the direction of both the volatility and the interest rate, and a space-continuous approximation for the underlying asset price process coming from a Euler–Maruyama type scheme. We test our numerical schemes by computing European and American option prices.

Download Full-text

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

The ANZIAM Journal ◽

10.1017/s1446181121000225 ◽

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.

Download Full-text

Pricing Various Types of Power Options under Stochastic Volatility

Symmetry ◽

10.3390/sym12111911 ◽

2020 ◽

Vol 12 (11) ◽

pp. 1911

Author(s):

Youngrok Lee ◽

Yehun Kim ◽

Jaesung Lee

Keyword(s):

Financial Markets ◽

Stochastic Volatility ◽

Asset Price ◽

Stochastic Volatility Model ◽

Exotic Options ◽

Option Prices ◽

Black Scholes Model ◽

Volatility Model ◽

Black Scholes ◽

Pricing Power

The exotic options with curved nonlinear payoffs have been traded in financial markets, which offer great flexibility to participants in the market. Among them, power options with the payoff depending on a certain power of the underlying asset price are widely used in markets in order to provide high leverage strategy. In pricing power options, the classical Black–Scholes model which assumes a constant volatility is simple and easy to handle, but it has a limit in reflecting movements of real financial markets. As the alternatives of constant volatility, we focus on the stochastic volatility, finding more exact prices for power options. In this paper, we use the stochastic volatility model introduced by Schöbel and Zhu to drive the closed-form expressions for the prices of various power options including soft strike options. We also show the sensitivity of power option prices under changes in the values of each parameter by calculating the resulting values obtained from the formulas.

Download Full-text

STOCHASTIC VOLATILITY AND JUMP-DIFFUSION — IMPLICATIONS ON OPTION PRICING

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024999000212 ◽

1999 ◽

Vol 02 (04) ◽

pp. 409-440 ◽

Cited By ~ 5

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.

Download Full-text

Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

Mathematical Problems in Engineering ◽

10.1155/2021/6634779 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Ying Chang ◽

Yiming Wang ◽

Sumei Zhang

Keyword(s):

Brownian Motion ◽

Stochastic Volatility ◽

Stock Price ◽

Heston Model ◽

Characteristic Functions ◽

Option Prices ◽

Approximation Factor ◽

Numerical Result ◽

The Impact

We establish double Heston model with approximative fractional stochastic volatility in this article. Since approximative fractional Brownian motion is a better choice compared with Brownian motion in financial studies, we introduce it to double Heston model by modeling the dynamics of the stock price and one factor of the variance with approximative fractional process and it is our contribution to the article. We use the technique of Radon–Nikodym derivative to obtain the semianalytical pricing formula for the call options and derive the characteristic functions. We do the calibration to estimate the parameters. The calibration demonstrates that the model provides the best performance among the three models. The numerical result demonstrates that the model has better performance than the double Heston model in fitting with the market implied volatilities for different maturities. The model has a better fit to the market implied volatilities for long-term options than for short-term options. We also examine the impact of the positive approximation factor and the long-memory parameter on the call option prices.

Download Full-text