scholarly journals Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

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.

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.

scholarly journals ANALYSIS OF MARKET VOLATILITY VIA A DYNAMICALLY PURIFIED OPTION PRICE PROCESS

2014 ◽  
Vol 09 (03) ◽  
pp. 1450006 ◽  
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.

scholarly journals The Impact of International Sanctions on Russian Financial Markets

Economies ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 107
Author(s):  
Mirzosaid Sultonov
Keyword(s):  
Exchange Rate ◽  
Stock Price ◽  
Price Index ◽  
The United States ◽  
The European Union ◽  
Stock Price Index ◽  
The Exchange Rate ◽  
Long Term Impact ◽  
The Impact

Russia’s international comportment and geostrategic moves, particularly the invasion of Ukraine and the annexation of Crimea in 2014, caused a substantial change in its international economic and political relations. In response to Russia’s invasion, the United States of America, the European Union, and their allies imposed a series of sanctions. In this study, by applying an exponential generalized autoregressive conditional heteroscedasticity model to daily logarithmic returns of the ruble exchange rate and the closing price index of the Russian Trading System, we analyze how the returns and volatility of the exchange rate and the stock price index responded to the sanctions and oil price changes. The estimation results show that the sanctions have a significant positive short-term impact on exchange rate returns. Economic sanctions have a significant negative long-term impact on the returns and variance of the exchange rate and a significant positive long-term impact on the returns of the stock price index. Financial sanctions have a positive/negative long-term impact on the returns of the exchange rate/stock price index and a positive long-term impact on the variance of the exchange rate and the stock price index. Corporate sanctions have a positive long-term impact on exchange rate returns.

VALUATION OF VULNERABLE OPTIONS UNDER THE DOUBLE EXPONENTIAL JUMP MODEL WITH STOCHASTIC VOLATILITY

2018 ◽  
Vol 33 (1) ◽  
pp. 81-104 ◽  
Author(s):  
Xingyu Han
Keyword(s):  
Stochastic Volatility ◽  
Numerical Solutions ◽  
Characteristic Functions ◽  
Transform Method ◽  
Put Options ◽  
Fourier Cosine ◽  
Jump Model ◽  
Double Exponential ◽  
Vulnerable Options ◽  
The Impact

In this paper, we extend the framework of Klein [15] [Journal of Banking & Finance 20: 1211–1229] to a general model under the double exponential jump model with stochastic volatility on the underlying asset and the assets of the counterparty. Firstly, we derive the closed-form characteristic functions for this dynamic. Using the Fourier-cosine expansion technique, we get numerical solutions for vulnerable European put options based on the characteristic functions. The inverse fast Fourier transform method provides a fast numerical algorithm for the twice-exercisable vulnerable Bermuda put options. By virtue of the modified Geske and Johnson method, we obtain an approximate pricing formula of vulnerable American put options. Numerical simulations are made for investigating the impact of stochastic volatility on vulnerable options.

scholarly journals PRICING HOLDER-EXTENDABLE CALL OPTIONS WITH MEAN-REVERTING STOCHASTIC VOLATILITY

2019 ◽  
Vol 61 (4) ◽  
pp. 382-397
Author(s):  
S. N. I. IBRAHIM ◽  
A. DÍAZ-HERNÁNDEZ ◽  
J. G. O’HARA ◽  
N. CONSTANTINOU
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Stochastic Volatility ◽  
Fourier Method ◽  
Heston Model ◽  
Computational Time ◽  
Characteristic Functions ◽  
Underlying Asset ◽  
Call Options ◽  
Integral Forms

Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carlo simulation, and we determine the efficiency and accuracy of the Fourier method in pricing holder-extendable call options for Heston parameters calibrated from the subprime crisis. We show that the fast Fourier transform reduces the computational time required to produce a range of holder-extendable call option prices by at least an order of magnitude. Numerical results also demonstrate that when the Heston correlation is negative, the Black–Scholes model under-prices in-the-money and over-prices out-of-the-money holder-extendable call options compared with the Heston model, which is analogous to the behaviour for vanilla calls.

scholarly journals A Stochastic Volatility Alternative to SABR

2008 ◽  
Vol 45 (04) ◽  
pp. 1071-1085
Author(s):  
L. C. G. Rogers ◽  
L. A. M. Veraart
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Underlying Asset ◽  
Volatility Models ◽  
Sabr Model ◽  
Modified Dynamics

We present two new stochastic volatility models in which option prices for European plain-vanilla options have closed-form expressions. The models are motivated by the well-known SABR model, but use modified dynamics of the underlying asset. The asset process is modelled as a product of functions of two independent stochastic processes: a Cox-Ingersoll-Ross process and a geometric Brownian motion. An application of the models to options written on foreign currencies is studied.

LONG-TERM ADJUSTMENT OF CAPITAL STRUCTURE: EVIDENCE FROM SINGAPORE, HONG KONG AND TAIWAN

2012 ◽  
Vol 57 (04) ◽  
pp. 1250027
Author(s):  
TERENCE TAI-LEUNG CHONG ◽  
DANIEL TAK-YAN LAW ◽  
LIN ZOU
Keyword(s):  
Hong Kong ◽  
Capital Structure ◽  
Stock Price ◽  
Pecking Order ◽  
Price Performance ◽  
Growth Opportunity ◽  
Timing Effects ◽  
The Impact ◽  
Internal Fund

This paper examines the impact of profitability, stock price performance and growth opportunity on the capital structure of firms in Singapore, Taiwan and Hong Kong. In contrast to Kayhan and Titman (2007), it is found that firms in these three Chinese-dominated economies strongly prefer debt to equity or internal fund financing. They also take advantage of stock price appreciation by issuing more shares. An adjustment model for debt ratios is estimated. The results suggest that the leverage ratios of these firms slowly adjust toward their target levels. Deviations from the target due to the pecking order and market timing effects are found to be significant.

scholarly journals LONG MEMORY VERSION OF STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL WITH STOCHASTIC INTENSITY

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Somayeh Fallah ◽  
Farshid Mehrdoust
Keyword(s):  
Stochastic Volatility ◽  
Long Range ◽  
Diffusion Model ◽  
Long Memory ◽  
Stock Price ◽  
Real Data ◽  
Jump Diffusion ◽  
Heston Model ◽  
Long Range Dependence ◽  
Jump Diffusion Model

It is widely accepted that certain financial data exhibit long range dependence. We consider a fractional stochastic volatility jump diffusion model in which the stock price follows a double exponential jump diffusion process with volatility described by a long memory stochastic process and intensity rate expressed by an ordinary Cox, Ingersoll, and Ross (CIR) process. By calibrating the model with real data, we examine the performance of the model and also, we illustrate the role of long range dependence property by comparing our presented model with the Heston model.

Pricing derivatives with fractional volatility

2017 ◽  
Vol 04 (01) ◽  
pp. 1750014 ◽  
Author(s):  
Hideharu Funahashi
Keyword(s):  
Brownian Motion ◽  
Analytical Formula ◽  
Approximation Formula ◽  
Barrier Options ◽  
Hurst Index ◽  
Option Prices ◽  
Important Lesson ◽  
Highly Sensitive ◽  
Path Dependent ◽  
The Impact

This paper studies the effect of fractional volatility on path-dependent options, which are highly sensitive to the volatility structure of a targeted underlying asset process. To this end, we propose an approximation formula for average and barrier options when volatility follows a fractional Brownian motion. Furthermore, using the analytical formula, we investigate the impact of the Hurst index on option prices. Overall, our important finding is that when the maturity is short and speed of mean-reversion is slow, the impact of the Hurst index strongly influences the option prices and that is non-negligible. This is an important lesson for practitioners who uses standard Brownian motion.

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