CONVERGENCE SPEED OF GARCH OPTION PRICE TO DIFFUSION OPTION PRICE

2009 ◽  
Vol 12 (03) ◽  
pp. 359-391 ◽  
Author(s):  
JIN-CHUAN DUAN ◽  
YAZHEN WANG ◽  
JIAN ZOU
Keyword(s):  
Discrete Time ◽  
Option Price ◽  
Garch Model ◽  
Convergence Speed ◽  
Time Interval ◽  
Square Root ◽  
Option Prices ◽  
European Option ◽  
The Garch Model

It is well known that as the time interval between two consecutive observations shrinks to zero, a properly constructed GARCH model will weakly converge to a bivariate diffusion. Naturally the European option price under the GARCH model will also converge to its bivariate diffusion counterpart. This paper investigates the convergence speed of the GARCH option price. We show that the European option prices under the two corresponding models are equal up to an order near the square root of the length of discrete time interval.

An Analytical Approximation for Option Price under the Affine GARCH Model - A Comparison with the Closed-Form Solution of Heston-Nandi

GIS Business ◽  
2017 ◽  
Vol 12 (4) ◽  
pp. 32-46
Author(s):  
Noureddine Lahouel ◽  
Slaheddine Hellara
Keyword(s):  
Option Pricing ◽  
Closed Form ◽  
Empirical Work ◽  
Closed Form Solution ◽  
Garch Model ◽  
Analytical Approximation ◽  
Form Solution ◽  
Option Prices ◽  
European Option ◽  
Comparative Performance

In the option pricing theory, two important approaches have been developed to evaluate the prices of a European option. The first approach develops an almost closed-form option pricing formula under a specific GARCH process (Heston & Nandi, 2000). The second approach develops an analytical approximation for computing European option prices with more widespread NGARCH models (Duan, Gauthier & Simonato, 1999). The analytical approximation was also developed under GJR-GARCH and EGARCH models by Duan, Gauthier, Sasseville & Simonato (2006). However, no empirical work was performed to study the comparative performance of these two formulas (closed-form solution and analytical approximation). Also, it is possible to develop an analytical approximation under the specific GARCH model of Heston & Nandi (2000). In this paper, we have filled up those gaps. We started with the development of an analytical approximation, for computing European option prices, under Heston-Nandis GARCH model. In the second step, we carried out a comparative analysis of the three formulas using CAC 40 index returns from 31 December 1987 to 31 December 2013.

REPLICATION SCHEME FOR THE PRICING OF EUROPEAN OPTIONS

2021 ◽  
pp. 2150014
Author(s):  
HIDEHARU FUNAHASHI
Keyword(s):  
Diffusion Process ◽  
Density Function ◽  
Numerical Experiments ◽  
Analytical Formula ◽  
Option Price ◽  
Option Prices ◽  
European Options ◽  
European Option ◽  
Volatility Models ◽  
Replication Scheme

This paper proposes an efficient method for calculating European option prices under local, stochastic, and fractional volatility models. Instead of directly calculating the density function of a target underlying asset, we replicate it from a simpler diffusion process with a known analytical solution for the European option. For this purpose, we derive six functions that characterize the density function of a diffusion process, for both the original and simpler processes and match these functions so that the latter mimics the former. Using the analytical formula, we then approximate the option price of the target asset. By comparison with previous works and numerical experiments, we show that the accuracy of our approximation is high, and the calculation is fast enough for practical purposes; hence, it is suitable for calibration purposes.

A REGULARIZED FOURIER TRANSFORM APPROACH FOR VALUING OPTIONS UNDER STOCHASTIC DIVIDEND YIELDS

2010 ◽  
Vol 13 (02) ◽  
pp. 211-240 ◽  
Author(s):  
BAYE M. DIA
Keyword(s):  
Fourier Transform ◽  
Option Pricing ◽  
Inverse Fourier Transform ◽  
Option Price ◽  
Square Root ◽  
Option Prices ◽  
European Options ◽  
Dividend Yield ◽  
New Approach ◽  
Main Effects

This paper studies the option pricing problem in a class of models in which dividend yields follow a time-homogeneous diffusion. Within this framework, we develop a new approach for valuing options based on the use of a regularized Fourier transform. We derive a pricing formula for European options which gives the option price in the form of an inverse Fourier transform and propose two methods for numerically implementing this formula. As an application of this pricing approach, we introduce the Ornstein-Uhlenbeck and the square-root dividend yield models in which we explicitly solve the pricing problem for European options. Finally we highlight the main effects of a stochastic dividend yield on option prices.

scholarly journals On Forecasting Taiwanese Stock Index Option Prices: The Role of Implied Volatility Index

2017 ◽  
Vol 9 (9) ◽  
pp. 133 ◽  
Author(s):  
Jying-Nan Wang ◽  
Hung-Chun Liu ◽  
Lu-Jui Chen
Keyword(s):  
Implied Volatility ◽  
Option Price ◽  
Garch Model ◽  
Predictive Performance ◽  
Stock Index ◽  
Additional Information ◽  
Volatility Index ◽  
Volatility Models ◽  
Rolling Window ◽  
The Garch Model

This paper aims to propose four volatility measures: The first is the GARCH model advocated by Bollerslev (1986); the second is the GARCHVIX model which extends the GARCH model by including the volatility index (VIX) as explanatory variable for volatility; the last two are HS20D and HS252D, which represent the historical volatilities generated by traditional rolling window technique with 20- and 252-day historical index returns data, respectively. We examine the price information on VIX to improve the predictive performance of GARCH model for valuing TAIEX stock index call options (TXO) over the period from January 2014 to May 2015. Empirical results firstly indicate that both the GARCH and GARCHVIX models consistently perform better than the historical volatility models for forecasting call value of TXO under different moneynesses. Secondly, the GARCHVIX model significantly outperforms the GARCH model for most cases, indicating that the GARCH-based option price forecasts can be effectively improved with the additional information contained in VIX. Finally, the use of GARCHVIX model can greatly reduce model mispricing especially for out-the-money TXO option case. Thus, volatility index is crucial for option traders to efficiently predict TXO option value with GARCH model.

scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

Psychometrika ◽  
2021 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen L. Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Auto Regressive ◽  
Conceptual Shift

AbstractNetwork analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

scholarly journals Implementation of an FPGA-Based Current Control and SVPWM ASIC with Asymmetric Five-Segment Switching Scheme for AC Motor Drives

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1462
Author(s):  
Ming-Fa Tsai ◽  
Chung-Shi Tseng ◽  
Po-Jen Cheng
Keyword(s):  
Discrete Time ◽  
Control Function ◽  
Current Control ◽  
Motor Drives ◽  
Modulation Scheme ◽  
Time Interval ◽  
Switching Scheme ◽  
Two Phase ◽  
Ac Motor ◽  
Ac Motor Drives

This paper presents the design and implementation of an application-specific integrated circuit (ASIC) for a discrete-time current control and space-vector pulse-width modulation (SVPWM) with asymmetric five-segment switching scheme for AC motor drives. As compared to a conventional three-phase symmetric seven-segment switching SVPWM scheme, the proposed method involves five-segment two-phase switching in each switching period, so the inverter switching times and power loss can be reduced by 33%. In addition, the produced PWM signal is asymmetric with respect to the center-symmetric triangular carrier wave, and the voltage command signal from the discrete-time current control output can be given in each half period of the PWM switching time interval, hence increasing the system bandwidth and allowing the motor drive system with better dynamic response. For the verification of the proposed SVPWM modulation scheme, the current control function in the stationary reference frame is also included in the design of the ASIC. The design is firstly verified by using PSIM simulation tool. Then, a DE0-nano field programmable gate array (FPGA) control board is employed to drive a 300W permanent-magnet synchronous motor (PMSM) for the experimental verification of the ASIC.

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