scholarly journals Option Pricing Under GARCH Models Applied to the SET50 Index of Thailand

2021 ◽  
Vol 20 ◽  
pp. 112-121
Author(s):  
Somphorn Arunsingkarat ◽  
Renato Costa ◽  
Masnita Misran ◽  
Nattakorn Phewchean
Keyword(s):  
Historical Data ◽  
Stock Exchange ◽  
Garch Models ◽  
Option Prices ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Stock Exchange Of Thailand ◽  
Black Scholes ◽  
Neutral Models ◽  
Changes Over Time

Variance changes over time and depends on historical data and previous variances; as a result, it is useful to use a GARCH process to model it. In this paper, we use the notion of Conditional Esscher transform to GARCH models to find the GARCH, EGARCH and GJR risk-neutral models. Subsequently, we apply these three models to obtain option prices for the Stock Exchange of Thailand and compare to the well-known Black-Scholes model. Findings suggest that most of the pricing options under GARCH model are the nearest to the actual prices for SET50 option contracts with both times to maturity of 30 days and 60 days.

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

Pricing options on a mean-reverting asset by the analytical operator splitting method

2021 ◽  
pp. 2150002
Author(s):  
C. F. Lo ◽  
Y. W. He
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Dynamical Symmetry ◽  
Call Option ◽  
Option Prices ◽  
Pricing Options ◽  
Operator Splitting Method ◽  
European Call Option ◽  
Price Formula ◽  
Black Scholes

In this paper, we propose an operator splitting method to valuate options on the inhomogeneous geometric Brownian motion. By exploiting the approximate dynamical symmetry of the pricing equation, we derive a simple closed-form approximate price formula for a European call option which resembles closely the Black–Scholes price formula for a European vanilla call option. Numerical tests show that the proposed method is able to provide very accurate estimates and tight bounds of the exact option prices. The method is very efficient and robust as well.

scholarly journals Bounds for perpetual American option prices in a jump diffusion model

2006 ◽  
Vol 43 (03) ◽  
pp. 867-873 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
American Option ◽  
Option Prices ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Jump Diffusion Model ◽  
Perpetual American Option

We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black–Scholes model. We also investigate the dependence of the bounds on different parameters of the model.

scholarly journals Option Pricing by Probability Distortion Operator Based on the Quantile Function

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Luogen Yao ◽  
Gang Yang
Keyword(s):  
Option Pricing ◽  
Simulation Analysis ◽  
Quantile Function ◽  
Martingale Measure ◽  
Option Prices ◽  
New Class ◽  
Pricing Options ◽  
Black Scholes ◽  
Exponential Lévy Models

A new class of distortion operators based on quantile function is proposed for pricing options. It is shown that option prices obtained with our distortion operators are just the prices under mean correcting martingale measure in exponential Lévy models. In particular, Black-Scholes formula can be recuperated by our distortion operator. Simulation analysis shows that our distortion operator is superior to normal distortion operator and NIG distortion operator.

scholarly journals Pricing Various Types of Power Options under Stochastic Volatility

Symmetry ◽  
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.

China's Carbon Emissions Pricing Options: Based on Black-Scholes Model Testing

2012 ◽  
Vol 573-574 ◽  
pp. 1010-1016
Author(s):  
Li Li Zhou
Keyword(s):  
Carbon Emissions ◽  
Emissions Trading ◽  
Greenhouse Gas Emission ◽  
Low Cost ◽  
Policy Implications ◽  
Carbon Emissions Trading ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Pricing Power

In this paper, by analyzing the cause of the weak power for China's carbon emissions, we design the trading and OTC options contracts of China's carbon emissions. By testing we found that the pricing method can indeed improve the pricing power of carbon emissions and acquire more transactions in negotiations .The policy implications of this article: Firstly, China should combine with domestic and international progress to plan the framework of China's carbon emissions trading as soon as possible. Secondly, we also launch the research of carbon emissions trading market and experimental work; the third, establishing trading center with the market-oriented to guide China's implementation of greenhouse gas emission reduction projects and to achieve Low-cost emission.

scholarly journals VALUATION OF EUROPEAN PUT OPTION BY USING THE QUADRATURE METHOD UNDER THE VARIANCE GAMMA PROCESS

2020 ◽  
Vol 4 (5) ◽  
pp. 1-5
Author(s):  
Akash Singh ◽  
Ravi Gor Gor ◽  
Rinku Patel
Keyword(s):  
Quadrature Method ◽  
European Option ◽  
Brownian Motion Process ◽  
Asset Pricing Model ◽  
Pricing Options ◽  
Put Option ◽  
Variance Gamma Process ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Dynamic Asset Pricing

Dynamic asset pricing model uses the Geometric Brownian Motion process. The Black-Scholes model known as standard model to price European option based on the assumption that underlying asset prices dynamic follows that log returns of asset is normally distributed. In this paper, we introduce a new stochastic process called levy process for pricing options. In this paper, we use the quadrature method to solve a numerical example for pricing options in the Indian context. The illustrations used in this paper for pricing the European style option.  We also try to develop the pricing formula for European put option by using put-call parity and check its relevancy on actual market data and observe some underlying phenomenon.

scholarly journals Accuracy Tests Of American Put Valuation Models For Pharmaceutical Equity Options

2011 ◽  
Vol 6 (2) ◽  
Author(s):  
Yong H. Kim ◽  
Sangwoo Heo ◽  
Peter Cashel-Cordo ◽  
Yong S. Jang
Keyword(s):  
Option Prices ◽  
Equity Options ◽  
Forecasting Accuracy ◽  
Put Options ◽  
True Value ◽  
Black Scholes Model ◽  
American Put Options ◽  
Black Scholes ◽  
Variance Estimate ◽  
American Put

This study compares the performance of the Macmillan (1986), Barone-Adesi and Whaley (1987) MBAW model, Ju and Zhong (1999) MQuad model, Black-Scholes model and Put-Call Parity in pricing American put options of pharmaceutical companies. These are evaluated using actual option prices for three companies over 2000 to 2005, as opposed to the previous use of generated binomial option pricing data. We compare the forecasting accuracy by maturity, moneyness, and variance estimate. Contrary to Ju and Zhong (1999), we find that the MBAW outperforms the other models for at-the-money, and out-of-the-money options. The MQuad model performs best for in-the-money options. However, in this case both the MBAW and MQuad models estimates are very similar. Our results are consistent irrespective of option maturities and volatility estimates. These findings raise questions regarding the practice of using actual prices as the true value, compared to the previous results that use simulated prices.

An extremely efficient numerical method for pricing options in the Black–Scholes model with jumps

2020 ◽  
Vol 44 (2) ◽  
pp. 1843-1862
Author(s):  
Davood Ahmadian ◽  
Luca Vincenzo Ballestra ◽  
Nader Karimi
Keyword(s):  
Numerical Method ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Black Scholes
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