A Threshold Model for Local Volatility: Evidence of Leverage and Mean Reversion Effects on Historical Data PDF Download
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Author: Antoine Lejay
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Tests are performed on the daily prices of 21 assets. They show empirical evidence for leverage and mean-reversion effects, consistent with the results in the literature.
Author: Antoine Lejay
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Tests are performed on the daily prices of 21 assets. They show empirical evidence for leverage and mean-reversion effects, consistent with the results in the literature.
Author: Dinghai Xu
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
Author: Bluford H Putnam
Publisher: World Scientific
ISBN: 1944659609
Category : Business & Economics
Languages : en
Pages : 273
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Book Description
'It is written in clear English, without equations, and with plenty of charts to ground one’s understanding in the real world … The authors make a compelling case that economists need to take their simplifying assumptions more seriously, to embrace statistical techniques that can track dynamic markets with time-varying parameters, and to always be aware of the importance of shifts in the underlying context.'Global Commodities Applied Research DigestEconomics Gone Astray is a collection of essays on critical topics in macroeconomics that frame the issues in terms of clearly stated assumptions, highlighting the errors often made by professional economists, and allowing readers to better analyze market behavior and the economic consequences of policy decisions.The book differs from textbook economics, as it tackles sophisticated topics without using mathematics or technical jargon. This makes the book highly accessible to all types of readers, from investors and investment professionals, to professors and their students.The book's style integrates a large quantity of clearly drawn charts which help anchor the readers' perceptions of the topics being examined, from inflation to taxes, to demographics.
Author: Turan G. Bali
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
This paper presents a comprehensive study of continuous time GARCH modeling with the thin-tailed normal and the fat-tailed Student-t and generalized error distributions. The paper measures the degree of mean reversion in stock return volatility based on the relationship between discrete time GARCH and continuous time diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean-reverting behavior of stock return volatility. The empirical evidence obtained from several stock market indices indicates that the conditional variance, log-variance, and standard deviation of stock market returns are pulled back to some long-run average level over time.
Author: Timothy Ling
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The local volatility model is a well-known extension of the Black-Scholes constant volatility model whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide range of implied volatility surfaces. The model is easy to calibrate and still very popular in foreign exchange option trading. In this paper we address a question of validation of the Local Volatility model. Different stochastic models for the underlying asset can be calibrated to provide a good fit to the current market data but should be recalibrated every trading date. A good fit to the current market data does not imply that the model is appropriate and historical backtesting should be performed for validation purposes. We study delta hedging errors under the local volatility model using historical data from 2005 to 2011 for the AUD/USD implied volatility. We performed backtests for a range of option maturities and strikes using sticky delta and theoretically correct delta hedging. The results show that delta hedging errors under the standard Black-Scholes model are no worse than that of the Local Volatility model. Moreover, for the case of in and at the money options, the hedging error for the Back-Scholes model is significantly better.
Author: Philippe J. Deschamps
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
This paper investigates three formulations of the leverage effect in a stochastic volatility model with a skewed and heavy-tailed observation distribution. The first formulation is the conventional one, where the observation and evolution errors are correlated. The second is a hierarchical one, where log-volatility depends on the past log-return multiplied by a time-varying latent coefficient. In the third formulation, this coefficient is replaced by a constant. The three models are compared with each other and with a GARCH formulation, using Bayes factors. MCMC estimation relies on a parametric proposal density estimated from the output of a particle smoother. The results, obtained with recent S&P500 and Swiss Market Index data, suggest that the last two leverage formulations strongly dominate the conventional one. The performance of the MCMC method is consistent across models and sample sizes, and its implementation only requires a very modest (and constant) number of filter and smoother particles.
Author:
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Category :
Languages : en
Pages :
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Author: Amaan Mehrabian
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
A striking empirical feature of many financial time series is that when the price drops, the future volatility increases. This negative correlation between the financial return and future volatility processes was initially addressed in Black 76 and explained based on financial leverage, or a firm's debt-to-equity ratio: when the price drops, financial leverage increases, the firm becomes riskier, and hence, the future expected volatility increases. The phenomenon is, therefore, traditionally been named the leverage effect. In a discrete time Stochastic Volatility (SV) model framework, the leverage effect is often modelled by a negative correlation between the innovation processes of return and volatility equations. These models can be represented as state space models in which the returns and the volatilities are considered as the observed and the latent state variables respectively. Including the leverage effect in the SV model not only results in a better fit ...
Author: Hong Jiang
Publisher:
ISBN:
Category : Asset-liability management
Languages : en
Pages : 125
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Author: Rabiul Beg
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
Most asset prices are subject to significant volatility. Arrival of new information is viewed as the main source of volatility. As new information is continually released, financial asset prices exhibit volatility persistence, which affects financial risk analysis and risk management strategies. This paper proposes a nonlinear regime switching threshold generalized autoregressive conditional heteroskedasticity (RS-TGARCH) model which can be used to analyze financial data. The empirical results based on quasi maximum likelihood estimation presented in this paper suggest that the proposed model is capable of extracting information about the sources of volatility persistence in the presence of leverage effect.
