Tag Archives: Volatility

The Mathematics of Scalping

NOTE:  if you are unable to see the Mathematica models below, you can download the free Wolfram CDF player and you may also need this plug-in. You can also download the complete Mathematica CDF file here. In this post I want … Continue reading

Posted in Futures, Mathematca, Mathematica, Scalping, Trading, Volatility Modeling | Tagged , , , , , , , , , , , , , , , , | Comments Off

Implied Volatility in Merton’s Jump Diffusion Model

The “implied volatility” corresponding to an option price is the value of the volatility parameter for which the Black-Scholes model gives the same price. A well-known phenomenon in market option prices is the “volatility smile”, in which the implied volatility … Continue reading

Posted in Options, Stochastic Differential Equations, Volatility Modeling | Tagged , , , | Comments Off

Option Prices in the Variance Gamma Model

Posted in Mathematica, Options, Volatility Modeling | Tagged , , , | Comments Off

Volatility Forecasting in Emerging Markets

The great majority of empirical studies have focused on asset markets in the US and other developed economies.   The purpose of this research is to determine to what extent the findings of other researchers in relation to the characteristics of … Continue reading

Posted in Asian markets, Cointegration, Econometrics, Emerging Markets, FIGARCH, Forecasting, Fractional Cointegration, Fractional Integration, Granger Causality, Hurst Exponent, Long Memory, REGARCH | Tagged , , , , , , , , , , | Comments Off

On Testing Direction Prediction Accuracy

As regards the question of forecasting accuracy discussed in the paper on Forecasting Volatility in the S&P 500 Index, there are two possible misunderstandings here that need to be cleared up.  These arise from remarks by one commentator  as follows: … Continue reading

Posted in Direction Prediction, Forecasting, Modeling, Options, S&P500 Index, Volatility Modeling, volatility sign prediction forecasting Engle | Tagged , , , , , , , | Comments Off

Long Memory and Regime Shifts in Asset Volatility

This post covers quite a wide range of concepts in volatility modeling relating to long memory and regime shifts. The post discusses autocorrelation, long memory, fractional integration, black noise, white noise, Hurst Exponents, regime shift detections, Asian markets and various topics froms nonlinear dynamics. Continue reading

Posted in ARFIMA, Asian markets, Black Noise, Correlation Dimension, Correlation Integral, FIGARCH, Forecasting, Fractional Brownian Motion, Fractional Integration, Henon Attractor, Hurst Exponent, Logistic Attractor, Long Memory, Modeling, Nonlinear Dynamics, Pink Noise, Regime Shifts, Strange Attractor, Uncategorized, Volatility Modeling, White Noise | Tagged , , , , , , , , , , , , | Comments Off

Modeling Asset Volatility

I am planning a series of posts on the subject of asset volatility and option pricing and thought I would begin with a survey of some of the central ideas. The attached presentation on Modeling Asset Volatility sets out the foundation … Continue reading

Posted in Black Noise, Cointegration, Derivatives, Direction Prediction, Dispersion, Forecasting, Fractional Brownian Motion, Fractional Cointegration, Fractional Integration, Long Memory, Mean Reversion, Momentum, Multifactor Models, Options, Pink Noise, REGARCH, Regime Shifts, Volatility Modeling, White Noise | Tagged , , , , , , , , , , , , , , , , | Comments Off

Market Timing in the S&P 500 Index Using Volatility Forecasts

To illustrate some of the possibilities of this approach, we constructed a simple market timing strategy in which a position was taken in the S&P 500 index or in 90-Day T-Bills, depending on an ex-ante forecast of positive returns from the logit regression model (and using an expanding window to estimate the drift coefficient). We assume that the position is held for 30 days and rebalanced at the end of each period. In this test we make no allowance for market impact, or transaction costs.
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Posted in Binary Options, Forecasting, Logit Regression, Market Timing, S&P500 Index, Volatility Modeling, volatility sign prediction forecasting Engle | Tagged , , , , , , , , | Comments Off

Forecasting Volatility in the S&P500 Index

Echoing the findings of parallel empirical research, this study points to the conclusion that historical realized volatility adds little to the explanatory power of implied volatility forecasts. However, one perplexing feature of implied volatility forecasts is their persistent upwards bias. As a result, forecasting models using high-frequency historical data may have an edge over implied volatility forecasts in predicting the direction of future realized volatility. The ability to time the market by correctly predicting its direction approximately 62% of the time appears to offer the potential to generate abnormal returns by a simple strategy of buying and selling at-the-money straddles and delta-hedging the resulting positions on a daily basis through to expiration, even after allowing for realistic transaction and hedging costs. Continue reading

Posted in Derivatives, Forecasting, GARCH, Market Efficiency, Options, Volatility Modeling, volatility sign prediction forecasting Engle | Tagged , , , , , , , , | Comments Off

Using Volatility to Predict Market Direction

Although asset returns are essentially unforecastable, the same is not true for asset return signs (i.e. the direction-of-change). As long as expected returns are nonzero, one should expect sign dependence, given the overwhelming evidence of volatility dependence. Even in assets where expected returns are zero, sign dependence may be induced by skewness in the asset returns process. Hence market timing ability is a very real possibility, depending on the relationship between the mean of the asset returns process and its higher moments.
Empirical tests demonstrate that sign dependence is very much present in actual US equity returns, with probabilities of positive returns rising to 65% or higher at various points over the last 20 years. A simple logit regression model captures the essentials of the relationship very successfully Continue reading

Posted in Forecasting, Volatility Modeling | Tagged , | Comments Off