Category Archives: Options

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

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Option Prices in the Variance Gamma Model

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Range-Based EGARCH Option Pricing Models (REGARCH)

The research in this post and the related paper on Range Based EGARCH Option pricing Models is focused on the innovative range-based volatility models introduced in Alizadeh, Brandt, and Diebold (2002) (hereafter ABD).  We develop new option pricing models using … Continue reading

Posted in Financial Engineering, Forecasting, Long Memory, Multifactor Models, Options, REGARCH, S&P500 Index, Volatility Modeling | 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

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

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