JonathanData, Derivatives, Mathematica, Matlab, OptionsData Analysis, Historical data, Mathematica, Options

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Home Archive by Category "Derivatives"

JonathanDerivatives, Financial Engineering, MathematicaDerivatives, Financial engineering, Geometric Brownian Motion, Mathematica, Stochastic Calculus, Wiener Process

Wolfram Research introduced random processes in version 9 of Mathematica and for the first time users were able to tackle more complex modeling challenges such as those arising in stochastic calculus. The software’s capabilities in this area have grown and matured over the last two versions to a point where it is now feasible to teach…

JonathanBlack 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 NoiseBlack Noise, Cointegration, Direction Prediction, Fractional Brownian Motion, Fractional Cointegration, Fractional Integration, GARCH, Long Memory, Mean Reversion, Momentum, MultiFactor Models, Pink Noise, REGARCH, Regime Shifts, Volatility, Volatility Dynamics, White Noise

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 for a number of key concepts and the basis for the research to follow. Perhaps…

JonathanDerivatives, Forecasting, GARCH, Market Efficiency, Options, Volatility Modeling, volatility sign prediction forecasting EngleARFIMA, Direction Prediction, GARCH, Kurtosis, Long Memory, Market Efficiency, Option Pricing, Volatility, Volatility Risk

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.

JonathanDerivatives, Financial Engineering, Hybrid Products, Model ReviewDerivatives, Financial engineering, Hybrid Products, Model Review

The LNVM model is a mixture of lognormal models and the model density is a linear combination of the underlying densities, for instance, log-normal densities. The resulting density of this mixture is no longer log-normal and the model can thereby better fit skew and smile observed in the market. The model is becoming increasingly widely used for interest rate/commodity hybrids.

In this review of the model, Iexamine the mathematical framework of the model in order to gain an understanding of its key features and characteristics.

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