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In finance, the Heston model, named after Steven L. Heston, is a mathematical model that describes the evolution of the volatility of an underlying asset. [1] It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process.
Volatility as described here refers to the actual volatility, more specifically: . actual current volatility of a financial instrument for a specified period (for example 30 days or 90 days), based on historical prices over the specified period with the last observation the most recent price.
The Timer Call is an Exotic option, that allows buyers to specify the level of volatility used to price the instrument.. As with many leading ideas, the principle of the timer call is remarkably simple: instead of a dealer needing to use an implied volatility to use in pricing the option, the volatility is fixed, and the maturity is left floating.
Volatility is up, and the S&P 500 chalked both its best and worst day of the year this past week. And that you can have both in the span of a few days is an important market lesson.
Starting from a constant volatility approach, assume that the derivative's underlying asset price follows a standard model for geometric Brownian motion: = + where is the constant drift (i.e. expected return) of the security price , is the constant volatility, and is a standard Wiener process with zero mean and unit rate of variance.
The volatility of volatility controls its curvature. The above dynamics is a stochastic version of the CEV model with the skewness parameter β {\displaystyle \beta } : in fact, it reduces to the CEV model if α = 0 {\displaystyle \alpha =0} The parameter α {\displaystyle \alpha } is often referred to as the volvol , and its meaning is that of ...
The slope of the implied volatility smile reflects the market's expectations for future changes in the stock price, with a steeper slope indicating higher expected volatility. The author shows that the slope of the implied volatility smile is a significant predictor of stock returns, even after controlling for traditional risk factors.
The main idea behind these two models is that volatility is dependent upon past realizations of the asset process and related volatility process. This is a more precise formulation of the intuition that asset volatility tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time.