Herding and Stochastic Volatility

Stochastic volatility and stochastic leverage

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by m...

Herding, Information Cascades and Volatility Spillovers in Futures Markets

Stochastic Volatility

The volatility of a nancial asset is the variance per unit time of the logarithm of the price of the asset. Volatility has a key role to play in the determination of risk and in the valuation of options and other derivative securities. The widespread Black-Scholes model for asset prices assumes constant volatility. The purpose of this chapter is to review the evidence for non-constant volatilit...

Stochastic volatility

Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic time-varying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that...

Stochastic Volatility

In the original Black-Scholes model, the risk is quantified by a constant volatility parameter. It has been proposed by many authors that the volatilities should be modeled by a stochastic process to obtain a more realistic model. The volatility that corresponds to actual market data for option prices in Black-Scholes model is called the implied volatility. This volatility is in general depende...