In this paper we examine the effect of stochastic volatility on optimal portfolio choice in both partial and general equilibrium settings. In a partial equilibrium setting we derive an analog of the classic Samuelson–Merton optimal portfolio result and define volatility-adjusted risk aversion as the effective risk aversion of an individual investing in an asset with stochastic volatility. We ex...

This paper proposes a class of nonlinear stochastic volatility models. The proposed class encompasses many parametric stochastic volatility models that have appeared in the literature, including the well known lognormal stochastic volatility model. The new class is based on the Box-Cox transformation and offers an alternative to the one introduced in Andersen (1994). An advantage of our propose...

We show that there are two distinct ways to make volatility stochastic that are differentiated by their consequences for skewness. Most models in the literature have adopted the relatively tractable methodology of using stochastic time changes to engineer stochastic volatility. Unfortunately, this is also the one that can conflict with the relationship occasionally observed in markets between v...

This thesis examines the performance of five option pricing models with respect to the pricing of barrier options. The models include the Black-Scholes model and four stochastic volatility models ranging from the single-factor stochastic volatility model first proposed by Heston (1993) to a multi-factor stochastic volatility model with jumps in the spot price process. The stochastic volatility ...

The availability of intra-day data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets, called realised volatility, to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic distribution of the realised volatility erro...

In this paper, we study a family of stochastic volatility processes ; this family features a mean reversion term for the volatility and a double CEV-like exponent that generalizes SABR and Heston’s models. We derive approximated closed form formulas for the digital prices, the local and implied volatilities. Our formulas are efficient for small maturities. Our method is based on differential ge...

Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. Dynamic panel data models have become increasingly popular in macroeconomics to study common relationships across countries or regions. This paper estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao-Blackw...