This book provides an advanced treatment of option valuation. The general setting is that of 2D continuous-time models with stochastic volatility. Explicit equilibrium risk adjustments and many other new results are provided. Mathematica code for the more important formulas is included. For a...

This paper proposes a new explanation for the smile and skewness effects in implied volatilities. Starting from a microeconomic equilibrium approach, we develop a diffusion model for stock prices explicitly incorporating the technical demand induced by hedging strategies. This leads to a...

In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of erivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes model; they have been developed in an effort to build models that are flexible enough to cope...

In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied Black-Scholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities....

This book provides an advanced treatment of option valuation. The general setting is that of 2D continuous-time models with stochastic volatility. Explicit equilibrium risk adjustments and many other new results are provided. Mathematica code for the more important formulas is included. For a...

This paper studies the behavior of the implied volatility function (smile) when the true distribution of the underlying asset is consistent with the stochastic volatility model proposed by Heston (1993). The main result of the paper is to extend previous results applicable to the smile as a...

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages,...

This book provides an advanced treatment of option valuation. The general setting is that of 2D continuous-time models with stochastic volatility. Explicit equilibrium risk adjustments and many other new results are provided. Mathematica code for the more important formulas is included. For a...

In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate...

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular...