Price movements in many commodity markets exhibit significant seasonal patterns. In this paper, we study the effects of seasonal volatility on models’ option pricing performance. In terms of options pricing, a deterministic seasonal component at the price level can be neglected. In contrast,...

Many commodity markets contain a strong seasonal component in volatility. In this paper, the importance of this seasonal behavior for the pricing of commodity options is analyzed. We propose a stochastic volatility model where the drift term of the variance process captures the observed seasonal...

In this paper we study the stochastic behavior of the prices and volatilities of a sample of six of the most important commodity markets and we compare these properties to those of the equity market. We observe a substantial degree of heterogeneity in the behavior of the series. Our findings...

The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle can not be applied. In this paper, we derive a model-free analytical formula for the implied...

In this paper we develop a continuous time factor model of commodity prices that allows for higher order autoregression and moving average components. The need for these components is documented by analyzing the convenience yield's time series dynamics. Making use of the affine model structure,...

Different theoretical and numerical methods for calculating the fair-value of a variance swap give rise to systematic biases that are most pronounced during volatile periods. For instance, differences of 10-20 percentage points would have been observed on fair-value index variance swap rates...

Most research on option hedging has compared the performance of delta hedges derived from different stochastic volatility models with Black-Scholes-Merton (BSM) deltas, and in particular with the `implied BSM’ model in which an option’s delta is based on its own market implied volatility....

Conditional returns distributions generated by a GARCH process, which are important for many problems in market risk assessment and portfolio optimization, are typically generated via simulation. This paper extends previous research on analytic moments of GARCH returns distributions in several...

This paper examines the ability of several different continuous-time one and two-factor jump-diffusion models to capture the dynamics of the VIX volatility index for the period between 1990 and 2010. For the one-factor models we study affine and non-affine specifications, possibly augmented with...

A comprehensive description of the trading and statistical characteristics of VIX futures and their exchange-traded notes motivates our study of their benefits to equity investors seeking to diversify their exposure. We analyze when diversification into VIX futures is ex-ante optimal for...