arXiv · arXiv q-fin · 2018
We introduce a multi-factor stochastic volatility model for commodities that incorporates seasonality and the Samuelson effect. Conditions on the seasonal term under which the corresponding volatility factor is well-defined are given, and five different specifications of the seasonality pattern are proposed. We calculate the joint characteristic function of two futures prices for different maturities in the risk-neut…
Lorenz Schneider, Bertrand Tavin
arXiv · arXiv q-fin · 2015
We introduce a multi-factor stochastic volatility model based on the CIR/Heston volatility process that incorporates seasonality and the Samuelson effect. First, we give conditions on the seasonal term under which the corresponding volatility factor is well-defined. These conditions appear to be rather mild. Second, we calculate the joint characteristic function of two futures prices for different maturities in the p…
Lorenz Schneider, Bertrand Tavin
arXiv · arXiv q-fin · 2014
We introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping factors to their volatility coefficients. The pricing of single underlying European options on futures contracts is straightforward and can incorporate the volatility smile or skew o…
Lorenz Schneider, Bertrand Tavin
arXiv · arXiv q-fin · 2026
In this paper, we develop a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect. After the theoretical analysis of this general model, we focus on the rBergomi and rHeston models and their calibration to market data of vanilla futures options on WTI Crude Oil. Finally, numerical r…
Roberto Daluiso, Héctor Folgar-Cameán, Andrea Pallavicini, Carlos Vázquez
arXiv · arXiv q-fin · 2025
This paper investigates optimal execution strategies in intraday energy markets through a mutually exciting Hawkes process model. Calibrated to data from the German intraday electricity market, the model effectively captures key empirical features, including intra-session volatility, distinct intraday market activity patterns, and the Samuelson effect as gate closure approaches. By integrating a transient price impac…
Konstantinos Chatziandreou, Sven Karbach
arXiv · arXiv q-fin · 2017
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure, decorrelation of moves in different points on the forward curve, and implied volatility skew and smile. This model is a "forward curve model" - it describes the stochastic evolution of…
Mark Higgins
arXiv · arXiv q-fin · 2025
We consider a competitive market with risk-averse participants. We assume that agents' risks are measured by coherent risk measures introduced by Artzner et al. (1999). Fundamental theorems of welfare economics have long established the equivalence of competitive equilibria and system welfare optimization (see, e.g., Samuelson (1947)). These have been extended to the case of risk-averse agents with complete risk mark…
Iman Khajepour, Geoffrey Pritchard, Danny Ralph, Golbon Zakeri
arXiv · arXiv q-fin · 2020
We formulate an equilibrium model of intraday trading in electricity markets. Agents face balancing constraints between their customers consumption plus intraday sales and their production plus intraday purchases. They have continuously updated forecast of their customers consumption at maturity with decreasing volatility error. Forecasts are prone to idiosyncratic noise as well as common noise (weather). Agents prod…
René Aid, Andrea Cosso, Huyên Pham
arXiv · arXiv q-fin · 2020
In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period of time. In this paper, we introduce a market price for the delivery periods of electricity swaps, thereby opening an arbitrage-free pricing framework for derivatives based on these contracts. Furthermore, we use a weighted geometric averaging of an artificial geometric futures price over the corresp…
Annika Kemper, Maren D. Schmeck, Anna Kh. Balci
arXiv · arXiv q-fin · 2017
Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probability measures should be of second order (and non-Markovian), instead of first order models à la Bach…
Nguyen Tien Zung
arXiv · arXiv q-fin · 2008
A financial market is called "diverse" if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of "weak diversity" and "asymptotic weak diversity") in precise terms. We show that diversity is possible to achieve, but delica…
Robert Fernholz, Ioannis Karatzas, Constantinos Kardaras
arXiv · arXiv q-fin · 1998
Some problems with the recent stimulating proposal of a ``Gauge Theory of Finance'' by Ilinski and collaborators are outlined. First, the derivation of the log-normal distribution is shown equivalent both in information and mathematical content to the simpler and well-known derivation, dating back from Bachelier and Samuelson. Similarly, the re-derivation of Black-Scholes equation is shown equivalent to the standard …
D. Sornette