Analytic Formulas for Futures and Options for a Linear Quadratic Jump Diffusion Model with Stochastic Convenience Yield and Seasonality: Do Fish Jump?

30 Pages Posted: 2 Apr 2020

See all articles by Christian Oliver Ewald

Christian Oliver Ewald

University of Glasgow; Høgskole i Innlandet

Yihan Zou

University of Glasgow - Adam Smith Business School

Multiple version iconThere are 2 versions of this paper

Date Written: December 28, 2019

Abstract

In this article we derive tractable analytic solutions for futures and options prices for a linear-quadratic jump-diffusion model with seasonal adjustments in stochastic volatility and convenience yield. We then calibrate our model to data from the fish pool futures market, using the extended Kalman filter and a quasi-maximum likelihood estimator and alternatively using an implied-state quasi-maximum likelihood estimator. We find no statis- tical evidence of jumps. However, we do find evidence for the positive correlation between salmon spot prices and volatility, seasonality in volatility and convenience yield. In addition we observe a positive relationship between seasonal risk premium and uncertainty within the EU salmon demand. We further show that our model produces option prices that are conform with the observation of implied volatility smiles and skews. Our work connects to a number of results that have recently appeared in the Operations Research literature.

Keywords: Finance, Derivatives, Jump-Diffusion Models, Kalman Filter, Quasi-Maximum Likelihood

Suggested Citation

Ewald, Christian Oliver and Zou, Yihan, Analytic Formulas for Futures and Options for a Linear Quadratic Jump Diffusion Model with Stochastic Convenience Yield and Seasonality: Do Fish Jump? (December 28, 2019). Available at SSRN: https://ssrn.com/abstract=3549778 or http://dx.doi.org/10.2139/ssrn.3549778

Christian Oliver Ewald

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Høgskole i Innlandet ( email )

Lillehammer, 2624
Norway

Yihan Zou (Contact Author)

University of Glasgow - Adam Smith Business School ( email )

United Kingdom

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