Barndorff‐Nielsen and Shephard model for hedging energy with quantity risk

Abstract

In this paper, the Barndorff‐Nielsen and Shephard (BN‐S) model is implemented to find an optimal hedging strategy in the presence of quantity risk for oil produced in the Bakken, a new region of oil extraction that is benefiting from fracking technology. Hedging and price risk management become much more involved with the inclusion of quantity risk. Explorers and drillers have uncertainty on the quantity of oil that would be extracted, and governments have uncertainty of the quantity of oil that will be extracted, sold, and available for imposing tax regimes. One of the main assumptions typically made in a portfolio model of hedging is that the quantity of inventory or demand is known. This is inappropriate in many hedging situations. Quantity risk compounds the difficulty of determining the optimal size of the position under both price and production risk. In this paper, we provide a novel way of handling the quantity risk in connection with the BN‐S model. The model is analyzed as a quadratic hedging problem and related analytical results are developed. The results indicate that oil can be optimally hedged with a combination of variance swaps and options. For various quantity risks, the model is implemented to analyze hedging decisions numerically for managing price risk in the Bakken oil commodities.

Stochastic Analysis and Neural Network-Based Yield Prediction with Precision Agriculture

“…There are some special cases of the proposed model that are studied in the literature in connection to the financial market; for example, the Barndorff-Nielsen and Shephard model (BN-S model). For such a model, the target variable is the stock, see, Shephard (2001a, 2001b); Habtemicael and SenGupta (2016); Issaka and SenGupta (2017) or the commodity price (see, Roberts and SenGupta (2020); SenGupta et al ( 2019); Shoshi and SenGupta (2021); Wilson et al (2019), S = (S t ) t≥0 . On some filtered probability space (Ω, G, (G t ) 0≤t≤T , P) it is modeled by S t = S 0 exp(X t ),…”

A data-science-driven short-term analysis of Amazon, Apple, Google, and Microsoft stocks

“…There are some special cases of the proposed model that are studied in literature in connection with the financial market, such as the Barndorff-Nielsen and Shephard (BN-S) model. For the BN-S model, the share price (see , [4,5,13]) or commodity price (see, [17,18]) S t on some risk-neutral probability space (Ω, G, (G t ) 0≤t≤T , Q) is modeled by…”

Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging

“…In this subsection, we analyze an optimal hedging strategy in terms of quadratic hedging in connection to the fractional BN-S stochastic volatility model. Quadratic hedging is a hedging strategy that minimizes the hedging error in the mean square sense (see [28,29,33]). For the simplicity of notation, we denote the arbitrage-free variance swap price (P Var (t, σ 2 t )) by P (t, σ 2 t ).…”

“…Swaps written on the market volatility are financial instruments that are becoming increasingly useful for hedging and speculation of volatility. In recent literature (see [28,33]) variance swaps are implemented to reduce the quadratic hedging errors of oil commodities. In general, a swap is a financial derivative in which two counter-parties exchange cash flows of two securities, interest rates, or other financial instruments for the mutual benefit of the exchangers.…”