Pricing and hedging options in energy markets using Black-76

Benth, Fred Espen; Schmeck, Maren Diane

doi:10.21314/jem.2014.114

Cited by 14 publications

(27 citation statements)

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“…for independent standard Brownian motions B i , also independent of B, and constants β i > 0 and σ i > 0 for i ∈ I = {1, .., n}. In (2.3), we choose the drivers of the stationary components to be Gaussian in contrast to Benth and Schmeck [5], who use pure jump Lévy processes. There, the main target are the spikes.…”

Section: The Spot Price Dynamics and Implied Forward And Option Pricesmentioning

confidence: 99%

Pricing Options on Forwards in Energy Markets: The Role of Mean Reversion's Speed

Schmeck

2016

Int. J. Theor. Appl. Finan.

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Consider the problem of pricing options on forwards in energy markets, when spot prices follow a geometric multi-factor model in which several rates of mean reversion appear. In this paper we investigate the role played by slow mean reversion when pricing and hedging options. In particular, we determine both upper and lower bounds for the error one makes neglecting low rates of mean reversion in the spot price dynamics.Keywords: electricity spot prices, multi-scale mean reversion, delivery period, options on forwards, hedging, pricing error, upper and lower bounds.

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Section: The Spot Price Dynamics and Implied Forward And Option Pricesmentioning

confidence: 99%

Pricing Options on Forwards in Energy Markets: The Role of Mean Reversion's Speed

Schmeck

2016

Int. J. Theor. Appl. Finan.

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“…We consider spread options, where one bets on the difference of two risky assets. Article [3] discusses pricing and hedging of options in energy markets. Big spikes can generally appear in the spot price data, that return quickly back to the normal price level.…”

Section: The Brownian Approximation Of Small Jumpsmentioning

confidence: 99%

“…For a comprehensive text book on stochastic modeling of electricity markets, see Benth et al [19]. The models for the spot price that we use in Article [3] and Article [4] are based on the two-factor model for commodity prices from Schwartz and Smith [55] (see also Gibson and Schwartz [42]). It was applied to electricity spot prices by Lucia and Schwartz [47].…”

Section: Energy Marketsmentioning

confidence: 99%

“…It was applied to electricity spot prices by Lucia and Schwartz [47]. In Article [3] and [4] we do not concentrate on improving the pathwise fit of spot and futures, but are interested in option pricing. Therefore we choose tractable, established models, that might not be as sophisticated as the ones that where recently suggested, but provide a satisfying distributional fit.…”

Section: Energy Marketsmentioning

confidence: 99%

“…This is analysed for the implied forward dynamics in Benth et al [19]. In Article [3], we go further and quantify the impact of the spikes on the option prices.…”

Section: Energy Marketsmentioning

confidence: 99%

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Stability of Merton's portfolio optimization problem for Lévy models

Benth

Schmeck

2012

Stochastics

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In the process of modeling, the agent has to make a number of decisions. Therefore two agents can set up different models. This thesis compares the influence of different model choices to stochastic control theory and option pricing. On the one hand it quantifies analytically error bounds in terms of key parameters. On the other hand it checks the implications of model choices empirically. Lévy processes are popular in financial modeling since they are able to explain many of the stylized facts of asset prices. In particular, some processes like the normal inverse Gaussian (NIG) or the hyperbolic Lévy process have become particularly relevant since they are able to capture the return distribution of most asset prices. These Lévy processes are pure-jump, and therefore give distinctively different paths of the asset prices compared to a Brownian motion with continuous paths. In empirical analysis of financial price data, one may detect big jumps, however, the small jumps are very hard to separate from the observations of a Brownian motion. Thus, it is not a simple task to decide whether a Lévy process with jumps or a Brownian motion is governing the small variations in a stock price, say. First Merton's portfolio optimization problem is considered. We aim for a mathematical quantification of the difference of the optimal investment strategies and find error bounds that are proportional to the variation of the small jumps. Then option pricing is considered, where there are two underlying assets that are dependent. Here the error bounds turn out to be of the same type as in Article 1. The second part of the thesis considers the pricing of options on forwards in energy markets. Many models for the electricity spot price divide the price evolutions into a short-term and a long-term component. Electricity markets are well-known for their large price variations and rare, big spikes, which are captured by the short-term component. We examine the influence of the short-term and long-term factor on the spot and prove that the short-term factor is insignificant for pricing options in many relevant cases. The electricity spot is not a tradable asset and the no-arbitrage argumentation that is based on cost and carry strategies cannot be applied. Therefore one can use different measures to price the futures and the option. The goal of this paper is to examine empirically wether or not the traded options are priced under the same pricing measure as the futures. Before doing so, we need to specify a model for spot and futures and fit it to data. The results indicate that one should use a different measure to price the option. i ACKNOWLEDGMENTS I am grateful to many people for their support and help during my work on the thesis. First of all I would like to thank my principal supervisor Fred Espen Benth for his guidance, support and inspiring collaboration. This thesis would not exist without him. I also would like to thank my subsidiary supervisor Erik Bølviken as well as my co-authors Giulia Di Nunno and Asma Khedher for sharing...

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Valuation of Spark-Spread Option Written on Electricity and Gas Forward Contracts Under Two-Factor Models with Non-Gaussian Lévy Processes

Mehrdoust

Noorani

2022

Comput Econ

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Pricing and hedging options in energy markets using Black-76

Cited by 14 publications

References 0 publications

Pricing Options on Forwards in Energy Markets: The Role of Mean Reversion's Speed

Pricing Options on Forwards in Energy Markets: The Role of Mean Reversion's Speed

Stability of Merton's portfolio optimization problem for Lévy models

Valuation of Spark-Spread Option Written on Electricity and Gas Forward Contracts Under Two-Factor Models with Non-Gaussian Lévy Processes

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