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This chart is very similar to the Matlab output as we should expect. Below are 500 possible prices over the one year simulation period: See the Matlab post for the actual equations. The (risk neutral) natural gas price evolves over time according to a mean reverting one factor Hull-White stochastic differential equation. The payoff from exercising the swing is determined by the price of natural gas.

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Note that the user is free to change any of these assumptions. Additionally the inputs generally mirror the inputs of the Matlab model so refer to that post for specific details. The option can be exercised only once per day even if multiple exercise rights remain.īelow is the user panel for this model, I won’t go through each of the inputs as help balloons are enabled so just hover your cursor over an input’s name and a description will appear. The contract term is one year and the option can be exercised on any day during the year. The model assumes 5 exercise rights, as in the Matlab model, but the user can change this assumption. For benchmarks comparing Julia to Matlab see here.) The ModelĪs mentioned above the example here is a natural gas swing option which assumes a daily contract quantity and a given number of exercise rights during the contract term when the quantity can be “swung” above or below the daily contract quantity. However that model is not a swing option, just a standard American option. (An example Julia model using the LSM approach for option valuation is here. While Analytica is my favorite modeling environment, a plan for the summer is to redo many of my posts in Julia, which is a great open source alternative to Matlab. However unlike the Matlab example, the model here allows the user to enter the order of the approximating power series, which can only be of order three in the Matlab model. The price process is the same in the Analytica model and in the Matlab example. I might add these features in a separate post, so stay tuned.

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Additionally the Matlab example demonstrates how to bound the value of the option between upper and lower bounds using European and American option values.

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The Matlab model is a little more extensive than my example, as it also demonstrates using a smoothing spline regression as an alternative to approximating the continuation value with a power series regression.

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You can download the swing options example here:Ī comparable model in Matlab, on which my example is based, is demonstrated at the MathWorks website here. You will need the free version to open and change the model. The model here was created in Analytica, which remains my favorite modeling language.

Lastly Glasserman (2004) chapter 8 has an in depth discussion of how to solve options with early exercise features using the LSM approach along with several other Monte Carlo techniques and how they all fit together. Additionally see this nice answer on the StackExchange Quant Finance discussion describing the LSM algorithm in plain English. For further discussion and examples on LSM see my earlier posts where the LSM method is used to value a mine and also value a pharmaceutical patent. LSM is a powerful technique that combines Monte Carlo simulation with regression analysis and dynamic programming.

The valuation method used in this post is LSM. See Jaillet et al (2004) for a discussion of the relationship between the three option types.) (European and American options could be used but they would be excessively expensive due to their exercise features. A swing option in this situation would give the power company the ability to hedge their fuel needs on these hot days without having to pay the high daily spot price. A heat wave will cause a spike in electricity usage and energy prices as people crank up their air conditioners to stay cool. During the summer there is the risk of a heat wave hitting the city on any given day. be “swung”, between a high and a low volume level.Īs an example of why swing options are useful consider a power utility in Los Angeles that must prepare for the summer months. The options are called “swing” options because when the option is exercised the quantity can vary, i.e. These option contracts are important because of the high level of uncertainty in the volume needed to meet supply and demand as these conditions change rapidly over time. They allow managers flexibility in determining both the timing and quantity of delivery for energy and related commodities. Swing options are common option contracts in the energy industry. This post provides an example of how to value a natural gas swing option using the Least Squares Monte Carlo method (LSM).