Guidelines for the valuation of real options Whitepaper by Cyriel de Jong and Hans van Dijken. ‘Guidelines for the valuation of real options in energy markets’ discusses how flexible assets in energy markets such as gas storage, power plants, and transportation infrastructure, can be valued as real options. These assets give their owners the ability to respond dynamically to market conditions, creating additional value beyond simple fixed cash flows. The report emphasizes that accurate valuation is crucial for investment decisions, trading strategies, and risk management, enabling companies to better capture value and hedge exposures. Download directly this article Core components of valuation The valuation of real options relies on three essential building blocks. First, forward curves provide the market’s expectation of future prices and serve as the foundation for valuation. Second, price dynamics describe how prices evolve over time, with Monte Carlo simulations offering the most flexible and realistic representation compared to simplified formulas or tree models. Third, optimization determines how assets are operated under different price scenarios to maximize value. These elements must work together, as inaccuracies in any component can significantly distort the final valuation. Optimization approaches Different optimization techniques can be used to determine how assets should be operated. Approaches assuming perfect foresight, such as mixed integer linear programming (MILP) and dynamic programming (DP), are relatively straightforward but may overestimate value because they assume full knowledge of future prices. In contrast, methods that avoid perfect foresight, including stochastic trees and Least-Squares Monte Carlo (LSMC), better reflect real-world uncertainty. LSMC in particular combines simulation with regression techniques to estimate future value based only on available information, making it a powerful tool for complex energy assets. Modeling price dynamics A robust valuation requires realistic modeling of price behavior in both spot and forward markets. The paper stresses that models should be validated using statistical comparisons with historical data, such as mean values, volatility, and correlations. Simplified models, like trees, can be computationally efficient but may fail to capture the complexity of multi-commodity markets, where prices and spreads interact. Monte Carlo simulations are preferred because they can incorporate multiple commodities and realistic relationships between them. Conclusion: Best practices for valuation The study concludes that accurate valuation of real options depends on combining market-based forward curves, realistic price simulations, and robust optimization under uncertainty. While simpler methods may be faster, they often lead to mispricing, especially when flexibility is significant. Advanced approaches like Monte Carlo simulation combined with LSMC provide more reliable results, helping companies make better strategic decisions in energy markets characterized by volatility and complex price interactions. This whitepaper is realized by the software model KyOption. KyOption prices a wide variety of options used in the energy markets, such as calls and puts, single options and strips of options, commodity spread options and time spread options. Next to the value, KyOption also calculates the exposures of the options.

Option pricing for Power Prices with Spikes Energy Power Risk Management published an article by Cyriel de Jong and Ronald Huisman, February 2003. In ‘Option pricing for Power Prices with Spikes’, the authors conclude that European power prices are very volatile and subject to spikes. This is particularly true in German and Dutch markets. They examine the impact of spikes on option prices by comparing prices from a standard mean-reverting model and a regime model that disentangles the spike process from the mean-reverting dynamics. Download directly this article Why Electricity Prices Require a Different Valuation Approach Electricity markets behave differently from traditional financial markets and most commodity markets. Unlike oil or natural gas, electricity cannot be stored economically on a large scale and must be consumed as it is produced. As a result, power prices exhibit unique characteristics such as extreme volatility, sudden price spikes, mean reversion, and strong seasonal patterns. These features make standard option pricing models, which often assume log-normal price distributions, unsuitable for valuing electricity derivatives. The authors argue that existing valuation approaches fail to capture the impact of short-lived but significant price spikes. Traditional mean-reverting models tend to overestimate normal volatility while underestimating the true effect of extreme price movements. To address this problem, the paper introduces a new framework that separates normal price behaviour from spikes, enabling more accurate pricing of electricity options. This is particularly important for risk management, contract valuation, and strategic decision-making in power markets. The Two-Regime Model for Electricity Prices The proposed model assumes that electricity prices can exist in one of two regimes at any point in time: A normal regime, where prices follow a mean-reverting process and gradually return to a long-term equilibrium level. A spike regime, where prices suddenly rise to unusually high levels due to market disruptions such as generation outages or capacity shortages. Unlike previous three-regime models, the authors treat the normal and spike regimes as independent processes. When a spike ends, prices simply return to normal market conditions instead of passing through a separate correction phase. This simpler two-regime structure has an important advantage: it can accommodate multiple consecutive spikes, a common phenomenon in electricity markets. Previous models often struggled to represent prolonged periods of elevated prices. By separating spikes from normal price dynamics, the model also makes it easier to identify the specific contribution of spikes to option values. Calibration and Empirical Results from the Dutch Power Market To test the model, the authors use Dutch APX day-ahead electricity prices from January 2001 to June 2002, covering both base-load and peak-load products. The model parameters are estimated using maximum likelihood techniques and Kalman filtering, allowing the hidden regime structure to be inferred from observed prices. The results show that the two-regime model provides a significantly better fit to market data than a standard mean-reverting model. It identifies around 50% more spikes than an earlier three-regime approach and produces lower estimates for normal market volatility because sudden price shocks are explicitly assigned to the spike regime. The analysis indicates that spikes occur with a probability of roughly 8% to 14% on any given day and can lift prices to levels above €50/MWh. The model therefore captures the reality that extreme price events are not rare anomalies but an integral feature of electricity markets. Valuing Options Using Separate Normal and Spike Components A key innovation of the framework is the decomposition of option values into two distinct parts: a normal-price component and a spike component. Since the market can end up in either regime at option maturity, the total option value is calculated as a probability-weighted combination of the two outcomes. This approach provides a clearer understanding of risk than traditional models. Standard models effectively average the extreme volatility of spikes with the moderate volatility of normal market conditions. As a result, they significantly underestimate the probability of large price movements. The authors also ensure that the model remains consistent with observed forward market prices. Instead of attempting to forecast all future market expectations directly, they calibrate the model to existing forward curves and then apply their improved representation of spot-price dynamics. This allows market information and realistic price behaviour to be incorporated simultaneously. Impact of Spikes on Option Values The study demonstrates that spikes contribute substantially to option values, especially for out-of-the-money call options and longer maturities. When comparing the two-regime model with a traditional mean-reverting model, the differences are striking. Standard models suggest that many out-of-the-money options have almost no value because prices are expected to return quickly to equilibrium. The two-regime model shows that future spikes remain possible even when average prices revert, giving these options meaningful value. For example, a baseload call option with a strike price of €50/MWh and a 15-day maturity is valued at only €0.02/MWh under the mean-reverting model. Under the two-regime model, the same option is worth approximately €3.43/MWh. Such differences can have major consequences for pricing, hedging, and risk assessment. Implications for Electricity Contracts and Risk Management The findings have important practical implications. Many retail electricity contracts contain embedded caps that protect customers from excessive price increases. These caps are economically equivalent to a series of call options on electricity prices. If utilities use conventional mean-reverting models, they may dramatically underestimate the cost of providing such protection. The authors illustrate this with a capped July electricity contract: when spikes are properly incorporated, the cap is worth approximately €3.43/MWh. Using a standard model, the value falls to only €0.02/MWh. The paper concludes that any realistic valuation framework for electricity derivatives must explicitly account for price spikes. Ignoring them leads to mispriced options, inadequate hedging strategies, and potentially significant financial losses. The two-regime model offers a practical and more accurate way to value flexibility and risk in modern power markets.

Cointegration between gas and power spot prices Journal of Energy Management: article by Cyriel de Jong and Stefan Schneider, about the cointegration between gas and power spot prices. Fall 2009. Download directly this article Introduction and research objective This paper develops a framework to model the joint behaviour of gas and power spot prices across interconnected energy markets. Rather than analysing individual commodities in isolation, the authors focus on how prices move together, particularly through spread relationships. The study examines gas markets in the UK (NBP), Belgium (Zeebrugge), and the Netherlands (TTF), alongside power prices from the Dutch APX market. The goal is to use cointegration techniques to capture both short-term dynamics and long-term equilibrium relationships between these markets, which are crucial for valuation, trading, and risk management. Cointegration and market fundamentals Cointegration is introduced as a concept that captures long-term relationships between price series, even when individual prices are non-stationary. While correlation explains short-term co-movements, cointegration reflects underlying economic forces such as physical connections, transportation links, and fuel substitution. In energy markets, these relationships arise from gas flows between hubs and the use of gas in power generation. The authors model these interactions through mean-reverting spreads, where deviations from equilibrium are corrected over time. Modelling approach The paper combines mean-reverting spot price models with forward price information, treating spot prices as reverting toward month-ahead forward prices. A multi-market framework is then built, linking different markets through cointegration of their spot–forward spreads. For power prices, additional complexity is introduced through regime-switching models to capture price spikes. This integrated approach allows the model to replicate realistic dynamics, including volatility, seasonality, and abrupt price changes across multiple energy markets. Empirical findings Empirical results show strong cointegration among gas markets, particularly between geographically connected hubs such as TTF, Zeebrugge, and NBP. These markets exhibit stable long-term relationships driven by physical infrastructure. In contrast, the relationship between gas and power spot prices is weaker at the short-term level. Instead, their connection appears primarily through forward prices, reflecting longer-term economic linkages such as fuel costs for power generation. Conclusion and implications The study concludes that cointegration is a powerful tool for modelling interconnected energy markets. By focusing on spreads rather than absolute prices, the model captures both short-term fluctuations and long-term equilibria. The findings highlight that gas markets are tightly integrated, while the gas–power relationship is more indirect and driven by forward market dynamics. This framework provides a practical basis for pricing, hedging, and risk management in energy trading environments, where cross-commodity and cross-market interactions are essential. KYOS Analytical model KyStore This paper is based on the methodologies that are implemented in the KyStore software. Use KyStore for pricing, risk managing and optimizing gas storage assets or contracts. For more information about our gas storage valuation software: KyStore. The gas storage optimization software not only raises revenues from gas storage trading operations, but also provides accurate valuations and reduces risk with adequate hedge recommendations. The model uses advanced stochastics including Least Squares Monte Carlo techniques to capture the full optionality in gas storage facilities.