Financial Mathematics with Applications in Energy Markets
Optimal Regulation of Renewable Energy
Climate Finance
We investigate the optimal regulation of energy production in alignment with the long-term goals of the Paris Climate Agreement. We analyze the optimal regulatory incentives to foster the development of non-emissive electricity generation when the demand for power is met either by a single firm or by two interacting agents. The regulator aims to encourage green investments to limit carbon emissions while simultaneously reducing the intermittency of total energy production. We find that the regulator can achieve a higher certainty equivalent by regulating two interacting firms, each investing in one technology, rather than a single firm managing both technologies. This higher value is achieved thanks to a greater degree of freedom in the incentive mechanisms, which involve cross-subsidies between firms. Moreover, we find that it is optimal to compensate firms for shutting down their emissive production assets. We provide closed-form expressions of the second-best contracts and show that they take a rebate form, involving time-dependent prices for each state variable. A numerical study quantifies the impact of the designed second-best contract in both market structures compared to the business-as-usual scenario.
In this paper, we provide empirical evidence on the market price of risk for delivery periods (MPDP) of electricity swap contracts. As introduced by Kemper et al. (2022), the MPDP arises through the use of geometric averaging while pricing electricity swaps in a geometric framework. In preparation for empirical investigations, we adjust the work by Kemper et al. (2022) in two directions: First, we examine a Merton type model taking jumps into account. Second, we transfer the model to the physical measure by implementing mean-reverting behavior. We compare swap prices resulting from the classical arithmetic (approximated) average to the geometric weighted average. Under the physical measure, we discover a decomposition of the swap's market price of risk into the classical one and the MPDP. In our empirical study, we analyze two types of models, characterized either by seasonality in the delivery period or by a term-structure effect, and identify the resulting MPDP in both cases.
In this paper, we provide empirical evidence of the market price of risk for delivery periods (MPDP) of electricity swap contracts. The MPDP enables an accurate pricing of such contracts in the presence of the delivery period such that the typical approximations can be avoided. In our empirical study, we focus on term-structure effects and identify the resulting MPDP. In presence of the Samuelson effect, we find the most pronounced MPDP close to maturity, while the MPDP disappears proportional to the Samuelson effect far away from maturity. Thus, our theory improves the pricing accuracy close to maturity.
The Market Price of Risk for Delivery Periods: Pricing Swaps and Options in Electricity Markets (Energy Economics, 2022) with Maren D. Schmeck & Anna Kh.Balci
In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period of time. In this paper, we introduce a market price for the delivery periods of electricity swaps, thereby opening an arbitrage-free pricing framework for derivatives based on these contracts. Furthermore, we use a weighted geometric averaging of an artificial geometric futures price over the corresponding delivery period. Without any need for approximations, this averaging results in geometric swap price dynamics. Our framework allows for including typical features as the Samuelson effect, seasonalities, and stochastic volatility. In particular, we investigate the pricing procedures for electricity swaps and options in line with Arismendi et al. (2016), Schneider and Tavin (2018), and Fanelli and Schmeck (2019). A numerical study highlights the differences between these models depending on the delivery period.