**2. Related Literature**

Following the full-scale liberalization of electricity retailing, constructing forward market has become an urgen<sup>t</sup> agenda for the further vitalization of the electricity wholesale market, which is an important source of power procurement for electricity retailers. It is crucial to develop an electricity forwards market that can effectively aid the formation of fair and transparent price indicators and help to hedge against the risk of fluctuations in electricity wholesale prices.

Lucia et al. (2002) [5] and Pilipovic (1998) [6] examined the importance of the regular pattern in the behavior of electricity prices and its implications for the purposes of forward pricing. Other empirical papers, such as those by Escribano et al. (2002) [7], Eydeland et al. (2003) [8], Huisman et al. (2003) [9], and Maekawa et al. (2018) [10], have introduced a panel model for determining hourly electricity prices in forward markets and thus examined their characteristics. These models consider several factors: seasonality, regime switching, or price spikes.

Research in this field has been actively conducted recently. For example, Botterud et al. (2010) [11] analyzed 11 years of historical spot and forward prices from the hydro-dominated electricity market and found that forward prices tended to be higher than spot prices.

By using multivariate models, Raviv et al. (2015) [12] demonstrated that the disaggregated hourly prices contained useful predictive information of the daily average price in the Nord Pool market.

All these papers utilized an empirical perspective. However, to understand the relationship between spot prices and forward prices, it is essential to construct a microeconomic theoretical model. The power market has many special conditions, and it is difficult to simply adopt any particular economic point of view.

In response to these empirical studies, power market prices are being modeled in many studies. There is a long list of papers for wholesale power prices and electricity derivatives (e.g., Cartea et al. (2005) [13], Weron (2007) [14], Hikspoors et al. (2007) [15], Benth et al. (2008) [16], and Jaimungal et al. (2011) [17]). Their models are very sophisticated and their relevance to the empirical data is deep. However, because they emphasize the relationship between investors and the market, they are not an economically closed model. To understand the relationship between spot prices and forward prices, it is essential to construct a microeconomic theoretical model. However, the power market has many special conditions, and it is difficult to simply adopt any particular economic point of view. The construction of theoretical model is expected to facilitate easier utilization of economic findings. We introduce a speculative model with heterogeneous beliefs to the electricity market.

Similar to our research, Cartea et al. (2018) [18] derived an investor's optimal trading strategy of electricity contracts traded in two locations. Their strategy was based on ambiguity averse to price spikes. Our model is to analyze speculative behavior of the more essential power market. We add more fundamental condition of electricity market features to a speculative market model and analyze speculative trading by electric suppliers, not investors.

The purpose of this paper is to provide a new theoretical foundation to understand the factors that drive the electricity markets. In our model, speculative behavior has a strong influence on the price of the electricity market. In addition, it is due to the strong presence of market participant heterogeneity.

The field of speculative model construction along with heterogeneous belief has been the target of study for a long time. If all investors possess a common belief, there is no incentive for trading assets. However, as some heterogeneity exists in investors' belief, each investor assigns a different value to the asset, and a trade can occur.

At first, Miller (1977) [19] and Harrison et al. (1978) [20] created speculative models by using the heterogeneous belief agent. Townsend (1983) [21] and Singleton (1987) [22] pointed out the importance of heterogeneous beliefs in economics. Market prices are influenced by fundamentals, but players' beliefs are also essential factors for determining prices. Sheinkman et al. (2003) [23] evolved these models to adapt to more general asset models. Thus, heterogeneity is treated in the theoretical model as a large driving force that drives the market.

For instance, in the energy market, as discussed by Gabriel et al. (2009) [24], investors can exert both strategic and hedging behaviors by utilizing heterogeneous expectations. Utilizing significant evidence, Joets (2015) [25] found that energy markets are composed of heterogeneous traders who exhibit different behaviors depending on the intensity of the price fluctuations and the uncertainty.

This paper uses the heterogeneity of market participants to create a new price model of speculative electricity market. We found that the speculative trading relaxes the price spikes. Electric price spikes are discussed in many papers (Huisman et al. (2003) [9], Weron et al. (2004) [26], Cartea et al. (2005) [13], Escribano et al. (2002) [7], Knittel et al. (2005) [27] and Chan et al. (2008) [28]). In these papers, some quantitative models are embedded with price spikes by using several factors such as seasonality, risks and events. Although the relationship between our speculative behavior and the price spike is simple, it can also contribute to the development of these studies.

#### **3. Model Bases and Materials: Electricity Market Features**

Our model was created based on the features of these JEPX market attributions. The following conditions are assumed in our model.

• Cost function follows the "merit order curve".


Since the marginal cost is almost constant under the same power generation method, the power generation company efficiently generates power to meet the limits such that marginal costs remain low in accordance with the demand.

In a power market, "merit order effect" is used as a term to describe the mechanism by which the market price is determined. The electric power supply is determined based on the "merit order"; among these, the sources with the cheapest marginal costs (mostly renewable energy sources such as wind power, solar energy, hydroelectric power, and nuclear power) will be sold more quickly. Renewable energy sources such as photovoltaic solar power, wind power, and hydroelectric power are located at the left end in the merit order curve because they have little marginal costs. Based on this, nuclear power, coal, oil, and natural gas follow in order (see Figure 1).

#### **Figure 1.** Merit order curve.

For the purposes of this study, we assumed that there are two types of suppliers: normal suppliers and renewable suppliers. Although regional monopolistic companies participate in the electricity market, there are no regional differences in power prices in areas other than Hokkaido, and, as a result of inter-regional competition, a single company cannot wield exclusive market power in JEPX. Recently, new suppliers who deal with renewable energy sources have begun to participate in JEPX, but most of them are small and local companies.

This paper's major results include determining the relationship between forward price and spot price. Two types of products are currently being traded on JEPX: spot market products and forward market products. Moreover, there are four types of forward products: monthly 24-h products, weekly 24-h products, monthly daytime products, and weekly daytime products. For simplicity, we assume that there are two market types in the model: spot market and forward market.

Power demand also has specific characteristics in economic theories. It is well-known that electricity demand is very inelastic to price. Naturally, a major reason is that electricity is an essential item. Electric power is one of the essential infrastructures of modern society, and it is very difficult to live without electric power in countries where urbanization has advanced. The difficulty of saving electricity is another factor of the inelasticity. If an appropriate storage system is not in place, it is inflexible with respect to price, as it is impossible to buy electricity when its price is low and to consume it when its price is high.

In our model, electricity was supplied through two resources: renewable resources where the marginal costs are zero and non-renewable energy resources, such as thermal power, where the marginal costs can be denoted with a positive real number *a*.

Our model is based on the particular situation of JEPX. In Japan, JEPX, the only power trading market, was established during the trend of electricity liberalization. JEPX was established through investments from electric power companies and new electric power companies, and started trading from 2005 onwards. Since only members of JEPX can trade in the market, general consumers cannot buy electricity directly. Therefore, we assumed that all market players were price-takers. No one has the market power required for controlling electricity prices.
