In this chapter, we investigated a stochastic dynamic problem on natural gas supply portfolio of forward contract and spot procurement in a deregulated en-vironment. The problem was modeled as a multistage Markov decision process.
It was shown that a stage and price dependent base stock policy is optimal for dynamically allocating contracted gas over the planning horizon. The resulting policy is attractive in the sense that it provides a useful guideline for the GENCO to make contract delivery decision strategically. Moreover, using the theory of supermodularity, we proved that the optimal base stock target levels monotoni-cally decrease with spot prices, which is in agreement with our intuition. With the help of an appropriate discretized price trinomial tree, the optimal base stock levels can be easily computed. In the numerical experiments, we showed that when the price process exhibits low volatility, a suboptimal “no-volatility” policy can be exploited to approximate the optimal policy. However, if the spot market becomes more volatile, there is substantial value for the GENCO to take price volatility into account.
As discussed above, the natural gas contract allows the GENCO to reduce its fuel supply cost via interaction with the spot market, especially in a substantially volatile market. Then the following questions arise naturally: what is the value of the contract and how much would the GENCO be willing to pay for the contract in the presence of spot market? These issues will be addressed in the following chapter.
Chapter 4
Contract Negotiation and Price Determination
4.1 Introduction
Traditionally, natural gas trade is completed by long-term forward contracts to support supplier’s infrastructure investment. However, International Energy Agency reports that long-term contracts fail to deliver the transparency and in-formation required in the increasingly competitive natural gas market (Juris, 1998a; Jensen, 2011). Hence medium- and short- term contracts become more
and more popular in natural gas trading market because of their flexibility. These contract transactions are mainly completed by bilateral negotiation, allowing the contracting parties to engage into the contracts that suit for their needs. During the negotiation process, one of the essential issues for both contracting parties is how to determine the optimal price of the bilateral contract. As a rule of thumb, natural gas spot price is commonly chosen as a benchmark for bilateral contract trading, since it reflects the short run marginal cost in a competitive market (Ju-ris, 1998a). However, the spot price index may not accurately reflect the value of the contract, as it fails to account for future price and demand uncertainties. In
this chapter, we aim to develop a novel contract pricing scheme based on contract valuation in the presence of spot trading.
This chapter closely relates to the literature on contract pricing (see Bjorgan et al., 2000; Gabriel et al., 2006; Palamarchuk, 2012). Bjorgan et al. (2000) proposed to apply the no-arbitrage pricing principle to determine a reasonable contract price. They concluded that the arbitrage-free contract price for a risk-neutral decision maker is equivalent to the expected value of the contract deriving from its own operational strategy. However, the contract delivery schedule deter-mined by one party would probably be unacceptable to the other one in reality.
This phenomenon stimulates bilateral negotiation for the contracting parties to reach an agreement. Palamarchuk (2012) suggested both parties to find their own acceptable contract price range, followed by concluding a mutually accept-able contract price via negotiation. He proposed to solve an auxiliary SMILP problem to compromise the contract scheduling so that both parties can obtain relative benefits from the contract. Gabriel et al. (2006) investigated the con-tract price and quantity determination for an electric retailer taking into account the settlement risks from both contracting sides. Unlike the SMILP model in the aforementioned works, we formulate the problem as a SDP. With incorporation of contract valuations from both contracting parties, we show that there is al-ways a possibility for the contracting parties to negotiate and reach a mutually acceptable contract price.
In practice, the bilateral contract is typically concluded by compromising and negotiating, which necessitates game theory for mathematical analysis. Dong and Liu (2007) considered pricing a forward contract of a nonstorable commodity for risk-averse decision makers. The study provided managerial insights on the equi-librium contract price and quantity via an asymmetric Nash bargaining model.
Wu and Kleindorfer (2005) studied an optimization problem of pricing a forward contract in a competitive market involving one buyer and multiple sellers in the presence of spot trading. It was shown that the resulting optimal contract price
is characterized by a Bertrand-Nash Equilibrium. Similarly, Popescu and Seshadri (2013) developed a game theory framework that involves multiple risk-neutral producers competing in the forward and spot market. The work shed light on the impact of demand uncertainty on commodity contracting. Note that the afore-mentioned works mainly focus on providing a managerial insight into contract negotiation through a simplified one-stage problem. We extend these work to price a contract in the context of a more general multi-period scheduling. In this chapter, we propose a Nash bargaining model to determine the optimal contract quantity and corresponding price by incorporating the contract valuations for both the GENCO and the gas supplier, which can be evaluated by solving the multi-stage MDP models separately.
The remainder of this chapter is organized as below. In Section 4.2, the val-ues of the bilateral contract for the GENCO and the natural gas supplier are evaluated using MDP models, respectively. We provide a detailed analysis on the relationship of these two valuations and present a Nash bargaining model to price the bilateral contract and determine the corresponding optimal quantity to engage simultaneously in Section 4.3. Several numerical results under various market conditions are presented in Section 4.4 to demonstrate the feasibility of the proposed pricing framework. We also examine the impact of the spot price volatility on the optimal contract quantity. In Section 4.5, we close this chapter by a short discussion.