Utility indifference pricing and hedging for structured contracts in energy markets

Abstract

In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyer's utility indifference price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates for the optimal exercise strategy for the structured product as well as for the corresponding hedging strategy. Moreover, in a model with two correlated assets, one traded and one nontraded, we obtain a representation of the price as the value function of an auxiliary simpler optimization problem under a risk neutral probability, that can be viewed as a perturbation of the minimal entropy martingale measure. Finally, numerical results are provided.

Pricing reliability options under different electricity price regimes

“…therefore, our analysis provides a benchmark value for the RO under the assumption that the market for the derivative is liquid enough to bring about competition. 14 In this framework, the simplified mathematical model that we proposed can be seen as a starting point in the analysis of ROs. We obtain semi-explicit formulae for the value of the RO, under a set of di↵erent assumptions with increasing realism and complexity.…”

“…In fact, our approach is shared without concerns by other scholars who have evaluated other exotic options on electricity, such as spark-spread options (options on the di↵erential between power prices and the heat content of the fuel, [20,25]), Asian options (options written on average prices, [16]), and options which are implicit in demand response mechanisms, [38]. Our approach is also justified by utility-based arguments, see [14,Remark 3.6] for structured products in energy markets like that in Eq. ( 1) and the subsequent ones.…”

Stochastic control of single-species population dynamics model subject to jump ambiguity

“…They lead to a convergence result of the present scheme as shown later. These properties are indispensable in constructing convergent numerical schemes for a variety of degenerate elliptic/parabolic differential equations [16,17,55]. Oberman [56] has presented similar related mathematical framework, which is also useful in constructing convergent numerical schemes [41,64,77].…”

Pricing Reliability Options Under Different Electricity Prices’ Regimes

“…Here, µ is given by (9) and ν is a seasonality function for K of the same form, while the processes X and Y are solution to…”

“…Table 1 reports the estimated parameters for each different model, while Table 2 shows the estimated seasonality parameters. Table 2: Linear regression estimates, standard errors and p-values obtained using the specification in (9). The base group categories for each dummy variable are month1, f riday and hour1.…”