Utility indifference pricing and hedging for structured contracts in energy markets

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.Comment: 32 pages, 5 figure

Quadratic Hedging and Optimization of Option Exercise Policies in Incomplete Markets and Discrete Time

This paper extends quadratic hedging from European to Bermudan options in discrete time when markets are incomplete and investigates its use for supporting exercise policy optimization. The key idea is to construct date specific approximate replicating portfolios. Hedging any given exercise policy can be done by solving a collection of stochastic dynamic programs. Optimizing the exercise policy based on the resulting martingale measure requires care. If this measure is risk neutral (RN), the value of an optimal such policy, which can be obtained by augmenting the hedging model with an exercise policy optimization step, is a no arbitrage one. Otherwise this approach must be refined by imposing time consistency on exercise policies, although the value of the resulting exercise policy may not be arbitrage free. Following the common pragmatic strategy of specifying quadratic hedging under an RN measure, e.g., one calibrated to market prices, avoids these issues. In particular, it provides a simple hedging policy with immediate practical applicability and is equivalent to exercise policy optimization under RN valuation, thus complementing it with a consistent hedging policy. A simple numerical example shows that this procedure generates effective hedging policies

Applications of robust optimal control to decision making in the presence of uncertainty

This thesis is concerned with robustness of decision making in financial economics. Feedback control models developed in engineering are applied to three separate though linked problems in order to examine the role and impact of robustness in the creation and application of decision rules. Three problems are examined using robust optimal control techniques to evaluate the impact of robustness and stability in financial economic models. The first problem examines the use of linear models of robust optimal control in the pricing of castastrophe based derivatives and finds its relative performance to be superior to the popular jump diffusion and stochastic volatility models in the pricing of these emerging instruments. The novelty of the approach arises from the examination of the impact of robustness and stability of the pricing solution. The second problem involves robustness and stability of hedging. An alternative method of creating hedging rules is developed. The method is based on robust control Lyapunov functions that are simple, robust and stable in operation, yet in practice are not so conservative that they eliminate all trading gains. The third problem involves the development of robust control policies for managing risk, using non-linear robust optimal control techniques to provide clear evidence of superior performance of robust models when compared with existing VAR and EVT approaches to risk management. The novelty in the approach arises from the development of a simple and powerful risk management metric

Price Calibration of basket default swap: Evidence from Japanese market

The aim of this paper is the price calibration of basket default swap from Japanese market data. The value of this instruments depend on the number of factors including credit rating of the obligors in the basket, recovery rates, intensity of default, basket size and the correlation of obligors in the basket. A fundamental part of the pricing framework is the estimation of the instantaneous default probabilities for each obligor. Because default probabilities depend on the credit quality of the considered obligor, well-calibrated credit curves are a main ingredient for constructing default times. The calibration of credit curves take into account internal information on credit migrations and default history. We refer to Japan Credit Rating Agency to obtain rating transition matrix and cumulative default rates. Default risk is often considered as a rare-event and then, many studies have shown that many distributions have fatter tails than those captured by the normal distribution. Subsequently, the choice of copula and the choice of procedures for rare-event simulation govern the pricing of basket credit derivatives. Joshi and Kainth (2004) introduced an Importance Sampling technique for rare-event that forces a predetermined number of defaults to occur on each path. We consider using Gaussian copula and t-student copula and study their impact on basket credit derivative prices. We will present an application of the Canonical Maximum Likelihood Method (CML) for calibrating t-student copula to Japanese market data.Basket Default Swaps, Credit Curve, Monte Carlo method, Gaussian copula, t-student copula, Japanese market data, CML, Importance Sampling

Three essays on risk management in electric power markets

1 CD-ROMThis dissertation has arisen in the context of the electric power markets, the study of risk management and the relations between physical production and the electricity transactions using financial contracts in particular. Electricity is very difficult to compare with any other commodity, since it has a peculiar characteristic; electricity “must be produced at exactly the same time as it is consumed”. The technological inability to store electricity efficiently and the characteristics of marginal production costs create jumps in the spot price. The electricity power market is heavily incomplete. Load-matching problems occur because electricity prices show volatility because of unexpected variations due to climatic conditions and other associated risk factors. A branch of the literature in risk management has tried to give a definitive answer to the question of how agents in the markets with non-storable underlying asset could hedge their exposure to volatile price and quantity. The first essay tackles the basis of this question, which is the implication of the price of risk when forward risk premia are presented. This essay also shows how the properties and variations of forward risk premia is explained by risk factors variations on expected spot prices, and unexpected changes on the available quantity of water to generate electric power. Forward risk premia are the measure, hour by hour throughout the day, of the price of risk that the agents pay to trade electric power using forward contracts. In this essay forward premia were measured from the unregulated market segment. The results indicate that the average expected forward risk premia could have a positive behavior in seventeen out of twenty-four hours. These results represent the equilibrium compensation for bearing the price risk of the electric power for one year. In the Colombian market, the risk taker is the marketer, specifically in the unregulated market segment, because they are assuming the price risk in the long-term negotiations. The marketer, represented by this demand, tries to ensure their future Profit and Losses P&L and so they sacrifice their premia. It is relevant for further studies to evaluate the efficiency of this market, and the characteristics to determine why the marketer is willing to pay forward risk premia and why the generator has a better position to receive this bonus. Exploring the optimization problem of portfolios my second essay asks whether the agents in the electric power market could hedge their exposure to uncertainties; price and quantity. We propose a close form solution for the optimization problem of portfolios composed by two claims, price and weather, according to factors influencing electric power markets such as price volatility, price spikes, and climatic conditions that influence volume volatility. Results show a positive correlation among price, quantity, and the weather variable. In order to apply the optimal static hedging that includes the second claim on weather indexes for seasonal countries such as United States and tropical countries such as Colombia, the third essay shows an application of the static hedging model, using parameters from US market(PJM), and Colombian market (WPMC2). For the PJM, I used weather indexes from Chicago Mercantile Exchange Group, and the hydrological index from WPMC which is based on the hydrological contributions of rivers on dam levels. We verify that El Niño and La Niña phenomena also influence quantity variations, and the agents in those markets are exposed to both price and quantity volatiles.Introduction – I. Modelling Risk for Electric Power Market -- Bibliography – Appendix – II. Optimal Static Hedging of Energy Price and Volume Risk: Closed-Form Results – III. Applications of Optimal Static Hedging of Energy Price and Volume Risk to markets in the US and Colombia -- IV. Final Discussion -- Bibliograph