Cash Sub-additive Risk Measures and Interest Rate Ambiguity

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, non financial and insurance positions. The debated cash additive axiom is relaxed into the cash sub-additive axiom to preserve the original difference between the numeraire of the current reserve amounts and future positions. Consequently, cash sub-additive risk measures can model stochastic and/or ambiguous interest rates or defaultable contingent claims. Practical examples are presented and in such contexts cash additive risk measures cannot be used. Several representations of the cash sub-additive risk measures are provided. The new risk measures are characterized by penalty functions defined on a set of sub-linear probability measures and can be represented using penalty functions associated with cash additive risk measures defined on some extended spaces. The issue of the optimal risk transfer is studied in the new framework using inf-convolution techniques.Examples of dynamic cash sub-additive risk measures are provided via BSDEs where the generator can locally depend on the level of the cash sub-additive risk measure.

Understanding, modelling and managing longevity risk: key issues and main challenges

Claudia Ravanelli

This article investigates the latest developments in longevity-risk modelling, and explores the key risk management challenges for both the financial and insurance industries. The article discusses key definitions that are crucial for the enhancement of the way longevity risk is understood, providing a global view of the practical issues for longevity-linked insurance and pension products that have evolved concurrently with the steady increase in life expectancy. In addition, the article frames the recent and forthcoming developments that are expected to action industry-wide changes as more effective regulation, designed to better assess and efficiently manage inherited risks, is adopted. Simultaneously, the evolution of longevity is intensifying the need for capital markets to be used to manage and transfer the risk through what are known as Insurance-Linked Securities (ILS). Thus, the article will examine the emerging scenarios, and will finally highlight some important potential developments for longevity-risk management from a financial perspective with reference to the most relevant modelling and pricing practices in the banking industry.

Taylor & Francis2012

Investment decisions with flexibility under uncertainty in the competitive electricity supply industry

Jun Dong

The restructuring of the electricity supply industry (ESI) has introduced new actors and market mechanisms. Electricity prices are more market oriented and fluctuate greatly. These changes bring about more uncertainties and risks to the market participants. When there are high risks in the future, the actors tend towards short-term decisions in which the risks are relatively easier to be coped with than in the long-term decisions. Much research has been carried out on short and medium-term risk management. The contracts of financial derivatives are managed for hedging risks. However, the development of long-term planning and risk management methods in the liberalised ESI has so far not attracted much attention. Long-term anticipations and planning have always been a significant issue given the specific characteristics of the ESI and the importance of security of supply. In liberalised electricity markets, the traditional centralised least-cost generation capacity planning is less relevant. The planning activities have become decentralised, i.e., individual actor makes planning for achieving its goals under certain risks. The ESI is in a transition from monopoly to competitive market and the liberalised electricity market has a short history. It is dominated by structural changes and actors' game behaviour, which are usually not of a random nature. Therefore, it is not always able to model the long-term uncertainties with the widely used probability methods in risk management. Under the large uncertainties and with the difficulty of uncertainty modelling, how would the actors make long-term investment decisions and manage risks? This thesis is an attempt to answer this question. The problem under study in this research is generalised as "investment planning with flexibility in the competitive electricity market". We argue that to select a flexible alternative strategy is one of the ways for managing long-term risks. The flexibility means that the actor is capable of adapting the investment decisions under different market situations in the future. For example, a project can be deferred to wait for more information, be expanded if the market situation becomes favourable or be abandoned if the market situation becomes unfavourable. For an electricity generator, the problem is capacity planning, for example, to construct a new power plant. For a consumer, it is energy portfolio planning. The alternatives may include different purchasing contracts and investment for self-generation. The purpose of this research is to develop a new approach for dealing with these kinds of problems. The requirements of the new approach are proposed in this thesis as: The flexibility of the investment projects or strategies should be accounted in the decision-making; The uncertainty modelling should reflect the long-term trends and characteristics of the liberalised electricity markets; Electricity price forecasting should reflect the interactions among the market players; The approach is an integration of scenario building, market simulation, strategy evaluation and decision-making. The new approach is developed within a conceptual framework of an intelligent decision support system proposed by Dr E. Gnansounou. The framework consists of four modules: Scenario builder, Problem formulator and attributes evaluator, Electricity market multi-agent system and Decision making aid. The principal researches focus on the methods of attributes evaluation taking into account flexibility actions and agent-based market simulation. The attributes evaluation of investment alternatives emphasizes the incorporation of uncertainty modelling and flexibility actions. Two types of attributes evaluation methods are developed using real options theory and fuzzy set theory respectively. Real options theory, in which uncertainty is modelled with probability methods, is introduced for computing and incorporating the flexibility value. In addition, a new method is developed for attributes evaluation taking into account the flexibility actions, using fuzzy set to represent imprecise or vague knowledge in electricity markets. For a long-term perspective, the main factors influencing investment decisions, such as electricity prices, are affected mainly by the structural changes and strategic behaviours of the actors in the market. It is not pertinent to forecast the values of these variables from the historical data using statistic models. The agent-based market simulation system is developed to simulate the interactions among the market participants and to provide electricity price scenarios. Three applications are dealt with by applying the proposed approach. Firstly, agent-based market simulation is applied to an illustrative power system. Secondly, a generation capacity planning and project evaluation for an electricity generator is performed. Thirdly the energy portfolios of a consumer is evaluated and compared. The research found that the new method to take into account flexibility actions is practical. It incorporates the flexibility actions into the cash flows. The flexibility cost is given exogenously. The value of a base strategy with flexibility actions is calculated. The alternatives are compared with these values. It is different from the real options method. The real options method assumes that the future value of the strategy is known with a predefined probability distribution and the value of the option is calculated. It deals with the pricing of a contract or a project. Differently from that, the new method deals with the comparison of portfolio given the prices and the costs are assumed as known and included into the cash flows, and how to consider the flexibility in the portfolio comparison. The real options method is operative for incorporating flexibilities in investment decisions if the uncertain variables follow the Wiener stochastic process. The advantages of this method are that it provides flexibility values and optimal timing of a project; it models the future value of the project with the stochastic process therefore it does not require the estimations on the values of driving variables for the lifetime of the project; it uses risk-free rate that is easier to estimate than the discount rate used in the DCF method. The limitations are that the assumptions of probabilistic distributions of the future value of the project are not always satisfied. The determination of the stochastic process and the estimation of the volatility of the value of the project are not straightforward. As a complement to the real options method and dealing with a different problem, the fuzzy method is proved in this thesis to give a "softer" approach when modelling the imprecision with fuzzy numbers. This method is suitable to electricity markets with incomplete information, lack of sufficient data and non-random movement. It is found that the agent-based simulation model is effective for giving "what if" scenarios on electricity market states in the future. The model is flexible in simulating imperfect electricity markets where game play exists. The main contributions of the research are summarised as follows: A new approach of investment decision support is developed fitting to electricity markets with regard to uncertainty and flexibility modelling. Incorporation of flexibility into the investment decisions is developed as a way for managing long-term risks. Uncertainty modelling with the real options method and imprecision data modelling with the fuzzy method can be applied according to the pertinence to the situation of electricity markets. The attributes evaluation of the investment strategies is based on agent-based market simulation. Instead of traditional least-cost centralised planning, the generation expansion planning is considered as decentralised planning where the individual agent makes expansion planning, taking into account other agents' plans.

EPFL2004

Three Essays on Asset Pricing

Emmanuel Leclercq

In the first chapter,which is a joint work with Mathieu Cambou and Philippe H.A. Charmoy, we study the distribution of the hedging errors of a European call option for the delta and variance-minimizing strategies. Considering the setting proposed by Heston (1993), we assess the error distribution by computing its moments under the real-world probability measure. It turns out that one is better off implementing either a delta hedging or a variance-minimizing strategy, depending on the strike and maturity of the option under consideration. In the second paper, which is a joint work with Damir Filipovic and Loriano Mancini, we develop a practicable continuous-time dynamic arbitrage-free model for the pricing of European contingent claims. Using the framework introduced by Carmona and Nadtochiy (2011, 2012), the stock price is modeled as a semi-martingale process and, at each time t , the marginal distribution of the European option prices is coded by an auxiliary process that starts at t and follows an exponential additive process. The jump intensity that characterizes these auxiliary processes is then set in motion by means of stochastic dynamics of Itô's type. The model is a modification of the one proposed by Carmona and Nadtochiy, as only finitely many jump sizes are assumed. This crucial assumption implies that the jump intensities are taken values in only a finitedimensional space. In this setup, explicit necessary and sufficient consistency conditions that guarantee the absence of arbitrage are provided. A practicable dynamic model verifying them is proposed and estimated, using options on the S&P 500. Finally, the hedging of variance swap contracts is considered. It is shown that under certain conditions, a variance-minimizing hedging portfolio gives lower hedging errors on average, compared to a model-free hedging strategy. In the third and last chapter, which is a joint work with Rémy Praz, we concentrate on the commodity markets and try to understand the impact of financiers on the hedging decisions. We look at the changes in the spot price, variance, production and hedging choices of both producers and financiers, when the mass of financiers in the economy increases. We develop an equilibrium model of commodity spot and futures markets in which commodity production, consumption, and speculation are endogenously determined. Financiers facilitate hedging by the commodity suppliers. The entry of new financiers thus increases the supply of the commodity and decreases the expected spot prices, to the benefits of the end-users. However, this entry may be detrimental to the producers, as they do not internalize the price reduction due to greater aggregate supply. In the presence of asymmetric information, speculation on the futures market serves as a learning device. The futures price and open interest reveal different pieces of private information regarding the supply and demand side of the spot market, respectively. When the accuracy of private information is low, the entry of new financiers makes both production and spot prices more volatile. The entry of new financiers typically increases the correlation between financial and commodity markets.