Stochastic cash flows modelled by homogeneous and non-homogeneous discrete time backward semi-Markov reward processes

The main aim of this paper is to give a systematization on the stochastic cash flows evolution. The tools that are used for this purpose are discrete time semi-Markov reward processes. The paper is directed not only to semi-Markov researchers but also to a wider public, presenting a full treatment of these tools both in homogeneous and non-homogeneous environment. The main result given in the paper is the natural correspondence of the stochastic cash flows with the semi-Markov reward processes. Indeed, the semi-Markov environment gives the possibility to follow a multi-state random system in which the randomness is not only in the transition to the next state but also in the time of transition. Furthermore, rewards permit the introduction of a financial environment into the model. Considering all these properties, any stochastic cash flow can be naturally modelled by means of semi-Markov reward processes. The backward case offers the possibility of considering in a complete way the duration inside a state of the studied system and this fact can be very useful in the evaluation of insurance contract

Structural pricing of XVA metrics for energy commodities OTC trades

The aim of the present Chapter is to improve of the structural rst-passage framework built in Chapter 1 along several directions as well as test its robustness. Since typically commodity trades are not clearable under Central Clearing Counterparts (CCPs), it is worthy to assess the eect of bilateral Collateral Support Annex (CSA) agreements on CVA/DVA metrics. Moreover I introduce within my CCR modelling, the impact of state-dependent stochastic recovery rates. Furthermore, in order to stress-test my framework, I investigate the eects on CCR measures of multiplicative shocks to the two major drivers in the game: credit and volatility. Finally I propose an alternative balance-sheet calibration based on hybrid market/accounting data which is well suited in the commodity context in the light of small and medium size of corporations usually operating in the EU commodity derivatives market for risk-management purposes.The global nancial crisis revealed that no economic entity can be considered default-free any more. Because of that, both banks and corporations have to deal with bilateral Counterparty Credit Risk (CCR) in their OTC derivatives trades. Such evidence implies the fair pricing of these risks, namely the Credit Valuation Adjustment (CVA) and its counterpart, the Debt Valuation Adjustment (DVA). Despite the more commonly used reduced-form approach, in this work the random default time is addressed via a structural approach a la Black and Cox (1976), so that the bankruptcy of a given rm is modelled as the rst-passage time of its equity value from a predetermined lower barrier. As in Ballotta et al. (2015), I make use of a time-changed Levy process as underlying source of both market and credit risk. The main advantage of this setup relies on its superior capability to replicate non null short-term default probabilities, unlike pure diusion models. Moreover, a numerical computation of the valuation adjustments for bilateral CCR in the context of energy commodities OTC derivatives contracts has been performed.The global nancial crisis revealed that no economic entity can be considered default-free any more, so that both banks and corporate rms have to cope with bilateral Counterparty Credit Risk (CCR) when negotiating OTC derivatives. Since the mainstream approach typically used in practical settings is to evaluate derivatives in terms of the cost of their respective hedging strategies, the pricing of CCR metrics implicitly relates to the way these strategies are nanced. Within the numerical section of the present work, the valuation adjustments for CCR have been computed. Moreover, the role played by funding costs and their impact in widening bid-ask spreads have been assessed. A similar reasoning has been applied for the investigation of the cost of funding Initial Margins (IM), typically eective on top of Variation Margins (VM) when trading under Central Clearing Counterparties (CCPs). As the Initial Margin Valuation Adjustment (MVA) is concerned, it is here showed that, dierently from what can happen for FVAs, no osetting eect can materialize. As a consequence, in aggregate terms IMs can cause systemic liquidity eects. The computed XVA metrics are relative to energy commodities OTC derivative trades

Real rainbow options in commodity applications : valuing multi-factor output options under uncertainty

This thesis focuses on the valuation of real options when there is flexibility given by the choice between two risky outputs. We develop models to value these rainbow options and to determine optimal operating and investment policies. These models are studied in the context of commodity applications because output flexibility is particularly relevant in volatile commodity markets. We provide insights into the behaviour and sensitivities of option values and operating policies and discuss implications for decision-making.In the early stages of real options theory, research centred on basic options with closed-form solutions, modelling single uncertainty in most cases. The challenge is now to incorporate more complexities in the models in order to further bridge the gap between theoretical models and reality, thereby promoting the widespread application of real options theory in corporate finance. The new option models developed in this thesis are organised in three self-contained research papers to address specific research problems. The first research paper studies an asset with flexibility to continuously choose the best of two risky commodity outputs by switching between them. We develop quasi-analytical and numerical lattice solutions for this real option model, taking into account operating and switching costs. An empirical application to a flexible fertilizer plant shows that the value of flexibility between the two outputs, ammonia and urea, exceeds the required additional investment cost (given the parameter values) despite the high correlation between the commodities. Implications are derived for investors and policy makers. The real asset value is mainly driven by non-stationary commodity prices in combination with constant operating costs. In the second research paper, we study an asset with flexibility to continuously choose the best of two co-integrated commodities. The uncertainty in two commodity prices is reduced to only one source of uncertainty by modelling the spread, which is mean-reverting in the case of co-integration. Our quasi-analytical solution distinguishes between different risk and discount factors which are shown to be particularly relevant in the context of mean-reversion. In an empirical application, a polyethylene plant is valued and it is found that the value of flexibility is reduced by strong mean-reversion in the spread between the commodities. Hence, operating flexibility is higher when the commodities are less co-integrated. In the third research paper, we develop real option models to value European sequential rainbow options, first on the best of two correlated stochastic assets and then on the spread between two stochastic co-integrated assets. We present finite difference and Monte Carlo simulation results for both, and additionally a closed-form solution for the latter. Interestingly, the sequential option value is negatively correlated with the volatility of one of the two assets in the special case when the volatility of that asset is low and the option is in-the-money. Also, the sequential option on the mean-reverting spread does not necessarily increase in value with a longer time to maturity.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Assessing investment strategies in mining projects in the Asia-Pacific region

The Asia-Pacific region has experienced a significant period of development over the last four decades. Rapid urbanisation has resulted in an increased demand for mineral resources indicating the resource industry has contributed the primary income to the economies of many Asia-Pacific countries. The objective of this thesis is to shed light on investment opportunity using the strategy of timing flexibility. This thesis uses two methodologies, namely Net Present value (NPV) and real options valuation (ROV), to conduct an investment analysis assessing timing flexibility. This thesis finds that commodity prices affect the mining investors’ decisions. However, the impact of tax policy uncertainty is quite subtle

Information-based commodity pricing and the theory of signal processing with Levy information

In mathematical finance, increasing attention is being paid to (a) the construction of explicit models for the flow of market information, and (b) the use of such models as a basis for asset pricing. One notable approach in this spirit is the information-based asset pricing theory of Brody, Hughston and Macrina (BHM), in which so-called information processes are introduced and ingeniously integrated into the general theory of asset pricing. Building on the BHM theory, this thesis presents a number of new developments in this area. I begin with a brief review of the BHM framework, leading to a discussion of the simplest asset pricing models. Then the first main topic of the thesis, which is based in part on Brody, Hughston & Yang (2013b), is developed, which concerns asset pricing with continuous cash flows in the presence of noisy information. In particular, an information-based model for the pricing of storable commodities and associated derivatives thereof is introduced. The model employs the concept of market information about future supply and demand as a basis for valuation. Physical ownership of a commodity is regarded as providing the beneficiary with a continuous "convenience dividend", equivalent to a continuous cash flow. The market filtration is assumed to be generated jointly by: (i) an information process concerning the future convenience-dividend flow; and (ii) a convenience-dividend process that provides information about current and past dividend levels. The price of a commodity is given by the risk-neutral expectation of the cumulative future convenience dividends, suitably discounted, conditional on the information provided by the market filtration. In the situation where the convenience dividend is modelled by an Ornstein-Uhlenbeck process, the prices of options on commodities, both when the underlying is a spot price and when the underlying is a futures price, can be derived in closed form. The dynamical equation of the price process is worked out, leading to an identification of the associated innovations process. The resulting model is sufficiently tractable to allow for simulation studies of the resulting commodity price trajectories. The second main topic of the thesis, which is based in part on Brody, Hughston & Yang (2013a), concerns a generalisation of concept of information process to the situation where the noise is modelled by a general Levy process. There are many practical circumstances in which signal or noise, or both, exhibit discontinuities. This part of the thesis develops a rather general theory of signal processing involving Levy noise, with the view to the introduction of a broad and tractable family of information processes suitable for modelling situations involving discontinuous signals, discontinuous noise, and discontinuous information. In this context, each information process is associated with a certain "noise type", and an information process of a given noise type is distinguished by the message that it carries. More specifically, each information process is associated in a precise way to a Levy process, which I call the fiducial process. The fiducial process is the information process that results in the case of a null message, and can be regarded as a "pure noise" process of the given noise type. Information processes can be classified by the characteristics of the associated fiducial processes. To keep the discussion simple, I mainly consider the case where the message is represented by a single random variable. I construct the optimal filter in the form of a map that takes the a priori distribution of the message to an a posteriori distribution that depends on the information made available. A number of examples are presented and worked out in detail. The results vary remarkably in detail and character for the different types of information processes considered, and yet there is an overall unity in the scheme that allows for the construction of numerous explicit and interesting examples. The results presented in the second part of the thesis therefore have the potential to pave the way toward a variety of new applications, including applications to problems in finance.Open Acces

The effects of Big Bang on the gilt-edged market : term structure movements and market efficiency

This study is concerned with the impact of the 1986 Stock Market deregulation, or Big Bang, on the efficiency of the United Kingdom government securities market. The main theoretical finding is that the change to dual capacity dealing with negotiated commissions cannot be justified economically without the inclusion of a best execution rule for broker/dealers. The empirical section of the study has three parts. The first part uses established and new autocorrelation techniques to test market efficiency in the traditional weak-form efficient market hypothesis paradigm. The second part tests market efficiency through an analysis of pricing residuals from fitting term structure curves. A new method to fit these curves is developed. The third section tests market efficiency by examining evidence of anomalies in the shape and movements of the term structure. From all three sources, there is strong evidence that the changes introduced by Big Bang improved efficiency in the gilt-edged market

Decision-making and the role of feedback in complex tasks

This thesis investigates the process of decision-making in relation to complex tasks and considers the important role which dynamic information and real-time feedback play in shaping response behaviour and adaptation within such environments. Through empirical studies, the thesis explores the extent to which decision-makers can be said to act rationally when challenged by complex decision-making environments. Evidence relating to demand for information and the impact of feedback on behaviour is provided with two studies: The first uses a simulated auction platform to examine behaviour within overlapping auctions of short duration with close-to-identical items and minimal participation costs. Mouse tracking is used to capture data on relevant interactions of participants with the simulated online platform, including switching behaviour independent of bidding. The resulting data suggests that participants did behave in a manner consistent with utility maximisation, seeking to acquire the item at the lowest possible price and showing no bias in terms of auction preference. The impact of fixed-price offers in the form of a “Buy it Now” option is also examined with some evidence that participants again seek, and respond to, current information when deciding on their bidding strategy. The second study is a test of the impact of real-time feedback and demand for information within the context of financial markets. The study again uses a novel simulated environment which provides access to considerable amounts of relevant data which participants can choose to access. In addition, participants are exposed to regular feedback with regard to their own performance. Overall, demand for information is found to be dependent upon the type of feedback received and its context. Decision-makers then appear to behave objectively, apparently seeking the latest available information to support current decisions, although investor style is found to be important in determining overall trading propensity. The thesis starts by considering a number of the foundations and pathways which run through the judgment and decision-making literature. It is not a complete description, review or analysis of all of the prevailing lines of enquiry. Nevertheless, it seeks to achieve coherence in terms of bringing together some of the key themes dealing with risky choice under conditions of uncertainty and ambiguity. The field of judgment and decision-making is inevitably vast; its scope owing much to the fact that it transcends individual disciplines. The emergent behavioural sciences thus draw together important strands from various sources, notably Economics and Finance. In many areas, psychological traits can be applied to explain inconsistencies which are found in classical theory of rational behaviour. The recognition of behavioural traits has thus contributed greatly to the evolution of decisionmaking theories under conditions of uncertainty and ambiguity which are, in many cases, substantially more adaptable and robust than early normative theories of rational behaviour. The classical approach to rational decision making within Economics, together with some theoretical and empirical challenges to it, are considered in Chapter 1. It is here that we are introduced to the Rational Man. Like the mythical creatures found in Classical Antiquity, the Rational Man does not actually exist in the real world; he is nevertheless central to the concept of utility maximising rational choice which provided much of the foundation of Economics. Developments of expected utility theory (EUT) are considered, including its replacement of expected value, and the formalisation of rational behaviour within the context of axioms. When those logical axioms apply, decision-makers can be said to behave 'as if' they are utility maximises. The chapter ends with some empirical evidence, showing the types of approaches often used to explore rational decision-making. Some violations of EUT are explored, both in relation to notional gambles and consistency with regard to revealed preferences. Chapter 2 extends the narrative by considering rational decision-making in cases where there is no objective information about possible outcomes. Subjective utility theory (SEU) is then introduced, describing objective functions based upon preferences derived from combined utility and probability functions. The implications of the Allais’ and Ellsberg paradoxes are discussed, along with some possible solutions. It is here that we explore the concepts of uncertainty and ambiguity in more details and consider some theoretical formulations for addressing them. Chapter 3 covers the significant contribution to decision-making under conditions of uncertainty provided by Prospect Theory and, later, Cumulative Prospect Theory (CPT). Their evolution from the pioneering work of Markowitz is discussed within the context of reference points relative to which outcomes can be evaluated. The significance of stochastic dominance and rank dependence are explored. By this stage, we have examined numerous theories which have fundamentally transformed standard EUT into much more flexible and adaptable frameworks of rational choice. The core concepts of utility maximisation remain yet the initial, strictly concave utility function describing diminishing marginal utility is now substantially replaced by more complex weighted preference functions. From this theoretical base, the process of choice reduction and the application of heuristics in decision-making are considered. We again describe axiomatic behaviour compatible with rational choice. Therefore, decision-makers faced with multiple choices about which there may be little or no objective information about likely outcomes can nevertheless develop rational beliefs and expectations which can then be applied to reduce complex tasks to more manageable proportions. As well as considering these aspects from the point of view of actual choices, we also consider the processes by which decisions are taken. Thus, process tracing methods are introduced into the discussion. The chapter also explicitly considers the role of feedback in decision making. This includes a consideration of Bayesian inference as a process for updating probabilistic expectations subject to new information. From considering theoretical formulations form which we can judge rational behaviour, Chapter 5 looks at evidence for sub-optimal decision-making and bias. Bias with regard to probability assessments are considered along with empirical evidence of bias in relation to intertemporal discounting. Sunk cost bias is also considered as a clear example of irrational behaviour, leading in to a specific discussion about a number of persistent behavioural biases identified within financial markets. As an introduction to later chapters, this also covers the basic theoretical principles of market efficiency and evidence that real markets fail to adhere to those principles in important ways. Chapters 6 and 8 describe the empirical studies with Chapter 7 providing a more detailed introduction to the financial markets experiment, considering aspects of market efficiency, models of behaviour and other empirical evidence

AN OPTIONS APPROACH TO QUANTIFY THE VALUE OF DECISIONS AFTER PROGNOSTIC INDICATION

Safety, mission and infrastructure critical systems have started adopting prognostics and health management, a discipline consisting of technologies and methods to assess the reliability of a product in its actual life-cycle conditions to determine the advent of failure and mitigate system risks. The output from a prognostic system is the remaining useful life of the host system; it gives the decision-maker lead-time and flexibility in maintenance. Examples of flexibility include delaying maintenance actions to use up the remaining useful life and halting the operation of the system to avoid critical failure. Quantifying the value of flexibility enables decision support at the system level, and provides a solution to the fundamental tradeoff in maintenance of systems with prognostics: minimize the remaining useful life thrown while concurrently minimizing the risk of failure. While there are cost-benefit models to quantify the value of implementing prognostics, they are applicable to the fleet level, they do not incorporate the value of decisions after prognostic indication (value of flexibility or contingency actions), and do not use PHM information for dynamic maintenance scheduling. This dissertation develops a decision support model based on `options' theory- a financial derivative tool extended to real assets - to quantify maintenance decisions after a remaining useful life prediction. A hybrid methodology based on Monte Carlo simulations and decision trees is developed. The methodology incorporates the value of contingency actions when assessing the benefits of PHM. The model is extended and combined with least squares Monte Carlo methods to quantify the option to wait to perform maintenance; it represents the value obtained from PHM at the system level. The methodology also allows quantifying the benefits of PHM for individualized maintenance policies for systems in real-time, and to set a dynamic maintenance threshold based on PHM information. This work is the first known to quantify the flexibility enabled by PHM and to address the cost-benefit-risk ramifications after prognostic indication at the system level. The contributions of the dissertation are demonstrated on data for wind farms