Haskayne School of Business Research & Publications
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Browsing Haskayne School of Business Research & Publications by Department "Finance"
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Item Open Access Backward Stochastic Difference Equations for Dynamic Convex Risk Measures on a Binomial Tree(Applied Probability Trust, 2014-08-04) Elliott, Robert J.; Siu, Tak Kuen; Cohen, Samuel N.Using backward stochastic difference equations (BSDEs), this paper studies dynamic convex risk measures for risky positions in a simple discrete-time, binomial tree model. A relationship between BSDEs and dynamic convex risk measures is developed using nonlinear expectations. The time consistency of dynamic convex risk measures is discussed in the binomial tree framework. A relationship between prices and risks is also established. Two particular cases of dynamic convex risk measures, namely risk measures with stochastic distortions and entropic risk measures, and their mathematical properties are discussed.Item Open Access Bond valuation under a discrete-time regime-switching term-structure model and its continuous-time extension(Emerald, 2011) Elliott, Robert; Siu, Tak Kuen; Badescu, AlexPurpose – The purpose of this paper is to consider a discrete-time, Markov, regime-switching, affine term-structure model for valuing bonds and other interest rate securities. The proposed model incorporates the impact of structural changes in (macro)-economic conditions on interest-rate dynamics. The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account. Design/methodology/approach – The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account. Findings – The authors derive a simple way to give exponential affine forms of bond prices using backward induction. The authors also consider a continuous-time extension of the model and derive exponential affine forms of bond prices using the concept of stochastic flows.Item Open Access A BSDE approach to a risk-based optimal investment of an insurer(Elsevier, 2011) Elliott, Robert; Siu, Tak KuenWe discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer’s risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.Item Open Access Characteristic functions and option valuation in a Markov chain market(Elsevier, 2011) Elliott, Robert; Liew, Chuin Ching; Siu, Tak KuenWe introduce an approach for valuing some path-dependent options in a discrete-time Markov chain market based on the characteristic function of a vector of occupation times of the chain. A pricing kernel is introduced and analytical formulas for the prices of Asian options and occupation time call options are derived.Item Open Access COMPARISONS FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON MARKOV CHAINS AND RELATED NO-ARBITRAGE CONDITIONS(Institute of Matehmatical Statistics, 2010) Elliott, Robert; Cohen, Samuel NMost previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Us- ing solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expec- tations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their applications to dynamic risk measures on such spaces. In particular, we prove comparison theorems for scalar and vector valued solutions to BSDEs, and discuss arbitrage and risk measures in the scalar case.Item Open Access Control of discrete-time HMM partially observed under fractional Gaussian noises(Elsevier, 2011) Elliott, Robert; Siu, Tak KuenA discrete-time control problem of a finite-state hidden Markov chain partially observed in a fractional Gaussian process is discussed using filtering. The control problem is then recast as a separated problem with information variables given by the unnormalized conditional probabilities of the whole path of the hidden Markov chain. A dynamic programming result and a minimum principle are obtained.Item Open Access Discrete-Time Expectation Maximization Algorithms for Markov-Modulated Poisson Processes(IEEE Control Systems Society, 2008) Elliott, Robert; Malcolm, W. P.In this paper, we consider parameter estimation Markov-modulated Poisson processes via robust filtering and smoothing techniques. Using the expectation maximization algorithm framework, our filters and smoothers can be applied to estimate the parameters of ourmodel in either an online configuration or an offline configuration. Further, our estimator dynamics do not involve stochastic integrals and our new formulas, in terms of time integrals, are easily discretized, and are written in numerically stable forms inW. P.Malcolm, R. J. Elliott, and J. van der Hoek, “On the numerical stability of time-discretized state estimation via clark transformations,” presented at the IEEE Conf. Decision Control, Mauii, HI, Dec. 2003.Item Open Access Insurance Claims Modulated by a Hidden Brownian Marked Point Process(Elsevier, 2009) Elliott, Robert; Chen, Zhiping; Duan, QihongAimed at better modeling insurance claims in an economic environment driven by business cycles, a new Markov-modulated Poisson process model is proposed, and an algorithm is derived to estimate the hidden Markov process by using the observed information. Our method differs from existing ones in the following ways: the new hidden process can model more efficiently the cyclic state of the economic environment; our theory is based on a variation of the law of large numbers and is easy to understand; the Fourier expansion-based parameter estimation algorithm is flexible and can be more easily implemented than other algorithms. Simulation results not only demonstrate the practicality of our model and algorithm, but also show the efficiency and robustness of the estimation algorithm.Item Open Access Macroprudential capital requirements and systemic risk(2010) Lehar, Alfred; Gauthier, Celine; Souissi, MoezIn the aftermath of the financial crisis, there is interest in reforming bank regulation such that capital requirements are more closely linked to a bank’s contribution to the overall risk of the financial system. In our paper we compare alternative mechanisms for allocating the overall risk of a banking system to its member banks. Overall risk is estimated using a model that explicitly incorporates contagion externalities present in the financial system. We have access to a unique data set of the Canadian banking system, which includes individual banks’ risk exposures as well as detailed information on interbank linkages including OTC derivatives. We find that macroprudential capital allocations can differ by as much as 50% from observed capital levels and are not trivially related to bank size or individual bank default probability. Macroprudential capital allocation mechanisms reduce default probabilities of individual banks as well as the probability of a systemic crisis by about 25%. Our results suggest that financial stability can be enhanced substantially by implementing a systemic perspective on bank regulation.Item Open Access A model for energy pricing with stochastic emission costs(Elsevier, 2010) Elliott, Robert; Lyle, Matthew R.; Miao, HongWe use a supply-demand approach to value energy products exposed to emission cost uncertainty. We find closed form solutions for a number of popularly traded energy derivatives such as: forwards, European call options written on spot prices and European Call options written on forward contracts. Our modeling approach is to first construct noisy supply and demand processes and then equate them to find an equilibrium price. This approach is very general while still allowing for sensitivity analysis within a valuation setting. Our assumption is that, in the presence of emission costs, traditional supply growth will slow down causing output prices of energy products to become more costly over time. However, emission costs do not immediately cause output price appreciation, but instead expose individual projects, particularly those with high emission outputs, to much more extreme risks through the cost side of their profit stream. Our results have implications for hedging and pricing for producers operating in areas facing a stochastic emission cost environment.Item Open Access On filtering and estimation of a threshold stochastic volatility model(Elsevier, 2011) Elliott, Robert; Liew, Chuin Ching; Siu, Tak KuenWe derive a nonlinear filter and the corresponding filter-based estimates for a threshold autoregressive stochastic volatility (TARSV) model. Using the technique of a reference probability measure, we derive a nonlinear filter for the hidden volatility and related quantities. The filter-based estimates for the unknown parameters are then obtained from the EM algorithm.Item Open Access On pricing and hedging options in regime-switching models with feedback effect(Elsevier, 2011) Elliott, Robert; Siu, Tak Kuen; Badescu, AlexandruWe study the pricing and hedging of European-style derivative securities in a Markov, regime-switching, model with a feedback e ect depending on the economic condition. We adopt a pricing kernel which prices both nancial and economic risks explicitly in a dynamically incomplete market and we provide an equilibrium analysis. A martingale representation for a European-style index option's price is established based on the price kernel. The martingale representation is then used to construct the local risk-minimizing strategy explicitly and to characterize the corresponding pricing measure.Item Open Access A ‘simple’ hybrid model for power derivatives(Elsevier, 2009) Elliott, Robert; Lyle, Matthew R.This paper presents a method for valuing power derivatives using a supply–demand approach. Our method extends work in the field by incorporating randomness into the base load portion of the supply stack function and equating it with a noisy demand process. We obtain closed form solutions for European option prices written on average spot prices considering two different supply models: a mean-reverting model and a Markov chain model. The results are extensions of the classic Black–Scholes equation. The model provides a relatively simple approach to describe the complicated price behaviour observed in electricity spot markets and also allows for computationally efficient derivatives pricing.Item Open Access Three Essays on Updating Forecasts in Vector Autoregression Models(Queen's University, Department of Economics, 2010-04) Zhu, Hui (Julia)Forecasting firms' earnings has long been an interest of market participants and aca- demics. Traditional forecasting studies in a multivariate time series setting do not take into account that the timing of market data release for a speci¯c time period of observation is often spread over several days or weeks. This thesis focuses on the separation of announcement timing or data release and the use of econometric real- time methods, which we refer to as an updated vector autoregression (VAR) forecast, to predict data that have yet to be released. In comparison to standard time series forecasting, we show that the updated forecasts will be more accurate the higher the correlation coe±cients among the standard VAR innovations are. Forecasting with the sequential release of information has not been studied in the VAR framework, and our approach to U.S. nonfarm payroll employment and the six Canadian banks shows its value. By using the updated VAR forecast, we conclude that there are relative ef- ¯ciency gains in the one-step-ahead forecast compared to the ordinary VAR forecast, and compared to professional consensus forecasts. Thought experiments emphasize that the release ordering is crucial in determining forecast accuracy.Item Open Access Using Price Information as an Instrument of Market Discipline in Regulating Bank Risk(2011-01-26T20:47:39Z) Lehar, Alfred; Seppi, Duane; Strobl, GunterAn important trend in bank regulation is greater reliance on market discipline. In particular, information impounded in securities prices is increasingly used to complement supervisory activities of regulators with limited resources. The goal of this paper is to analyze the theoretical foundations of market-based bank regulation. We nd that price information only improves the e ciency of the regulator's monitoring function if the banks' risk-shifting incentives are not too large. Further, if the regulator cannot commit to an ex ante suboptimal auditing policy, market-based bank regulation can lead to more risk taking in equilibrium, increasing the expected payments by the deposit insurance agency. Finally, we show that the regulatory use of market information can decrease the investors' incentives to acquire costly information, thereby reducing the informativeness of stock prices.Item Open Access Utility-based indifference pricing in regime-switching models(Elsevier, 2011) Elliott, Robert; Siu, Tak KuenIn this paper, we study utility-based indifference pricing and hedging of a contingent claim in a continuous-time, Markov, regime-switching model. The market in this model is incomplete, so there is more than one price kernel. We specify the parametric form of price kernels so that both market risk and economic risk are taken into account. The pricing and hedging problem is formulated as a stochastic optimal control problem and is discussed using the dynamic programming approach. A verification theorem for the Hamilton–Jacobi–Bellman (HJB) solution to the problem is given. An issuer’s price kernel is obtained from a solution of a system of linear programming problems and an optimal hedged portfolio is determined.