PRICING AND SEMIMARTINGALE REPRESENTATIONS OF VULNERABLE CONTINGENT CLAIMS IN REGIME‐SWITCHING MARKETS

Using a suitable change of probability measure, we obtain a Poisson series representation for the arbitrage‐free price process of vulnerable contingent claims in a regime‐switching market driven by an underlying continuous‐time Markov process. As a result of this representation, along with a short‐time asymptotic expansion of the claim's price process, we develop an efficient novel method for pricing claims whose payoffs may depend on the full path of the underlying Markov chain. The proposed approach is applied to price not only simple European claims such as defaultable bonds, but also a new type of path‐dependent claims that we term self‐decomposable, as well as the important class of vulnerable call and put options on a stock. We provide a detailed error analysis and illustrate the accuracy and computational complexity of our method on several market traded instruments, such as defaultable bond prices, barrier options, and vulnerable call options. Using again our Poisson series representation, we show differentiability in time of the predefault price function of European vulnerable claims, which enables us to rigorously deduce Feynman‐Ka? representations for the predefault pricing function and new semimartingale representations for the price process of the vulnerable claim under both risk‐neutral and objective probability measures.     

Semi‐efficient valuations and put‐call parity

We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely, absence of arbitrage (in the sense of NUPBR) and absence of relative arbitrage among all buy‐and‐hold strategies (called static efficiency). A valuation process for a payoff is then called semi‐efficient consistent if the financial market enlarged by that process still satisfies this combination of properties. It turns out that this approach lies in the middle between the extremes of valuing by risk‐neutral expectation and valuing by absence of arbitrage alone. We show that this always yields put‐call parity, although put and call values themselves can be nonunique, even for complete markets. We provide general formulas for put and call values in complete markets and show that these are symmetric and that both contain three terms in general. We also show that our approach recovers all the put‐call parity respecting valuation formulas in the classic theory as special cases, and we explain when and how the different terms in the put and call valuation formulas disappear or simplify. Along the way, we also define and characterize completeness for general semimartingale financial markets and connect this to the classic theory.     

NO‐ARBITRAGE IN A NUMÉRAIRE‐INDEPENDENT MODELING FRAMEWORK

The classic approach to modeling financial markets consists of four steps. First, one fixes a currency unit. Second, one describes in that unit the evolution of financial assets by a stochastic process. Third, one chooses in that unit a numéraire, usually the price process of a positive asset. Fourth, one divides the original price process by the numéraire and considers the class of admissible strategies for trading. This approach has one fundamental drawback: Almost all concepts, definitions, and results, including no‐arbitrage conditions like NA, NFLVR, and NUPBR depend by their very definition, at least formally, on initial choices of a currency unit and a numéraire. In this paper, we develop a new framework for modeling financial markets, which is not based on ex‐ante choices of a currency unit and a numéraire. In particular, we introduce a “numéraire‐independent” notion of no‐arbitrage and derive its dual characterization. This yields a numéraire‐independent version of the fundamental theorem of asset pricing (FTAP). We also explain how the classic approach and other recent approaches to modeling financial markets and studying no‐arbitrage can be embedded in our framework.     

Pricing by Arbitrage Under Arbitrary Information

A substantial applications literature on pricing by arbitrage has effectively restricted information to that arising solely from securities markets; return distributions are then governed solely by past prices. We reconsider pricing by arbitrage in markets rendered incomplete by arbitrary information, which, moreover, may influence required returns. We show that contingent claims depending solely on securities' normalized price histories are priced by arbitrage if and only if all risk-adjusted probabilities agree upon the law of primitive securities' normalized prices. We show how existing diffusion-based results can be preserved, and resolve an issue relating to Merton's (1973) stochastic interest rate model.     

Dynamic Arbitrage‐Free Asset Pricing with Proportional Transaction Costs

This paper studies multiperiod asset pricing theory in arbitrage‐free financial markets with proportional transaction costs. The mathematical formulation is based on a Euclidean space for weakly arbitrage‐free security markets and strongly arbitrage‐free security markets. We establish the weakly arbitrage‐free pricing theorem and the strongly arbitrage‐free pricing theorem.     

RISK‐MINIMIZATION FOR LIFE INSURANCE LIABILITIES WITH DEPENDENT MORTALITY RISK

In this paper, we study the pricing and hedging of typical life insurance liabilities for an insurance portfolio with dependent mortality risk by means of the well‐known risk‐minimization approach. As the insurance portfolio consists of individuals of different age cohorts in order to capture the cross‐generational dependency structure of the portfolio, we introduce affine models for the mortality intensities based on Gaussian random fields that deliver analytically tractable results. We also provide specific examples consistent with historical mortality data and correlation structures. Main novelties of this work are the explicit computations of risk‐minimizing strategies for life insurance liabilities written on an insurance portfolio composed of primary financial assets (a risky asset and a money market account) and a family of longevity bonds, and the simultaneous consideration of different age cohorts.     

Generic Existence and Robust Nonexistence of Numéraires in Finite Dimensional Securities Markets

A numéraire is a portfolio that, if prices and dividends are denominated in its units, admits an equivalent martingale measure that transforms all gains processes into martingales. We first supply a necessary and sufficient condition for the generic existence of numéraires in a finite dimensional setting. We then characterize the arbitrage‐free prices and dividends for which the absence of numéraires survives any small perturbation preserving no arbitrage. Finally, we identify the cases when any small, but otherwise arbitrary, perturbation of prices and dividends preserves either the existence of numéraires, or their nonexistence under no arbitrage.     

Measuring the Financial Benefits of Cross‐Functional Integration Influences Management's Behavior

While many have suggested that cross‐functional, cross‐firm integration is beneficial, functional managers will have competing priorities and thus different perceptions of its benefits. Performance measurements tend to reward functional behaviors and are often in conflict across functions. Since senior management is held responsible for financial results, the benefits of cross‐functional integration should be measured in financial terms. The supply chain management literature provides little insight about the behavioral changes that can result when managers are provided with financial measures of the value created with customers and suppliers. Using a case study approach, the authors measured value in perceptual and financial terms using pairs of buyer–supplier relationships. In each pair of relationships, one involved cross‐functional teams and the other did not. Managers perceived that the relationships with cross‐functional involvement were more profitable. However, it was not until managers received financial measures showing the impact of joint initiatives on the profitability of each pair of relationships that their behaviors changed with regard to the implementation of cross‐functional relationships with key customers and suppliers. We developed a conceptual model comprised of five theoretical propositions that characterize the role of financial measurements as an enabler of cross‐functional integration and value co‐creation.     

DO ARBITRAGE‐FREE PRICES COME FROM UTILITY MAXIMIZATION?

In this paper we ask whether, given a stock market and an illiquid derivative, there exists arbitrage‐free prices at which a utility‐maximizing agent would always want to buy the derivative, irrespectively of his own initial endowment of derivatives and cash. We prove that this is false for any given investor if one considers all initial endowments with finite utility, and that it can instead be true if one restricts to the endowments in the interior. We show, however, how the endowments on the boundary can give rise to very odd phenomena; for example, an investor with such an endowment would choose not to trade in the derivative even at prices arbitrarily close to some arbitrage price.     

MARKETS FOR INFLATION‐INDEXED BONDS AS MECHANISMS FOR EFFICIENT MONETARY POLICY

We consider a continuous‐time framework featuring a central bank, private agents, and a financial market. The central bank's objective is to maximize a functional, which measures the classical trade‐off between output and inflation over time plus income from the sales of inflation‐indexed bonds minus payments for the liabilities that the inflation‐indexed bonds produce at maturity. Private agents are assumed to have adaptive expectations. The financial market is modeled in continuous‐time Black–Scholes–Merton style and financial agents are averse against inflation risk, attaching an inflation risk premium to nominal bonds. Following this route, we explain demand for inflation‐indexed securities on the financial market from a no‐arbitrage assumption and derive pricing formulas for inflation‐linked bonds and calls, which lead to a supply‐demand equilibrium. Furthermore, we study the consequences that the sales of inflation‐indexed securities have on the observed inflation rate and price level. Similar to the study of Walsh, we find that the inflationary bias is significantly reduced, and hence that markets for inflation‐indexed bonds provide a mechanism to reduce inflationary bias and increase central bank's credibility.     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.     

THE RANGE OF TRADED OPTION PRICES

Suppose we are given a set of prices of European call options over a finite range of strike prices and exercise times, written on a financial asset with deterministic dividends which is traded in a frictionless market with no interest rate volatility. We ask: when is there an arbitrage opportunity? We give conditions for the prices to be consistent with an arbitrage-free model (in which case the model can be realized on a finite probability space). We also give conditions for there to exist an arbitrage opportunity which can be locked in at time zero. There is also a third boundary case in which prices are recognizably misspecified, but the ability to take advantage of an arbitrage opportunity depends upon knowledge of the null sets of the model.     

Effect of corporate governance on default risk in financial versus nonfinancial firms: Canadian evidence

This paper investigates the influence of corporate governance variables on default risk of Canadian firms after the 2008 financial crisis. We provide evidence that important governance mechanisms have differential impacts between Canadian financial and nonfinancial firms. Ownership structure, (e.g., institutional ownership and insider ownership), has a significant impact on the default risk of financial firms but not on nonfinancial firms. Nonfinancial firms with more independent boards are associated with lower default risk, while financial firms with larger boards and more independent boards have higher default risk. In addition, although cross‐listing in the US reduces the default risk for Canadian nonfinancial firms, it actually increases the risk for Canadian financial firms during the postcrisis period. Copyright © 2016 ASAC. Published by John Wiley & Sons, Ltd.     

ON ARBITRAGE AND DUALITY UNDER MODEL UNCERTAINTY AND PORTFOLIO CONSTRAINTS

We consider the fundamental theorem of asset pricing (FTAP) and the hedging prices of options under nondominated model uncertainty and portfolio constraints in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super‐martingale under these measures. We also get the nondominated optional decomposition with constraints. From this decomposition, we obtain the duality of the super‐hedging prices of European options, as well as the sub‐ and super‐hedging prices of American options. Finally, we get the FTAP and the duality of super‐hedging prices in a market where stocks are traded dynamically and options are traded statically.     

ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS

We develop a theory of robust pricing and hedging of a weighted variance swap given market prices for a finite number of co‐maturing put options. We assume the put option prices do not admit arbitrage and deduce no‐arbitrage bounds on the weighted variance swap along with super‐ and sub‐replicating strategies that enforce them. We find that market quotes for variance swaps are surprisingly close to the model‐free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi‐infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model‐independent and probability‐free setup. In particular, we use and extend Föllmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the “log contract” and similar connections for weighted variance swaps. Our results take the form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk‐neutral expectations of discounted payoffs.     

NO‐ARBITRAGE PRICING FOR DIVIDEND‐PAYING SECURITIES IN DISCRETE‐TIME MARKETS WITH TRANSACTION COSTS

We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete‐time markets with dividend‐paying securities. Specifically, we show that the no‐arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk‐neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a contingent claim contract. Our results are illustrated with a vanilla credit default swap contract.     

TIME‐CONSISTENT AND MARKET‐CONSISTENT EVALUATIONS

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market‐consistent evaluation procedure which we call “two‐step market evaluation.” This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two‐step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time‐consistent and market‐consistent is a two‐step market evaluation. We also give characterization results and examples in terms of g‐expectations in a Brownian‐Poisson setting.     

Does US quantitative easing affect exchange rate pass‐through in China?

In this paper, we show theoretically and empirically that the US quantitative easing (QE ) policy results in lower exchange rate pass‐through into the destination prices of Chinese exporters. In addition, the more the exchange rate in the export destination appreciates than the Chinese yuan, the stronger this effect becomes. Our model combines various marginal effects of QE policy on the destinations of Chinese exporters and variable markups of export firms due to strategic complementarities. The model predicts that the impact of US QE policy on the pass‐through of Chinese exporters depends on its spillover on the exchange rate between China and the export destination of different firms. We provide strong support for the model predictions using Chinese firm‐product‐level data with information on export destinations. The baseline result and the heterogeneity we find in the response of exchange rate pass‐through of Chinese exporters to US QE policy remain robust to alternative measures of samples and controls.     

PRICE‐ADMISSIBILITY CONDITIONS FOR ARBITRAGE‐FREE LINEAR PRICE FUNCTION MODELS FOR THE TERM STRUCTURE OF INTEREST RATES

To assure price admissibility—that all bond prices, yields, and forward rates remain positive—we show how to control the state variables within the class of arbitrage‐free linear price function models for the evolution of interest rate yield curves over time. Price admissibility is necessary to preclude cash‐and‐carry arbitrage, a market imperfection that can happen even with a risk‐neutral diffusion process and positive bond prices. We assure price admissibility by (i) defining the state variables to be scaled partial sums of weighted coefficients of the exponential terms in the bond pricing function, (ii) identifying a simplex within which these state variables remain price admissible, and (iii) choosing a general functional form for the diffusion that selectively diminishes near the simplex boundary. By assuring that prices, yields, and forward rates remain positive with tractable diffusions for the physical and risk‐neutral measures, an obstacle is removed from the wider acceptance of interest rate methods that are linear in prices.     

ON AGENT’S AGREEMENT AND PARTIAL‐EQUILIBRIUM PRICING IN INCOMPLETE MARKETS

We consider two risk‐averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with nontraded random endowments, we provide necessary and sufficient conditions for negotiation to be successful, i.e., for the trade to occur. We also study the asymptotic case where the size of the claim is small compared to the random endowments and we give a full characterization in this case. Finally, we study a partial‐equilibrium problem for a bundle of divisible claims and establish existence and uniqueness. A number of technical results on conditional indifference prices is provided.