Employer‐employee profit‐sharing and the incentives to innovate when the dismissal regulation matters

We develop a simple incomplete‐contract model of the relationship between worker participation to revenue sharing and innovation performance of firms, under firing regimes with different stringency. Stronger worker participation to profits is shown to increase innovation probability when employer‐side hold‐up is prevented by stringent layoff regulation and the human capital matters significantly. Vice‐versa, under a strict layoff regulation, when the financial capital is relatively more important, the effects of worker participation devices may be reduced or inverted. Our results may help in understanding why there is no one‐size‐fits‐all optimal strategy in the design of worker financial participation mechanisms for knowledge‐intensive productions.     

Knock‐in American options

A knock‐in American option under a trigger clause is an option contract in which the option holder receives an American option conditional on the underlying stock price breaching a certain trigger level (also called barrier level). We present analytic valuation formulas for knock‐in American options under the Black‐Scholes pricing framework. The price formulas possess different analytic representations, depending on the relation between the trigger stock price level and the critical stock price of the underlying American option. We also performed numerical valuation of several knock‐in American options to illustrate the efficacy of the price formulas. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:179–192, 2004     

OPTIMAL MULTI‐AGENT PERFORMANCE MEASURES FOR TEAM CONTRACTS

We present a continuous‐time contracting model under moral hazard with many agents. The principal contracts many agents as a team, and they jointly produce correlated outcomes. We show the optimal contract for each agent is linear in outcomes of all other agents as well as his/her own. The structure of the optimal contract strikingly reveals that the optimal aggregate performance measure in general can be orthogonally decomposed into two statistics: one is a sufficient statistic, and the other a nonsufficient statistic. As a consequence, the optimal aggregate performance measure in general is not a sufficient statistic, unless the principal is risk neutral. We further discuss agents' optimal effort choices using a “quadratic‐cost” example, which also strikingly suggests that team contracts sometimes provide lower‐powered effort incentives than individually separate contracts do.     

A MODEL‐FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER‐REPLICATION THEOREM

We propose a Fundamental Theorem of Asset Pricing and a Super‐Replication Theorem in a model‐independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as options written on this risky asset. As a technical condition, we assume the existence of a traded option with a superlinearly growing payoff‐function, e.g., a power option. This condition is not needed when sufficiently many vanilla options maturing at the horizon T are traded in the market.     

NO‐ARBITRAGE PRICING UNDER SYSTEMIC RISK: ACCOUNTING FOR CROSS‐OWNERSHIP

We generalize Merton’s asset valuation approach to systems of multiple financial firms where cross‐ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no‐arbitrage. An existence result and a uniqueness result are proven. Examples and an algorithm for the simultaneous calculation of all no‐arbitrage prices are provided. A result on capital structure irrelevance for groups of firms regarding externally held claims is discussed, as well as financial leverage and systemic risk caused by cross‐ownership.     

A CLOSED‐FORM EXACT SOLUTION FOR PRICING VARIANCE SWAPS WITH STOCHASTIC VOLATILITY

In this paper, we present a highly efficient approach to price variance swaps with discrete sampling times. We have found a closed‐form exact solution for the partial differential equation (PDE) system based on the Heston's two‐factor stochastic volatility model embedded in the framework proposed by Little and Pant. In comparison with the previous approximation models based on the assumption of continuous sampling time, the current research of working out a closed‐form exact solution for variance swaps with discrete sampling times at least serves for two major purposes: (i) to verify the degree of validity of using a continuous‐sampling‐time approximation for variance swaps of relatively short sampling period; (ii) to demonstrate that significant errors can result from still adopting such an assumption for a variance swap with small sampling frequencies or long tenor. Other key features of our new solution approach include the following: (1) with the newly found analytic solution, all the hedging ratios of a variance swap can also be analytically derived; (2) numerical values can be very efficiently computed from the newly found analytic formula.     

A note on utility‐based futures hedging performance measure

This note considers the estimator for the utility‐based hedging performance. It shows that the estimator incurs a downward bias, regardless of whether the conventional mean‐variance expected utility function or the more general risk‐averse utility function is adopted. Consequently, the usefulness of the futures contract is under‐estimated. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

ARBITRAGE‐FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS

We develop an arbitrage‐free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on‐default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation‐induced contagion is illustrated with numerical examples.     

The design and pricing of fixed‐ and moving‐window contracts: An application of Asian‐Basket option pricing methods to the hog‐finishing sector

Asian‐Basket‐type moving‐window contracts are an increasingly used risk‐management tool in the North American hog sector. The moving‐window contract is decomposed into a portfolio of a long Asian‐Basket put and a short Asian‐Basket call option. A projected break‐even price is used to determine the floor price, and then Monte Carlo simulation methods are used to price both a moving‐ and a fixed‐window contract. These methods provide unbiased pricing of fixed‐ and moving‐window hog‐finishing contracts of 1‐year duration. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:1047–1073, 2003     

Optimal hedging with a regime‐switching time‐varying correlation GARCH model

The authors develop a Markov regime‐switching time‐varying correlation generalized autoregressive conditional heteroscedasticity (RS‐TVC GARCH) model for estimating optimal hedge ratios. The RS‐TVC nests within it both the time‐varying correlation GARCH (TVC) and the constant correlation GARCH (CC). Point estimates based on the Nikkei 225 and the Hang Seng index futures data show that the RS‐TVC outperforms the CC and the TVC both in‐ and out‐of‐sample in terms of variance reduction. Based on H. White's (2000) reality check, the null hypothesis of no improvement of the RS‐TVC over the TVC is rejected for the Nikkei 225 index contract but is not rejected for the Hang Seng index contract. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:495–516, 2007     

TUG‐OF‐WAR,MARKET MANIPULATION,AND OPTION PRICING

We develop an option pricing model based on a tug‐of‐war game. This two‐player zero‐sum stochastic differential game is formulated in the context of a multidimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the nonlinear and completely degenerate infinity Laplace operator.     

Efficiency of the IBEX spot–futures basis: The impact of the mini‐futures

This paper considers whether the introduction of the mini‐futures contract for the Spanish Ibex index affects overall market efficiency. Using linear, non‐linear, and fractional integration modeling techniques for the basis term, results of this study suggest the following salient points. First, the equilibrium speed of adjustment is reduced after the introduction of the mini‐futures contract. This effect is particularly pronounced in the mini‐futures second year when its contracts are more heavily traded. Second, fractional integration tests support longer memory in the basis term after the contract introduction, again particularly in the second year. Third, the relationship between the full‐size and mini‐futures contracts appears highly efficient, with a quick speed of adjustment and short memory. Finally, an examination of the volatility dynamics suggests that in the second year of the mini‐futures contract shocks to spot return volatility exhibit longer memory. The results reported here suggest that the increased use of the mini‐futures contract after its introduction has had a detrimental impact on price discovery. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 398–415, 2008     

Long‐term information,short‐lived securities

The authors explore strategic trade in short‐lived securities by agents who have private information that is potentially long‐term, but do not know how long their information will remain private. Trading short‐lived securities is profitable only if enough of the private information becomes public prior to contract expiration; otherwise the security will worthlessly expire. How this results in trading behavior fundamentally different from that observed in standard models of informed trading in equity is highlighted. Specifically, it is shown that informed speculators are more reluctant to trade shorter‐term securities too far in advance of when their information will necessarily be made public, and that existing positions in a shorter‐term security make future purchases more attractive. Because informed speculators prefer longer‐term securities, this can make trading shorter‐term contracts more attractive for liquidity traders. The conditions are characterized under which liquidity traders choose to incur extra costs to roll over short‐term positions rather than trade in distant contracts, providing an explanation for why most longer‐term derivative security markets have little liquidity and large bid‐ask spreads. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:465–502, 2006     

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.     

Addressing privacy predicaments in the digital marketplace: A power‐relations perspective

The utilization and governance of the internet and adjacent disruptive technologies have created numerous challenges to ensuring consumer online privacy. This study employs the power–responsibility equilibrium theory to explore emerging online privacy issues in the data‐driven marketplace. This exploratory study, based on semi‐structured interviews, explains why online shopping consumers are increasingly worried about their privacy and why they behave in a manner that could be detrimental to the consumer–vendor relationship. The findings suggest that deficiencies of corporate privacy responsibility and regulatory protection have deprived consumers of privacy empowerment. These deficiencies have also accentuated perceived privacy contract violations to trigger privacy concerns and subsequent defensive responses. We identify enhancement of consumer privacy empowerment and assuagement of privacy contract violations as two separate mechanisms of addressing online privacy issues. We also highlight the importance of addressing power and responsibility dynamics for maintaining a healthy information‐exchange environment.     

BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART II: CVA

The correction in value of an over‐the‐counter derivative contract due to counterparty risk under funding constraints is represented as the value of a dividend‐paying option on the value of the contract clean of counterparty risk and excess funding costs. This representation allows one to analyze the structure of this correction, the so‐called Credit Valuation Adjustment (CVA for short), in terms of replacement cost/benefits, credit cost/benefits, and funding cost/benefits. We develop a reduced‐form backward stochastic differential equations (BSDE) approach to the problem of pricing and hedging the CVA. In the Markov setup, explicit CVA pricing and hedging schemes are formulated in terms of semilinear partial differential equations.     

OPTIMAL INSURANCE DESIGN UNDER RANK‐DEPENDENT EXPECTED UTILITY

We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank‐dependent expected utility (RDEU) theory with a concave utility function and an inverse‐S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.     

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.     

Multidimensional Variance‐Optimal Hedging in Discrete‐Time Model—A General Approach

One of the well‐known approaches to the problem of option pricing is a minimization of the global risk, considered as the expected quadratic net loss. In the paper, a multidimensional variant of the problem is studied. To obtain the existence of the variance‐optimal hedging strategy in a model without transaction costs, we can apply the result of Monat and Stricker. Another possibility is a generalization of the nondegeneracy condition that appeared in a paper of Schweizer, in which a one‐dimensional problem is solved. The relationship between the two approaches is shown. A more difficult problem is the existence of an optimal solution in the model with transaction costs. A sufficient condition in a multidimensional case is formulated.     

Hedging long‐term commodity risk

This study focuses on the problem of hedging longer‐term commodity positions, which often arises when the maturity of actively traded futures contracts on this commodity is limited to a few months. In this case, using a rollover strategy results in a high residual risk, which is related to the uncertain futures basis. We use a one‐factor term structure model of futures convenience yields in order to construct a hedging strategy that minimizes both spot‐price risk and rollover risk by using futures of two different maturities. The model is tested using three commodity futures: crude oil, orange juice, and lumber. In the out‐of‐sample test, the residual variance of the 24‐month combined spot‐futures positions is reduced by, respectively, 77%, 47%, and 84% compared to the variance of a naïve hedging portfolio. Even after accounting for the higher trading volume necessary to maintain a two‐contract hedge portfolio, this risk reduction outweighs the extra trading costs for the investor with an average risk aversion. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:109–133, 2003