Hedging with small uncertainty aversion

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their “distance” to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security’s cash gamma.     

Arbitrage-free pricing of multi-person game claims in discrete time

We introduce a class of financial contracts involving several parties by extending the notion of a two-person game option to a contract in which an arbitrary number of parties is involved and each of them is allowed to make a wide array of decisions at any time, not restricted to simply exercising the option. The collection of decisions by all parties then determines the contract’s termination date as well as the terminal payoff for each party. We provide sufficient conditions under which a discrete-time multi-person game option has a unique arbitrage-free price, which is additive with respect to any partition of the contract. Our results are illustrated by the detailed study of a particular multi-person contract with puttable tranches.     

Market completion with derivative securities

Let \(S^{F}\) be a ?-martingale representing the price of a primitive asset in an incomplete market framework. We present easily verifiable conditions on the model coefficients which guarantee the completeness of the market in which in addition to the primitive asset, one may also trade a derivative contract \(S^{B}\). Both \(S^{F}\) and \(S^{B}\) are defined in terms of the solution \(X\) to a two-dimensional stochastic differential equation: \(S^{F}_{t} = f(X_{t})\) and \(S^{B}_{t}:=\mathbb{E}[g(X_{1}) | \mathcal{F}_{t}]\). From a purely mathematical point of view, we prove that every local martingale under ? can be represented as a stochastic integral with respect to the ?-martingale \(S :=(S^{F}, S^{B})\). Notably, in contrast to recent results on the endogenous completeness of equilibria markets, our conditions allow the Jacobian matrix of \((f,g)\) to be singular everywhere on \(\mathbb{R}^{2}\). Hence they cover as a special case the prominent example of a stochastic volatility model being completed with a European call (or put) option.     

Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals

Motivated by recent axiomatic developments, we study the risk- and ambiguity-averse investment problem where trading takes place in continuous time over a fixed finite horizon and terminal payoffs are evaluated according to criteria defined in terms of quasiconcave utility functionals. We extend to the present setting certain existence and duality results established for so-called variational preferences by Schied (Finance Stoch. 11:107–129, 2007). The results are proved by building on existing results for the classical utility maximization problem, combined with a careful analysis of the involved quasiconvex and semicontinuous functions.     

The role of measurability in game-theoretic probability

This paper argues that the requirement of measurability (imposed on trading strategies) is indispensable in continuous-time game-theoretic probability. The necessity of the requirement of measurability in measure theory is demonstrated by results such as the Banach–Tarski paradox and is inherited by measure-theoretic probability. The situation in game-theoretic probability turns out to be somewhat similar in that dropping the requirement of measurability allows a trader in a financial security with a non-trivial price path to become infinitely rich while risking only one monetary unit.     

Model uncertainty,recalibration, and the emergence of delta–vega hedging

We study option pricing and hedging with uncertainty about a Black–Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta–vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding indifference price corrections are determined by the disparity between the vegas, gammas, vannas and volgas of the non-traded and the liquidly traded options.     

Does the cessation of quarterly earnings guidance reduce investors’ short-termism?

The practice of providing quarterly earnings guidance has been criticized for encouraging investors to fixate on short-term earnings and encouraging managerial myopia. Using data from the post–Regulation Fair Disclosure period, we examine whether the cessation of quarterly earnings guidance reduces short-termism among investors. We show that, after guidance cessation, investors in firms that stop quarterly guidance are composed of a larger (smaller) proportion of long-term (short-term) institutions, put more (less) weight on long-term (short-term) earnings in firm valuation, become more (less) sensitive to analysts’ long-term (short-term) earning forecast revisions, and are less likely to dismiss chief executive officers for missing quarterly earnings targets by small amounts, relative to investors in firms that continue to issue quarterly earnings guidance. Our study provides new evidence of the benefit of stopping quarterly earnings guidance, that is, the reduction of short-termism among investors.     

Risk-Sensitive Asset Management in a Wishart-Autoregressive Factor Model with Jumps

Risk-sensitive asset management problems, both those with a finite horizon and those with an infinite horizon, are studied in a financial market model that has a Wishart autoregressive-type jump-diffusion factor, which is a positive-definite symmetric matrix-valued process. The model describes the stochasticity of the market covariance structure, the interest rates, and the risk-premium of the risky assets. We obtain explicit representations of the solutions to the problems.     

Rollover risk and credit risk under time-varying margin

For a firm financed by a mixture of collateralized (short-term) debt and uncollateralized (long-term) debt, we show that fluctuations in margin requirements, reflecting funding liquidity shocks, lead to increasing the firm’s default risk and credit spreads. The severity with which a firm is hit by increasing margin requirements highly depends on both its financing structure and debt maturity structure. Our results imply that an additional premium should be added when evaluating debt in order to account for rollover risks, especially for short-matured bonds. In terms of policy implications, our results strongly indicate that regulators should intervene fast to curtail margins in crisis periods and maintain a reasonably low margin level in order to effectively prevent creditors’ run on debt.     

The perceiver’s social role and a risk’s causal structure as determinants of environmental risk evaluation

We present a dual-process risk perception model that integrates cognitive and emotional as well as consequentialist and deontological components by distinguishing between two modes of evaluative processing: (a) a consequentialist evaluation that focuses on potential consequences and (b) a deontological evaluation that focuses on moral values. Each of these two modes is assumed to trigger specific cognitive evaluations, specific emotions, and specific behavioral tendencies concerning a perceived risk. We conducted an experiment (N = 270) that tested whether the relative dominance of the two evaluative modes would depend on the causal structure of the environmental risk being evaluated and on the social role of the evaluator. Three types of causal structure were varied by providing scenario information: (a) anthropogenic risks that endanger only nature, (b) naturally caused risks with potential harmful consequences for humans, and (c) anthropogenic risks that may harm humans. Participants evaluated each scenario from the perspective of one of three social roles: mayor, expecting parent, and environmental activist. For each scenario, participants specified their focus and evaluated the event’s morality and perceived risk, the intensity of specific emotions, and their preferences for prospective behaviors. Results showed that the consequentialist evaluation was generally stronger than the deontological evaluation and was less affected by the experimental manipulations. The deontological evaluation was substantially affected by the risk’s causal structure. It was stronger for anthropogenic than for natural causation; risks caused by humans were associated with greater perceived moral blameworthiness, more intense morality-based emotions (e.g. outrage), and a stronger tendency to perform agent-related behaviors (e.g. aggression) than naturally occurring risks. The effect of the social role was less pronounced than that of the causal structure. Furthermore, the effect of an evaluative focus on behavior was fully mediated by emotions for deontological evaluations and partially mediated for consequentialist evaluations. The implications for environmental risk perception and communication are discussed.