Disentangling Managers’ and Analysts’ Non‐GAAP Reporting

Researchers frequently proxy for managers’ non‐GAAP disclosures using performance metrics available through analyst forecast data providers (FDPs), such as I/B/E/S. The extent to which FDP‐provided earnings are a valid proxy for managers’ non‐GAAP reporting, however, has been debated extensively. We explore this important question by creating the first large‐sample data set of managers’ non‐GAAP earnings disclosures, which we directly compare to I/B/E/S data. Although we find a substantial overlap between the two data sets, we also find that they differ in systematic ways because I/B/E/S (1) excludes managers’ lower quality non‐GAAP numbers and (2) sometimes provides higher quality non‐GAAP measures that managers do not explicitly disclose. Our results indicate that using I/B/E/S to identify managers’ non‐GAAP disclosures significantly underestimates the aggressiveness of their reporting choices. We encourage researchers interested in managers’ non‐GAAP reporting to use our newly available data set of manager‐disclosed non‐GAAP metrics because it more accurately captures managers’ reporting choices.     

Machine learning in individual claims reserving

Machine learning techniques make it feasible to calculate claims reserves on individual claims data. This paper illustrates how these techniques can be used by providing an explicit example in individual claims reserving.     

Stock price informativeness on the sensitivity of strategic M&A investment to Q

Using a strategic merger sample that covers the period from 1985 to 2011, we find that the acquirer’s stock price firm-specific information, the new information created by investors about the value of firm fundamentals, increases the positive sensitivity of strategic merger investment to the acquirer’s Q; the target’s stock price firm-specific information increases the negative sensitivity of merger investment to the target’s Q. These results suggest that managers learn from financial markets in identifying strategic merger investment opportunities by transferring assets from poorly managed firms to well managed firms. In addition, the target’s stock price firm-specific information itself increases the acquisition size, indicating that informed acquirer managers are more likely to take out large merger investment. Last but not the least, stock price informativeness increases merger synergies and post-merger performance, suggesting that informed managers make better merger investment that increases shareholder value. Our study contributes to the recent increasing stream of studies on managerial learning from the market.     

Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.     

An expansion in the model space in the context of utility maximization

In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian), an explicit second-order expansion formula for the power investor’s value function—seen as a function of the underlying market price of risk process—is provided. This allows us to provide first-order approximations of the optimal primal and dual controls. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Chebyshev interpolation for parametric option pricing

Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real time. We concentrate on parametric option pricing (POP) as a generic instance of parametric conditional expectations and show that polynomial interpolation in the parameter space promises to considerably reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence and explicit error bounds. The method is most promising when the computation of the prices is most challenging. We therefore investigate its combination with Monte Carlo simulation and analyze the effect of (stochastic) approximations of the interpolation. For a wide and important range of problems, the Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo. We conclude with a numerical efficiency study.     

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.     

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the linear part of the drift being a generator of a \(C_{0}\)-semigroup) driven by an infinite-dimensional cylindrical Wiener process. In particular, we prove, under some sufficient conditions on the coefficients, the existence and uniqueness of solutions for these stochastic evolution equations in a class of Banach spaces satisfying the so-called \(H\)-condition. Moreover, we analyse the Markov property of the solutions.Secondly, we apply the abstract results obtained in the first part to prove the existence and uniqueness of solutions to the Heath–Jarrow–Morton–Musiela (HJMM) equations in weighted Lebesgue and Sobolev spaces.Finally, we study the ergodic properties of the solutions to the HJMM equations. In particular, we find a sufficient condition for the existence and uniqueness of invariant measures for the Markov semigroup associated to the HJMM equations (when the coefficients are time-independent) in the weighted Lebesgue spaces.Our paper is a modest contribution to the theory of financial models in which the short rate can be undefined.     

Classical meets modern in the IDEA protocol for structured expert judgement

Expert judgement is pervasive in all forms of risk analysis, yet the development of tools to deal with such judgements in a repeatable and transparent fashion is relatively recent. This work outlines new findings related to an approach to expert elicitation termed the IDEA protocol. IDEA combines psychologically robust interactions among experts with mathematical aggregation of individual estimates. In particular, this research explores whether communication among experts adversely effects the reliability of group estimates. Using data from estimates of the outcomes of geopolitical events, we find that loss of independence is relatively modest and it is compensated by improvements in group accuracy.