Monetary policy under model and data-parameter uncertainty

Empirical Taylor rules are much less aggressive than those derived from optimization-based models. This paper analyzes whether accounting for uncertainty across competing models and (or) real-time data considerations can explain this discrepancy. It considers a central bank that chooses a Taylor rule in a framework that allows for an aversion to the second-order risk associated with facing multiple models and measurement-error configurations. The paper finds that if the central bank cares strongly enough about stabilizing the output gap, this aversion leads to significant declines in the coefficients of the Taylor rule even if the central bank's loss function assigns little weight to reducing interest rate variability. Furthermore, a small degree of aversion can generate an optimal rule that matches the empirical Taylor rule.     

International stock return predictability under model uncertainty

This paper examines return predictability when the investor is uncertain about the right state variables. A novel feature of the model averaging approach used in this paper is to account for finite-sample bias of the coefficients in the predictive regressions. Drawing on an extensive international dataset, we find that interest-rate related variables are usually among the most prominent predictive variables, whereas valuation ratios perform rather poorly. Yet, predictability of market excess returns weakens substantially, once model uncertainty is accounted for. We document notable differences in the degree of in-sample and out-of-sample predictability across different stock markets. Overall, these findings suggest that return predictability is neither a uniform, nor a universal feature across international capital markets.     

Portfolio optimization under model uncertainty and BSDE games

We consider robust optimal portfolio problems for markets modeled by (possibly non-Markovian) Itô–Lévy processes. Mathematically, the situation can be described as a stochastic differential game, where one of the players (the agent) is trying to find the portfolio that maximizes the utility of her terminal wealth, while the other player (“the market”) is controlling some of the unknown parameters of the market (e.g., the underlying probability measure, representing a model uncertainty problem) and is trying to minimize this maximal utility of the agent. This leads to a worst case scenario control problem for the agent. In the Markovian case, such problems can be studied using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation, but these methods do not work in the non-Markovian case. We approach the problem by transforming it into a stochastic differential game for backward stochastic differential equations (a BSDE game). Using comparison theorems for BSDEs with jumps we arrive at criteria for the solution of such games in the form of a kind of non-Markovian analogue of the HJBI equation. The results are illustrated by examples.     

Forecasting exchange rates under parameter and model uncertainty

We introduce a forecasting method that closely matches the econometric properties required by exchange rate theory. Our approach formally models (i) when (and if) predictor variables enter or leave a regression model, (ii) the degree of parameter instability, (iii) the (potentially) rapidly changing relevance of regressors, and (iv) the appropriate shrinkage intensity over time. We consider (short-term) forecasting of six major US dollar exchange rates using a standard set of macro fundamentals. Our results indicate the importance of shrinkage and flexible model selection/averaging criteria to avoid poor forecasting results.     

Portfolio optimization in discrete time with proportional transaction costs under stochastic volatility

This paper is devoted to evaluating the optimal self-financing strategy and the optimal trading frequency for a portfolio with a risky asset and a risk-free asset. The objective is to maximize the expected future utility of the terminal wealth in a stochastic volatility setting, when transaction costs are incurred at each discrete trading time. A HARA utility function is used, allowing a simple approximation of the optimization problem, which is implementable forward in time. For each of various transaction cost rates, we find the optimal trading frequency, i.e. the one that attains the maximum of the expected utility at time zero. We study the relation between transaction cost rate and optimal trading frequency. The numerical method used is based on a stochastic volatility particle filtering algorithm, combined with a Monte-Carlo method. The filtering algorithm updates the estimate of the volatility distribution forward in time, as new stock observations arrive; these updates are used at each of these discrete times to compute the new portfolio allocation.     

Strategy under uncertainty

At the heart of the traditional approach to strategy lies the assumption that by applying a set of powerful analytic tools, executives can predict the future of any business accurately enough to allow them to choose a clear strategic direction. But what happens when the environment is so uncertain that no amount of analysis will allow us to predict the future? What makes for a good strategy in highly uncertain business environments? The authors, consultants at McKinsey & Company, argue that uncertainty requires a new way of thinking about strategy. All too often, they say, executives take a binary view: either they underestimate uncertainty to come up with the forecasts required by their companies' planning or capital-budging processes, or they overestimate it, abandon all analysis, and go with their gut instinct. The authors outline a new approach that begins by making a crucial distinction among four discrete levels of uncertainty that any company might face. They then explain how a set of generic strategies--shaping the market, adapting to it, or reserving the right to play at a later time--can be used in each of the four levels. And they illustrate how these strategies can be implemented through a combination of three basic types of actions: big bets, options, and no-regrets moves. The framework can help managers determine which analytic tools can inform decision making under uncertainty--and which cannot. At a broader level, it offers executives a discipline for thinking rigorously and systematically about uncertainty and its implications for strategy.     

A generalized probability framework to model economic agents' decisions under uncertainty

The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance have produced valuable results. The principal movement which has steered this research direction is known under the name of ‘econophysics’. In this paper, we illustrate and advance some of the findings that have been obtained by applying the mathematical formalism of quantum mechanics to model human decision making under ‘uncertainty’ in behavioral economics and finance. Starting from Ellsberg's seminal article, decision making situations have been experimentally verified where the application of Kolmogorovian probability in the formulation of expected utility is problematic. Those probability measures which by necessity must situate themselves in Hilbert space (such as ‘quantum probability’) enable a faithful representation of experimental data. We thus provide an explanation for the effectiveness of the mathematical framework of quantum mechanics in the modeling of human decision making. We want to be explicit though that we are not claiming that decision making has microscopic quantum mechanical features.     

Dynamically consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences.We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and ?itkovi? (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk \(\hat{\lambda}\) and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with \(\hat{\lambda}\) and with the leverage being proportional to the investor’s confidence in her estimate.     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

Liquidity preference under uncertainty: A model of dynamic investment in illiquid opportunities

Whereas frictionless exchange markets provide a high degree of liquidity for financial assets, investments in real assets and productive capacity may be very costly to modify, and thus effectively irreversible in the short-run. This paper addresses the problem of an investor (individual or enterprise) who must allocate a limited resource to productive investments over time. Investment opportunities arrive in a random sequence and are irreversible in the short-run: thus investment decisions are made under uncertainty as to future opportunities (which may have to be foregone). The analysis demonstrates that a rational investor will demand a higher return on long-lasting opportunities than on those which are instantaneously reversible. The liquidity premium increases with the average duration of the non-liquid investments.     

Valuation before and after tax in the discrete time, finite state no arbitrage model

We establish necessary and sufficient conditions for a linear taxation system to be neutral—within the multi-period discrete time “no arbitrage” model—in the sense that valuation is invariant to the exact sequence of tax rates, realization dates as well as immune to timing options attempting to twist the time profile of taxable income through wash sale transactions.

“In the study of investments, taxes are largely a source of embarrassment to financial economists.” (Introduction to Dybvig and Ross 1986) “Accordingly, my approach in this chapter is to examine the restrictions on the income measurement rules applicable to financial instruments implied by the requirement that the rules be linear. . . . Linearity is a desideratum of a tidy tax system.” (Bradford 2000, p. 373–374)

     

Carbon pricing under uncertainty

International Tax and Public Finance - Economists have adopted the Pigouvian approach to climate policy, which sets the carbon price to the social cost of carbon. We adjust this carbon price for...     

Optimal stopping under model uncertainty and the regularity of lower Snell envelopes

The analysis of American options in incomplete markets has motivated the development of robust versions of the classical Snell envelopes: The cost of superhedging an American option is characterized by the upper Snell envelope, while the infimum of the arbitrage prices is given by the lower Snell envelope. Lower Snell envelopes also appear in the problem of optimal stopping under model uncertainty. In this paper we focus on the lower Snell envelope. We construct a regular version of this stochastic process. To this end, we apply results due to Dellacherie and Lenglart on the regularization of stochastic processes and 𝒯-Systems.     

Partial hedging and cash requirements in discrete time

This paper develops a discrete time version of the continuous time model of Bouchard et al. [J. Control Optim., 2009, 48, 3123–3150], for the problem of finding the minimal initial data for a controlled process to guarantee reaching a controlled target with probability one. An efficient numerical algorithm, based on dynamic programming, is proposed for the quantile hedging of standard call and put options, exotic options and quantile hedging with portfolio constraints. The method is then extended to solve utility indifference pricing, good-deal bounds and expected shortfall problems.