Stochastic Discount Factor Bounds with Conditioning Information

Hansen and Jagannathan (1991) (hereafter HJ) derive restrictionson the volatility of stochastic discount factors that pricea given set of returns. This article studies the sampling propertiesof HJ bounds that use conditioning information. One approachis to multiply the returns by the lagged variables. We alsostudy optimized HJ bounds with conditioning information fromGallant, Hansen, and Tauchen (1990) and based on portfoliosderived in Ferson and Siegel (2001). We document striking finite-samplebiases in the HJ bounds, where the bounds reject asset-pricingmodels too often. We provide a useful bias correction. We alsoevaluate asymptotic standard errors for the bounds from Hansen,Heaton, and Luttmer (1995).     

General closed-form basket option pricing bounds

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms; hence, they do not suffer from the curse of dimensionality and can be applied also to high-dimensional problems where most existing methods fail. In particular, we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate.     

Reduction of Value-at-Risk bounds via independence and variance information

We derive lower and upper bounds for the Value-at-Risk of a portfolio of losses when the marginal distributions are known and independence among (some) subgroups of the marginal components is assumed. We provide several actuarial examples showing that the newly proposed bounds strongly improve those available in the literature that are based on the sole knowledge of the marginal distributions. When the variance of the joint portfolio loss is small enough, further improvements can be obtained.     

Assessing time-varying stock market integration in Economic and Monetary Union for normal and crisis periods

In this paper, we examine the stock market integration process amongst 17 Economic and Monetary Union (EMU) countries from January 2002 to June 2013 over a normal period as well as for the Global Financial Crisis (GFC) and Eurozone Debt Crisis (EDC) periods. We classify the economies in three groups (A, B and C) based on their GDP to examine whether the economic size influences financial integration. Seven indicators are used for the purpose, namely, beta convergence, sigma convergence, variance ratio, asymmetric DCC, dynamic cointegration, market synchronisation measure and common components approach. The results suggest that large-sized EMU economies (termed as Group A) exhibit strong stock market integration. Moderate integration is observed for middle-sized EMU economies with old membership (termed as Group B). Small-sized economies (termed as Group C) economies seemed to be least integrated within the EMU stock market system. The findings further suggest presence of contagion effects as one moves from normal to crisis periods, which are specifically stronger for more integrated economies of Group A. We recommend institutional, regulatory and other policy reforms for Group B and especially Group C to achieve higher level of integration.     

Tracking Resource Use in a Welfare Organization: Needs, Costs and Co-production

Public sector welfare organizations are situated at the sharp end of resource allocations in society and must cope in an environment where demand frequently far exceeds supply. In consequence, the resource problem of meeting the need for social welfare is never fully resolvable and evaluations of the ways in which scarce resources are used within the public sector are of critical importance for public policy. This paper draws on an empirical study of a welfare service for homeless young people in order to illustrate, first, the cost implications of two different approaches to service delivery (one more superficial – termed 'people-processing'; one more in depth – termed, 'people-changing') and, second, how the characteristics of the clients served (in particular, their ability to fully engage with the service termed –'co-production') can have a marked impact on the cost of the services delivered to them.     

Non-exponential bounds for stop-loss premiums and ruin probabilities

We present an inventory of non-exponential bounds for ruin probabilities and stop-loss premiums in the general Sparre-Andersen model (renewal model) of risk theory. Various additional bounds are given if one assumes that the ladder height distribution F associated with the risk process belongs to a certain class of distributions, in particular if it is concave or it exhibits a (positive or negative) aging property. In most cases, these bounds are shown to improve existing ones in the literature and/or possess the correct asymptotic behaviour when the distribution F is subexponential. Since in the classical (compound Poisson) risk model the ladder height distribution is always concave, all the bounds given in the paper are also valid for this model. Finally, in many cases the results of the paper are also valid for any compound geometric distribution.     

Shedding light on a dark matter: Jump diffusion and option-implied investor preferences

We compare equilibrium jump diffusion option prices with endogenously determined stochastic dominance (SD) option bounds. We use model parameters from earlier studies and find that most equilibrium model prices consistent with SD bounds yield economically meaningless results. Further, the implied distributions of the SD bounds exhibit a tail risk comparable to that of the underlying return data, thus shedding light on the dark matter of the inconsistency of physical and risk-neutral tail probabilities. Since the SD bound assumptions are weaker, we conclude that these bounds should either replace or be used to verify the equilibrium model results.     

Universal bounds for asset prices in heterogeneous economies

We establish universal bounds for asset prices in heterogeneous complete market economies with scale invariant preferences. Namely, for each agent in the economy we consider an artificial homogeneous economy populated solely by this agent, and calculate the “homogeneous” price of an asset in each of these economies. Dumas (Rev. Financ. Stud. 2, 157–188, [1989]) conjectured that the risk free rate in a heterogeneous economy must lie in the interval determined by the minimal and maximal of the “homogeneous” risk free rates. We show that the answer depends on the risk aversions of the agents in the economy: the upper bound holds when all risk aversions are smaller than one, and the lower bound holds when all risk aversions are larger than one. The bounds almost never hold simultaneously. Furthermore, we prove these bounds for arbitrary assets.      

Conditioning Information and Variance Bounds on Pricing Kernels with Higher- Order Moments: Theory and Evidence

We develop a strategy for utilizing higher moments, variancerisk premia, and conditioning information efficiently, and henceimprove on the variance bounds computed by Hansen and Jagannathan(1991); Gallant, Hansen, and Tauchen (1990); and Bekaert andLiu (2004). Our bounds reach existing bounds when nonlinearitiesin returns are not priced. We also use higher moments, variancerisk premia, and conditioning information to provide distancemeasures that improve on the Hansen and Jagannathan (1997) distancemeasure. Empirical results indicate that when accounting forthe impact of higher moments and variance risk premia, the existingpricing kernels have difficulty in explaining returns on theassets and derivatives.     

Out of Bounds: Do SPF Respondents Have Anchored Inflation Expectations?

Since the Federal Open Market Committee announced a 2% inflation target in 2012, the median long-run inflation forecast of professional forecasters has been near target. We show, however, that most individual forecasters' long-run inflation expectations fluctuate substantially, with sizeable departures from target. We propose a new “bounds anchoring” indicator based on deviations of individuals' long-run forecasts from target. This indicator sheds new light on gradual changes in expectations since the 2012 announcement. We find that bounds anchoring gradually strengthened in the years following the target announcement, but that this trend has recently started to reverse.     

Negative oil price shocks transmission: The comparative effects of the GFC,shale oil boom,and Covid-19 downturn on French gasoline prices

This article analyzes the transmission mechanisms between oil prices and fuel prices in France over the period 2005−2020. The econometric procedure focuses on three singular years marked by significant negative oil prices shocks: 2008 (the global financial crisis), 2014 (the sharp drop in prices due to the boom of US shale oil), 2020 (Covid-19 economic downturn). To analyze the linkages between oil and fuel prices, we use the ARDL bounds testing approach of cointegration with weekly data between January 7, 2005 and October 30, 2020. We find that over the entire period, fuel distributors report increases in oil prices more than decreases. We find that this asymmetry is highest in 2008. Our paper provides some policy recommendations based on our findings.     

Investor Heterogeneity and the Cross-section of U.K. Investment Trust Performance

We use the upper and lower bounds derived by Ferson and Lin (2010) to examine the impact of investor heterogeneity on the performance of U.K. investment trusts relative to alternative linear factor models. We find using the upper bounds that investor heterogeneity has an important impact for nearly all investment trusts. The upper bounds are large in economic terms and significantly different from zero. We find no evidence of any trusts where all investors agree on the sign of performance beyond what we expect by chance. Using the lower bound, we find that trusts with a larger disagreement about trust performance have a weaker relation between the trust premium and past Net Asset Value (NAV) performance.     

Primal–dual quasi-Monte Carlo simulation with dimension reduction for pricing American options

The pricing of American options is one of the most challenging problems in financial engineering due to the involved optimal stopping time problem, which can be solved by using dynamic programming (DP). But applying DP is not always practical, especially when the state space is high dimensional. However, the curse of dimensionality can be overcome by Monte Carlo (MC) simulation. We can get lower and upper bounds by MC to ensure that the true price falls into a valid confidence interval. During the recent decades, progress has been made in using MC simulation to obtain both the lower bound by least-squares Monte Carlo method (LSM) and the upper bound by duality approach. However, there are few works on pricing American options using quasi-Monte Carlo (QMC) methods, especially to compute the upper bound. For comparing the sample variances and standard errors in the numerical experiments, randomized QMC (RQMC) methods are usually used. In this paper, we propose to use RQMC to replace MC simulation to compute both the lower bound (by the LSM) and the upper bound (by the duality approach). Moreover, we propose to use dimension reduction techniques, such as the Brownian bridge, principal component analysis, linear transformation and the gradients based principle component analysis. We perform numerical experiments on American–Asian options and American max-call options under the Black–Scholes model and the variance gamma model, in which the options have the path-dependent feature or are written on multiple underlying assets. We find that RQMC in combination with dimension reduction techniques can significantly increase the efficiency in computing both the lower and upper bounds, resulting in better estimates and tighter confidence intervals of the true price than pure MC simulation.     

Portfolio efficiency and discount factor bounds with conditioning information: An empirical study

Stochastic discount factor bounds provide a useful diagnostic tool for testing asset pricing models by specifying a lower bound on the variance of any admissible discount factor. In this paper, we provide a unified derivation of such bounds in the presence of conditioning information, which allows us to compare their theoretical and empirical properties. We find that, while the location of the ‘unconditionally efficient (UE)’ bounds of [Ferson, W., Siegel, A., 2001. The efficient use of conditioning information in portfolios. Journal of Finance 56 (3), 967–982] is statistically indistinguishable from the (theoretically) optimal bounds of [Gallant, R., Hansen, L., Tauchen, G., 1990. Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution. Journal of Econometrics 45 (1), 141–179] (GHT), the former exhibit better sampling properties. We demonstrate that the difference in sampling variability of the UE and GHT bounds is due to the different behavior of the efficient return weights underlying their construction.     

Model uncertainty and VaR aggregation

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.     

Insurance contracts portfolios with heterogenous parametric life distributions

In this paper we consider two portfolios: one of m endowment insurance contracts and one of m whole life insurance contracts. We introduce the majorization order, Schur functions, and parametric families of distribution functions. We assume that the owners of the portfolios are exposed to different members of a known parametric family of distributions and study the effect of this stochastic heterogeneity on the premiums and death benefits of the insurance contracts. We show that the premiums paid in both contracts are Schur concave and that the death benefit awarded in the whole life contract is Schur convex. We provide upper and lower bounds for the premiums and for the death benefit, and compute the bounds for four parametric families of distribution functions used frequently in the Actuarial Sciences.     

Market Efficiency, Bounded Rationality, and Supplemental Business Reporting Disclosures

The AICPA Special Committee on Financial Reporting has urged disclosure of relevant forward-looking information on risks and opportunities to supplement conventional financial statements. We conduct a laboratory market experiment to assess the effects of such disclosures on capital allocation decisions. We develop two sets of competing hypotheses regarding how capital markets react to supplemental disclosures. One set is based on the assumption of semi-strong market efficiency, while the other posits that the bounded rationality of individual traders leads to inefficient market prices. We find that explicit disclosure of management's best estimate of an uncertain quantity improves market efficiency, even though this disclosure is redundant with information in financial statements. Second, we find disclosure of an upper bound of management's estimate has the potential to bias security prices upward, while informationally equivalent disclosure of both upper and lower bounds removes this bias. These results suggest that experimental market reactions to these supplemental disclosures are inconsistent with market efficiency. Supplemental analyses of individuals' price predictions and trading behavior support our conclusion that inefficiencies are at least partially attributable to individual information processing biases.     

Additive and multiplicative duals for American option pricing

We investigate and compare two dual formulations of the American option pricing problem based on two decompositions of supermartingales: the additive dual of Haugh and Kogan (Oper. Res. 52:258–270, 2004) and Rogers (Math. Finance 12:271–286, 2002) and the multiplicative dual of Jamshidian (Minimax optimality of Bermudan and American claims and their Monte- Carlo upper bound approximation. NIB Capital, The Hague, 2003). Both provide upper bounds on American option prices; we show how to improve these bounds iteratively and use this to show that any multiplicative dual can be improved by an additive dual and vice versa. This iterative improvement converges to the optimal value function. We also compare bias and variance under the two dual formulations as the time horizon grows; either method may have smaller bias, but the variance of the multiplicative method typically grows much faster than that of the additive method. We show that in the case of a discrete state space, the additive dual coincides with the dual of the optimal stopping problem in the sense of linear programming duality and the multiplicative method arises through a nonlinear duality.      

Robust pricing and hedging of double no-touch options

Double no-touch options are contracts which pay out a fixed amount provided an underlying asset remains within a given interval. In this work, we establish model-independent bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of super- and sub-hedging strategies to establish the bounds, and the use of Skorokhod embedding techniques to show the bounds are the best possible.