Investment Strategies and Market Structure: An Empirical Analysis of Bank Branching Decisions

This paper analyzes the relationship between the competitive environment faced by depository institutions and the decisions these institutions make regarding the size of their branch networks. Specifically, we consider branches as a sunk investment that potentially increases utility for consumers and examine how local competition and product differentiation affect firms’ decisions regarding whether to make such investments. We account for endogenous market structure using an equilibrium structural model, which corrects for bias caused by correlation in the unobservables associated with market structure and branching activity. We estimate the model using data from 1,882 concentrated rural markets. Our results demonstrate the importance of accounting for market structure and product differentiation, and are consistent with a potential entry-deterring effect of bank branch investments.     

How to choose the return model for market risk? Getting towards a right magnitude of stressed VaR

Value at Risk (VaR) and stressed value at Risk (SVaR) or expected shortfall are important risk measures widely used in the financial services industry for risk management and market risk capital computation. Fundamental to any (S)VaR model is the choice of the return type model for each risk factor. Because the resulting SVaR numbers are highly sensitive to the chosen return type model it is important to make a prudent choice on the return type modelling. We propose to estimate the return type model from historic data without making an a priori model assumption on the return model. We explain the fundamentals of return type modelling and how it impacts the magnitude of SVaR. We further show how to obtain a global return type model from a set of similar return type models by using geometric calculus. Numerical simulations and illustrations are provided. In this paper, we consider interest rate data, but the proposed methodology is general and can be applied to any other asset class such as inflation, credit spread, equity or fx.     

Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models

This paper demonstrates how to value American interest rate options under the jump-extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie et al., 2000) and lognormal jumps (see Johannes, 2004) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.     

Generalized volatility-stabilized processes

We consider systems of interacting diffusion processes which generalize the volatility-stabilized market models introduced in Fernholz and Karatzas (Ann Finance 1(2):149–177, 2005). We show how to construct a weak solution of the underlying system of stochastic differential equations. In particular, we express the solution in terms of time changed squared-Bessel processes, and discuss sufficient conditions under which one can show that this solution is unique in distribution (respectively, does not explode). Sufficient conditions for the existence of a strong solution are also provided. Moreover, we discuss the significance of these processes in the context of arbitrage relative to the market portfolio within the framework of Stochastic Portfolio Theory.     

Bootstrapping Parametric Models of Mortality

We consider a general problem of modeling a mortality law of a population of failing units with some parametric function. In this setting we define a mortality table of crude rates as a statistical estimator with multinomial distribution and show its consistency as well as asymptotic normality. We further derive the statistical properties of parameter estimators in a parametric mortality model based on a weighted square loss function. We use the obtained results to study consistency and appropriateness of the parametric bootstrap method in our setting. We derive the conditions on the assumed parametric mortality law and the loss function, under which the bootstrap is consistent for estimating the model parameters, their standard errors and corresponding confidence intervals. We apply our results to a model of Aggregate US Mortality Table based on a so called mixture of extreme value distributions suggested by Carriere ().     

Co-monotonicity of optimal investments and the design of structured financial products

We prove that, under very weak conditions, optimal financial products on complete markets are co-monotone with the reversed state price density. Optimality is meant in the sense of the maximization of an arbitrary preference model, e.g., expected utility theory or prospect theory. The proof is based on a result from transport theory. We apply the general result to specific situations, in particular the case of a market described by the Capital Asset Pricing Model or the Black–Scholes model, where we derive a generalization of the two-fund-separation theorem and give an extension to APT factor models and structured products with several underlyings. We use our results to derive a new approach to optimization in wealth management, based on a direct optimization of the return distribution of the portfolio. In particular, we show that optimal products can (essentially) be written as monotonic functions of the market return. We provide existence and nonexistence results for optimal products in this framework. Finally we apply our results to the study of bonus certificates, show that they are not optimal, and construct a cheaper product yielding the same return distribution.     

Inflation and capital accumulation under a finite horizon

The effect of inflation on demand for capital and the aggregate capital-labor ratio is investigated in a finite-horizon utility-maximization model. It is shown that deriving saving and asset choice decisions from utility maximization does not in itself lead to superneutrality (independence of steady-state capital-labor ratio from the rate of monetary growth) as in the work of Sidrauski, and that a finite horizon is crucial in explaining this difference. It is further shown that it is possible under very general conditions to show that increases in the rate of inflation will increase the aggregate capital-labor ratio, allowing us to extend the Mundell-Tobin effect to a wider class of models.     

Portfolio choice and equilibrium in capital markets with safety-first investors

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets. The valuation formula reduces to the well-known two-parameter capital asset pricing model (CAPM) when investors approximate the tail of the portfolio distribution using Tchebychev's inequality or when the assets have normal or stable Paretian distributions. This shows the robustness of the CAPM to safety-first investors under traditional distributional assumptions. In addition, we indicate how additional information about the portfolio distribution can be incorporated to the safety-first valuation formula to obtain alternative empirically testable models.     

Computing finite-time survival probabilities using multinomial approximations of risk models

We consider the problem of computing finite-time survival probabilities for various risk models. We develop an approximating discrete-time multinomial lattice that mimics the evolution of the corresponding continuous risk process. A simple recursive algorithm to compute survival probabilities is described. Numerical results show that the proposed scheme yields accurate values in all the considered cases.     

Asymmetric information in health insurance: evidence from the National Medical Expenditure Survey.

Adverse selection is perceived to be a major source of market failure in insurance markets. There is little empirical evidence on the extent of the problem. We estimate a structural model of health insurance and health care choices using data on single individuals from the NMES. A robust prediction of adverse-selection models is that riskier types buy more coverage and, on average, end up using more care. We test for unobservables linking health insurance status and health care consumption. We find no evidence of informational asymmetries.     

Subprime Loan Default Resolutions: Do They Vary Across Mortgage Products and Borrower Demographic Groups?

This paper examines default outcomes for subprime first lien loans during the recent subprime mortgage boom. It conducts this investigation in two phases. The paper first examines factors associated with pre-foreclosure outcomes for subprime mortgages in default. It then examines factors associated with different outcomes for loans that enter foreclosure. These factors include less understood elements such as mortgage product features and borrower demographics. The analysis is based on detailed loan-level data and employs multinomial logit models in a hazard framework. Results show that default resolutions vary with product features and borrower demographics. Adjustable rate and interest-only mortgages, and loans with low- or no-documentation are more likely to enter foreclosure proceedings, and, once in foreclosure, are more likely to become REO. The existence of junior liens increases the probability of the loan remaining in default. Owner-occupancy is associated with lower likelihood of foreclosure initiation and REO, and greater likelihood of curing default. Additionally, default outcomes are impacted by local legal, economic and housing market conditions, and the equity in the home.     

Modeling asymmetric comovements of asset returns

Existing time-varying covariance models usually impose strongrestrictions on how past shocks affect the forecasted covariancematrix. In this article we compare the restrictions imposedby the four most popular multivariate GARCH models, and introducea set of robust conditional moment tests to detect misspecification.We demonstrate that the choice of a multivariate volatilitymodel can lead to substantially different conclusions in anyapplication that involves forecasting dynamic covariance matrices(like estimating the optimal hedge ratio or deriving the riskminimizing portfolio). We therefore introduce a general modelwhich nests these four models and their natural 'asymmetric'extensions. The new model is applied to study the dynamic relationbetween large and small firm returns.     

Affine forward variance models

We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterised by the affine form of their cumulant-generating function, which can be obtained as solution of a convolution Riccati equation. We further introduce the class of affine forward order flow intensity (AFI) models, which are structurally similar to AFV models, but driven by jump processes, and which include Hawkes-type models. We show that the cumulant-generating function of an AFI model satisfies a generalised convolution Riccati equation and that a high-frequency limit of AFI models converges in distribution to an AFV model.

     

Instability of sunspot equilibria in real business cycle models under adaptive learning

We provide conditions under which a general, reduced-form class of real business cycle (RBC) models has rational expectations equilibria that are both indeterminate and stable under adaptive learning. Indeterminacy of equilibrium allows for the possibility that non-fundamental “sunspot” variable realizations can be used to drive the model, and several researchers have offered calibrated structural models where sunspot shocks play such a role. However, we show that the structural restrictions researchers have adopted lead to reduced-form systems that are always unstable under adaptive learning dynamics, thus calling into question the plausibility of these sunspot-driven RBC models.     

Intertemporal price discrimination with two products

We study the two‐product monopoly profit maximization problem for a seller who can commit to a dynamic pricing strategy. We show that if consumers' valuations are not strongly ordered, then optimality for the seller can require intertemporal price discrimination: the seller offers a choice between supplying a complete bundle now, or delaying the supply of a component of that bundle until a later date. For general valuations, we establish a sufficient condition for such dynamic pricing to be more profitable than mixed bundling. So we show that the established no‐discrimination‐across‐time result does not extend to two‐product sellers under standard taste distributions.     

On a universal mechanism for long-range volatility correlations

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between 'active' and 'inactive' strategies is subordinated to random-walk-like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy. We show that real market data can be surprisingly well accounted for by these simple models.     

Search for differentiated products: identification and estimation

When consumers search for differentiated products, a given search decision can be explained either by low search cost or by low tastes for the set of products already found. We propose an identification strategy that allows to estimate the search cost distribution in the presence of unobserved tastes. The required data takes the form of conditional search decisions: observations of search actions combined with previously observed product displays. We develop an application using clickstream data from a hotel search platform. Estimates of price elasticity of demand in the search model differ from those in the static model, reflecting the bias due to endogeneity of search‐generated choice sets.     

Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

In this paper, we analyze properties of multinomial lattices that model general stochastic dynamics of the underlying stock by taking into account any given cumulants (or moments). First, we provide a parameterization of multinomial lattices, and demonstrate that mean, variance, skewness, and kurtosis of the underlying may be matched using five branches. Then, we investigate the convergence of the multinomial lattice when the basic time period approaches zero, and prove that the limiting process of the multinomial lattice that matches annualized mean, variance, skewness and kurtosis is given by a compound Poisson process. Finally, we illustrate the effect of higher order moments in the underlying asset process on the price of derivative securities through numerical experiments using the multinomial lattice, and provide a comparison with jump-diffusion models.     

Around and Around: The Expectations Hypothesis

We show how to construct models of the term structure of interest rates in which the expectations hypothesis holds. McCulloch (1993) presents such a model, thereby contradicting an assertion by Cox, Ingersoll, and Ross (1981), but his example is Gaussian and falls outside the class of finite-dimensional Markovian models. We generalize McCulloch's model in three ways: (i) We provide an arbitrage-free characterization of the unbiased expectations hypothesis in terms of forward rates; (ii) we extend this characterization to a whole class of expectations hypotheses; and (iii) we show how to construct finite-dimensional Markovian and non-Gaussian examples.