What do two plus two equal？

Amathematician, an accountant and an economist apply for the same job.The interviewer calls in the mathematician and asks ＂What do two plus two equal ？ ＂The mathematician replies ＂Four＂ The interviewer asks ＂Four, exactly ？＂ The mathematician looks at the interviewer incredulously and says ＂Yes, four, exactly.＂     

Measuring discretionary accruals: are ROA-matched models better than the original Jones-type models?

Discretionary accruals estimated from Jones-type models are elevated or depressed for firms with extreme performance. Kothari et al. (J Acc Econ 39:163–197, 2005) propose performance matching to address the issue, that is, to difference discretionary accruals estimated from Jones-type models for treatment and control firms matched on current ROA. This study shows (1) performance matching will systematically cause discretionary accruals of either sign to be underestimated, and (2) the measurement error will be negatively correlated with the true discretionary accruals. As a result, using discretionary accruals estimated with performance matching to test whether certain events induce earnings management will increase the frequency of Type II errors, and using them as the dependent or an independent variable in regression analysis will bias the regression coefficient toward zero. The results of our empirical tests are consistent with these predictions.     

Can learnability save new-Keynesian models?

McCallum (2009) argues that “learnability” can save new-Keynesian models from indeterminacies. He claims the unique bounded equilibrium is learnable, and the explosive equilibria are not. However, he assumes that agents can directly observe the monetary policy shock. Reversing this assumption, I find the opposite: the bounded equilibrium is not learnable and the unbounded equilibria are learnable. More generally, I argue that a threat by the Fed to move to an “unlearnable” equilibrium for all but one value of inflation is a poor foundation for choosing the bounded equilibrium of a new-Keynesian model.     

Tangent Lévy market models

In this paper, we introduce a new class of models for the time evolution of the prices of call options of all strikes and maturities. We capture the information contained in the option prices in the density of some time-inhomogeneous Lévy measure (an alternative to the implied volatility surface), and we set this static code-book in motion by means of stochastic dynamics of It?’s type in a function space, creating what we call a tangent Lévy model. We then provide the consistency conditions, namely, we show that the call prices produced by a given dynamic code-book (dynamic Lévy density) coincide with the conditional expectations of the respective payoffs if and only if certain restrictions on the dynamics of the code-book are satisfied (including a drift condition à la HJM). We then provide an existence result, which allows us to construct a large class of tangent Lévy models, and describe a specific example for the sake of illustration.     

Time consistency of Lévy models

Time consistency of the models used is an important ingredient to improve risk management. The empirical investigation in this article gives evidence for some models driven by Lévy processes to be highly consistent. This means that they provide a good statistical fit of empirical distributions of returns not only on the timescale used for calibration but on various other timescales as well. As a result these models produce more reliable risk numbers and derivative prices.     

Spectral calibration of exponential Lévy models

We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit inversion of the option price formula in the spectral domain and a cut-off scheme for high frequencies as regularisation.     

Existence of Lévy term structure models

Lévy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the Lévy driven Heath–Jarrow–Morton type term structure equation. This includes a full proof of existence and uniqueness in particular, which seems to have been lacking in the finance literature so far.      

Long-term factorization in Heath–Jarrow–Morton models

The long-term factorization decomposes the stochastic discount factor (SDF) into discounting at the rate of return on the long bond and a martingale that defines a long-term forward measure. We establish sufficient conditions for existence of the long-term factorization in HJM models. A condition on the forward rate volatility ensures existence of the long bond volatility. This yields existence of the long bond and convergence of \(T\)-forward measures to the long forward measure. It contrasts with the familiar risk-neutral factorization that decomposes the SDF into discounting at the short rate and a martingale defining the risk-neutral measure.     

Statistical estimation of Lévy-type stochastic volatility models

Volatility clustering and leverage are two of the most prominent stylized features of the dynamics of asset prices. In order to incorporate these features as well as the typical fat-tails of the log return distributions, several types of exponential Lévy models driven by random clocks have been proposed in the literature. These models constitute a viable alternative to the classical stochastic volatility approach based on SDEs driven by Wiener processes. This paper has two main objectives. First, using threshold type estimators based on high-frequency discrete observations of the process, we consider the recovery problem of the underlying random clock of the process. We show consistency of our estimator in the mean-square sense, extending former results in the literature for more general Lévy processes and for irregular sampling schemes. Secondly, we illustrate empirically the estimation of the random clock, the Blumenthal-Geetor index of jump activity, and the spectral Lévy measure of the process using real intraday high-frequency data.     

Tests of market models: heteroskedasticity or misspecification?

This paper investigates the nature and the incidence of heteroskedasticity and misspecification in the market models by utilizing tests that are generally applicable. The results show that heteroskedasticity appears more frequently than misspecification even though both are serious problems. The evidence also indicates that the use of a quadratic market model or equally weighted market returns may lead to a smaller percentage of heteroskedastic cases but that, in general, this advantage has to be offset against an increase in the occurrence of specification errors. Small firms and January returns are also observed to produce a higher incidence of both heteroskedasticity and misspecification.     

Multilevel Monte Carlo for exponential Lévy models

We apply the multilevel Monte Carlo method for option pricing problems using exponential Lévy models with a uniform timestep discretisation. For lookback and barrier options, we derive estimates of the convergence rate of the error introduced by the discrete monitoring of the running supremum of a broad class of Lévy processes. We then use these to obtain upper bounds on the multilevel Monte Carlo variance convergence rate for the variance gamma, NIG and \(\alpha\)-stable processes. We also provide an analysis of a trapezoidal approximation for Asian options. Our method is illustrated by numerical experiments.     

Leveraged Lévy processes as models for stock prices

Adopting a constant elasticity of variance formulation in the context of a general Lévy process as the driving uncertainty we show that the presence of the leverage effect? ?One explanation of the documented negative relation between market volatilities and the level of asset prices (the ‘smile’ or ‘skew’), we term the ‘leverage effect’, argues that this negative relation reflects greater risk taking by the management, induced by a fall in the asset price, with a view of maximizing the option value of equity shareholders. in this form has the implication that asset price processes satisfy a scaling hypothesis. We develop forward partial integro-differential equations under a general Markovian setup, and show in two examples (both continuous and pure-jump Lévy) how to use them for option pricing when stock prices follow our leveraged Lévy processes. Using calibrated models we then show an example of simulation-based pricing and report on the adequacy of using leveraged Lévy models to value equity structured products.     

Integrated models of capital adequacy – Why banks are undercapitalised

With the majority of large UK and many US banks collapsing or being forced to raise capital over the 2007–9 period, blaming bankers may be satisfying but is patently insufficient; Basel II and Federal oversight frameworks also deserve criticism. We propose that the current methodological void at the heart of Basel II, Pillar 2 is filled with the recommendation that banks develop fully-integrated models for economic capital that relate asset values to fundamental drivers of risk in the economy to capture systematic effects and inter-asset dependencies in a way that crude correlation assumptions do not. We implement a fully-integrated risk analysis based on the balance sheet of a composite European bank using an economic-scenario generation model calibrated to conditions at the end of 2007. Our results suggest that the more modular, correlation-based approaches to economic capital that currently dominate practice could have led to an undercapitalisation of banks, a result that is clearly of interest given subsequent events. The introduction of integrated economic-scenario-based models in future can improve capital adequacy, enhance Pillar 2’s application and rejuvenate the relevance of the Basel regulatory framework.     

Lévy term structure models: No-arbitrage and completeness

The Lévy term structure model due to Eberlein and Raible is extended to non-homogeneous driving processes. The classes of equivalent martingale and local martingale measures for various filtrations are characterized. It turns out that in a number of standard situations the martingale measure is unique.Received: May 2004, Mathematics Subject Classification (2000): 60H30, 91B28, 60G51JEL Classification: E43, G13Work supported in part by the European Communitys Human Potential Programme under contract HPRN-CT-2000-00100, DYNSTOCH.     

New analytical option pricing models with Weyl–Titchmarsh theory

Abstract

In this paper we consider the valuation of Bermudan callable derivatives with multiple exercise rights. We present in this context a new primal–dual linear Monte Carlo algorithm that allows for efficient simulation of the lower and upper price bounds without using nested simulations (hence the terminology). The algorithm is essentially an extension of the primal–dual Monte Carlo algorithm for standard Bermudan options proposed by Schoenmakers et al. [SIAM J. Finance Math., 2013, 4, 86–116] to the case of multiple exercise rights. In particular, the algorithm constructs upwardly a system of dual martingales to be plugged into the dual representation of Schoenmakers. At each level, the respective martingale is constructed via a backward regression procedure starting at the last exercise date. The thus constructed martingales are finally used to compute an upper price bound. The algorithm also provides approximate continuation functions that may be used to construct a price lower bound. The algorithm is applied to the pricing of flexible caps in a Hull and White model setup. The simple model choice allows for comparison of the computed price bounds with the exact price obtained by means of a trinomial tree implementation. As a result, we obtain tight price bounds for the considered application. Moreover, the algorithm is generically designed for multi-dimensional problems and is tractable to implement.     

A proposition of generalized stochastic Milevsky–Promislov mortality models

The aim of this article is to propose a new approach to the estimation of the mortality rates based on two extended Milevsky and Promislov models: the first one with colored excitations modeled by Gaussian linear filters and the second one with excitations modeled by a continuous non-Gaussian process. The exact analytical formulas for theoretical mortality rates based on Gaussian linear scalar filter models have been derived. The theoretical values obtained in both cases were compared with theoretical mortality rates based on a classical Lee–Carter model, and verified on the basis of empirical Polish mortality data. The obtained results confirm the usefulness of the switched model based on the continuous non-Gaussian process for modeling mortality rates.     

Multivariate asset models using Lévy processes and applications

In this paper, we propose a multivariate asset model based on Lévy processes for pricing of products written on more than one underlying asset. Our construction is based on a two-factor representation of the dynamics of the asset log-returns. We investigate the properties of the model and introduce a multivariate generalization of some processes which are quite common in financial applications, such as subordinated Brownian motions, jump-diffusion processes and time-changed Lévy processes. Finally, we explore the issue of model calibration for the proposed setting and illustrate its robustness on a number of numerical examples.     

How should we estimate value-relevance models? Insights from European data

We study the consequences of unobserved heterogeneity when employing different econometric methods in the estimation of two major value-relevance models: the Price Regression Model (PRM) and the Return Regression Model (RRM). Leveraging a large panel data set of European listed companies, we first demonstrate that robust Hausman tests and Breusch-Pagan Lagrange Multiplier tests are of fundamental importance to choose correctly among a fixed-effects model, a random-effects model, or a pooled OLS model. Second, we provide evidence that replacing firm fixed-effects with country and industry fixed-effects can lead to large differences in the magnitude of the key coefficients, with serious consequences for the interpretation of the effect of changes in earnings and book values per share on firm value. Finally, we offer recommendations to applied researchers aiming to improve the robustness of their econometric strategy.     

Contagion models a la carte: which one to choose?

We propose a copula contagion mixture model for correlated default times. The model includes the well-known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the default times of the underlying names in a reference portfolio to follow contagion intensity processes with exponential decay coupled with a copula dependence structure. We also model the default time of the counterparty and its dependence structure with the reference portfolio. Numerical tests show that correlation and contagion have an enormous joint impact on the rates of CDO tranches and the corresponding credit value adjustments are extremely high to compensate for the wrong-way risk.