A model-free approach to multivariate option pricing

Review of Derivatives Research - We propose a novel model-free approach to extract a joint multivariate distribution, which is consistent with options written on individual stocks as well as on...     

A practical approach to validating a PD model

The capital adequacy framework Basel II aims to promote the adoption of stronger risk management practices by the banking industry. The implementation makes validation of credit risk models more important. Lenders therefore need a validation methodology to convince their supervisors that their credit scoring models are performing well. In this paper we take up the challenge to propose and implement a simple validation methodology that can be used by banks to validate their credit risk modelling exercise. We will contextualise the proposed methodology by applying it to a default model of mortgage loans of a commercial bank in the Netherlands.     

A multivariate jump-driven financial asset model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that—opposite to other, non-jointly Gaussian settings—its risk-neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.     

Exposure to the world and trading-bloc risks: A multivariate capital asset pricing model

This paper employs a capital asset pricing model that incorporates both world and trading-bloc factors to show that the recent trend of trade regionalism has led to segmentation of world stock markets. The model is developed within a multivariate GARCH framework. The conditional time-varying betas are derived to examine the dynamics of risk exposures to the world and trading-bloc factors. The results show risk exposure behaviour that is not revealed using static risk estimates.     

Modelling and forecasting short-term interest rate volatility: A semiparametric approach

This paper employs a semiparametric procedure to estimate the diffusion process of short-term interest rates. The Monte Carlo study shows that the semiparametric approach produces more accurate volatility estimates than models that accommodate asymmetry, level effect and serial dependence in the conditional variance. Moreover, the semiparametric approach yields robust volatility estimates even if the short rate drift function and the underlying innovation distribution are misspecified. Empirical investigation with the U.S. three-month Treasury bill rates suggests that the semiparametric procedure produces superior in-sample and out-of-sample forecast of short rate changes volatility compared with the widely used single-factor diffusion models. This forecast improvement has implications for pricing interest rate derivatives.     

A Bayesian approach to detecting nonlinear risk exposures in hedge fund strategies

This paper proposes a model that allows for nonlinear risk exposures of hedge funds to various risk factors. We introduce a flexible threshold regression model and develop a Bayesian approach for model selection and estimation of the thresholds and their unknown number. In particular, we present a computationally flexible Markov chain Monte Carlo stochastic search algorithm which identifies relevant risk factors and/or threshold values. Our analysis of several hedge fund returns reveals that different strategies exhibit nonlinear relations to different risk factors, and that the proposed threshold regression model improves our ability to evaluate hedge fund performance.     

Determinants of sovereign yield spreads in the Eurozone: A Bayesian approach

We analyze the determinants of sovereign yields spreads of EMU member states applying Bayesian Model Averaging (BMA) to annual panel data from 1999 to 2009. BMA is well-suited in cases of small samples and high model uncertainty. This seems to be the case in modeling sovereign yield spreads in the Eurozone since the literature reports heterogeneous results with respect to significant explanatory variables. We are testing a number of variables reported to be significant in the literature and find that the most likely country specific drivers of yield spreads are fiscal variables such as budget balance and government debt, as well as external sector variables, such as terms of trade, trade balance and openness. Global financing conditions, indicated by the US interest rate, and market sentiments, indicated by corporate bond spreads, are likely to influence sovereign yield spreads.     

Comparing New Keynesian models of the business cycle: A Bayesian approach

The baseline New Keynesian model cannot replicate the observed persistence in inflation, output, and real wages for sensible parameter values. As a result, several extensions have been suggested to improve its fit to the data. We use a Bayesian approach to estimate and compare the baseline sticky price model of Calvo's [1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12, 383-398.] and three extensions. Our empirical results are as follows. First, we find that adding price indexation improves the fit of Calvo's [1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12, 383-398.] model. Second, models with both staggered price and wage setting dominate models with only price rigidities. Third, introducing wage indexation does not significantly improve the fit. Fourth, all model estimates suggest a high degree of price stickiness. Fifth, the estimates of labor supply elasticity are higher in models with both staggered price and wage contracts. Finally, the estimated inflation parameters of the Taylor rule are stable across models.     

The role of credit in the Great Moderation: A multivariate GARCH approach

During the Great Moderation, financial innovation in the US increased the size and scope of credit flows supporting the growth of wealth. We hypothesize that spending out of wealth came to finance a wider range of GDP components such that it smoothed GDP. Both these trends combined would be consistent with a decrease in the volatility of output. We suggest testable implications in terms of both growth of credit and output and volatility of growth. In a multivariate GARCH framework, we test this view for home mortgages and residential investment. We observe unidirectional causality in variance from total output, residential investment and non-residential output to mortgage lending before, but not during the Great Moderation. These findings are consistent with a role for credit dynamics in explaining the Great Moderation.     

Testing stock market linkages for Poland and Hungary: A multivariate GARCH approach

This paper examines the linkages between the emerging stock markets in Warsaw and Budapest and the established markets in Frankfurt and the U.S. By using a four-variable asymmetric GARCH-BEKK model, we find evidence of returns and volatility spillovers from the developed to the emerging markets. However, as the estimated time-varying conditional covariances and the variance decompositions indicate limited interactions among the markets, the emerging markets are weakly linked to the developed markets. The implication is that foreign investors may benefit from the reduction of risk by adding the stocks in the emerging markets to their investment portfolio.     

Pricing mortgage-backed securities in a multifactor interest rate environment: a multivariate density estimation approach

Multivariate density estimation (MDE) suggests that mortgage-backedsecurity (MBS) prices can be well described as a function ofthe level and slope of the term structure. We analyze how thisfunction varies across MBSs with different coupons. An importantfinding is that the interest rate level proxies for the moneynessof the option, the expected level of prepayments, and the averagelife of the cash flows, while the term structure slope controlsfor the average rate at which these cash flows should be discounted.     

A Bayesian non-parametric model for small population mortality

This paper proposes a Bayesian non-parametric mortality model for a small population, when a benchmark mortality table is also available and serves as part of the prior information. In particular, we extend the Poisson-gamma model of Hardy and Panjer to incorporate correlated and age-specific mortality coefficients. These coefficients, which measure the difference in mortality levels between the small and the benchmark population, follow an age-indexed autoregressive gamma process, and can be stochastically extrapolated to ages where the small population has no historical exposure. Our model substantially improves the computation efficiency of existing two-population Bayesian mortality models by allowing for closed form posterior mean and variance of the future number of deaths, and an efficient sampling algorithm for the entire posterior distribution. We illustrate the proposed model with a life insurance portfolio from a French insurance company.     

The credit rating process and estimation of transition probabilities: A Bayesian approach

The Basel II Accord requires banks to establish rigorous statistical procedures for the estimation and validation of default and ratings transition probabilities. This raises great technical challenges when sufficient default data are not available, as is the case for low default portfolios. We develop a new model that describes the typical internal credit rating process used by banks. The model captures patterns of obligor heterogeneity and ratings migration dependence through unobserved systematic macroeconomic shocks. We describe a Bayesian hierarchical framework for model calibration from historical rating transition data, and show how the predictive performance of the model can be assessed, even with sparse event data. Finally, we analyze a rating transition data set from Standard and Poor's during 1981–2007. Our results have implications for the current Basel II policy debate on the magnitude of default probabilities assigned to low risk assets.     

A new approach to assessing model risk in high dimensions

A central problem for regulators and risk managers concerns the risk assessment of an aggregate portfolio defined as the sum of d individual dependent risks $X_i$. This problem is mainly a numerical issue once the joint distribution of $\left(X_1\text{,}{X}_2\text{,}\dots \text{,}{X}_d\right)$ is fully specified. Unfortunately, while the marginal distributions of the risks $X_i$ are often known, their interaction (dependence) is usually either unknown or only partially known, implying that any risk assessment of the portfolio is subject to model uncertainty.Previous academic research has focused on the maximum and minimum possible values of a given risk measure of the portfolio when only the marginal distributions are known. This approach leads to wide bounds, as all information on the dependence is ignored. In this paper, we integrate, in a natural way, available information on the multivariate dependence. We make use of the Rearrangement Algorithm (RA) of Embrechts et al. (2013) to provide bounds for the risk measure at hand. We observe that incorporating the information of a well-fitted multivariate model may, or may not, lead to much tighter bounds, a feature that also depends on the risk measure used. In particular, the risk of underestimating the Value-at-Risk at a very high confidence level (as used in Basel II) is typically significant, even if one knows the multivariate distribution almost completely.Our results make it possible to determine which risk measures can benefit from adding dependence information (i.e., leading to narrower bounds when used to assess portfolio risk) and, hence, to identify those situations for which it would be meaningful to develop accurate multivariate models.     

Detecting structural breaks and identifying risk factors in hedge fund returns: A Bayesian approach

Extending previous work on asset-based style factor models, this paper proposes a model that allows for the presence of structural breaks in hedge fund return series. We consider a Bayesian approach to detecting structural breaks occurring at unknown times and identifying relevant risk factors to explain the monthly return variation. Exact and efficient Bayesian inference for the unknown number and positions of the breaks is performed by using filtering recursions similar to those of the forward–backward algorithm. Existing methods of testing for structural breaks are also used for comparison. We investigate the presence of structural breaks in several hedge fund indices; our results are consistent with market events and episodes that caused substantial volatility in hedge fund returns during the last decade.     

Modelling bicommunal conflict: 2. Structuring the model

The problems encountered in this exercise included those of drawing the system boundaries, selecting the most appropriate subsystems, deriving usable measures for complex parameters, and establishing relationships between variables. The article discusses the ways in which such problems were handled in a model of a complex social process.     

A multivariate stochastic volatility model with applications in the foreign exchange market

The main objective of this paper is to study the behavior of a daily calibration of a multivariate stochastic volatility model, namely the principal component stochastic volatility (PCSV) model, to market data of plain vanilla options on foreign exchange rates. To this end, a general setting describing a foreign exchange market is introduced. Two adequate models—PCSV and a simpler multivariate Heston model—are adjusted to suit the foreign exchange setting. For both models, characteristic functions are found which allow for an almost instantaneous calculation of option prices using Fourier techniques. After presenting the general calibration procedure, both the multivariate Heston and the PCSV models are calibrated to a time series of option data on three exchange rates—USD-SEK, EUR-SEK, and EUR-USD—spanning more than 11 years. Finally, the benefits of the PCSV model which we find to be superior to the multivariate extension of the Heston model in replicating the dynamics of these options are highlighted.     

A fractional cointegration approach to testing the Ohlson accounting based valuation model

We examine the long-run relationship between market value, book value, and residual income in the Ohlson (Contemp Acc Res 11(2):661–687, 1995) model. In particular, we test if market value is cointegrated with book value and residual income in light of their non-stationary behaviors. We find that cointegration applies to only 51 % of the sample firms, casting doubt that book value and residual income alone are adequate in tracking variations in market value, yet we find that market value is fractional cointegrated with book value and residual income for 89 % of the sample firms. This implies that the long-run relationship follows a slow but mean-reverting process. Our results therefore support the Ohlson model.