Latin hypercube sampling with dependence and applications in finance

In Monte Carlo simulation, Latin hypercube sampling (LHS) [McKay et al. (1979)] is a well-known variance reduction technique for vectors of independent random variables. The method presented here, Latin hypercube sampling with dependence (LHSD), extends LHS to vectors of dependent random variables. The resulting estimator is shown to be consistent and asymptotically unbiased. For the bivariate case and under some conditions on the joint distribution, a central limit theorem together with a closed formula for the limit variance are derived. It is shown that for a class of estimators satisfying some monotonicity condition, the LHSD limit variance is never greater than the corresponding Monte Carlo limit variance. In some valuation examples of financial payoffs, when compared to standard Monte Carlo simulation, a variance reduction of factors up to 200 is achieved. LHSD is suited for problems with rare events and for high-dimensional problems, and it may be combined with Quasi-Monte Carlo methods. --Monte Carlo simulation,variance reduction,Latin hypercube sampling,stratified sampling

Credit gap risk in a first passage time model with jumps

The payoff of many credit derivatives depends on the level of credit spreads. In particular, credit derivatives with a leverage component are subject to gap risk, a risk associated with the occurrence of jumps in the underlying credit default swaps. In the framework of first passage time models, we consider a model that addresses these issues. The principal idea is to model a credit quality process as an Itô integral with respect to a Brownian motion with a stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, one can derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. The model can be implemented efficiently using a technique called Panjer recursion. Calibration to a wide range of dynamics is supported. We illustrate the effectiveness of the model by valuing a leveraged credit-linked note. --gap risk,credit spreads,credit dynamics,first passage time models,stochastic volatility,general Ornstein-Uhlenbeck processes

Credit dynamics in a first passage time model with jumps

The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit spreads. In the framework of first passage time models we extend the model introduced in [Overbeck and Schmidt, 2005] to address these issues. In the extended a model, a credit quality process is driven by an Itô integral with respect to a Brownian motion with stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, we derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. We show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the OS-model and the extended model and provide examples. --gap risk,credit spreads,credit dynamics,first passage time models,Lévy processes,general Ornstein-Uhlenbeck processes

A factor-model approach for correlation scenarios and correlation stress-testing

In 2012, JPMorgan accumulated a USD~6.2 billion loss on a credit derivatives portfolio, the so-called `London Whale', partly as a consequence of de-correlations of non-perfectly correlated positions that were supposed to hedge each other. Motivated by this case, we devise a factor model for correlations that allows for scenario-based stress testing of correlations. We derive a number of analytical results related to a portfolio of homogeneous assets. Using the concept of Mahalanobis distance, we show how to identify adverse scenarios of correlation risk. In addition, we demonstrate how correlation and volatility stress tests can be combined. As an example, we apply the factor-model approach to the "London Whale" portfolio and determine the value-at-risk impact from correlation changes. Since our findings are particularly relevant for large portfolios, where even small correlation changes can have a large impact, a further application would be to stress test portfolios of central counterparties, which are of systemically relevant size

Validierung von Konzepten zur Messung des Marktrisikos: Insbesondere des Value at Risk und des Expected Shortfall

Market risk management is one of the key factors to success in managing financial institutions. Underestimated risk can have desastrous consequences for individual companies and even whole economies, not least as could be seen during the recent crises. Overestimated risk, on the other side, may have negative effects on a company's capital requirements. Companies as well as national authorities thus have a strong interest in developing market risk models that correctly quantify certain key figures such as Value at Risk or Expected Shortfall. This paper presents several state of the art methods to evaluate the adequacy of almost any given market risk model. Existing models are enhanced by in-depth analysis and simulations of statistical properties revealing some previously unknown effects, most notably inconsistent behaviour of alpha and beta errors. Furthermore, some new market risk validation models are introduced. In the end, a simulation with various market patterns demonstrates strenghts and weaknesses of each of the models presented under realistic conditions

Default probabilities and default correlations under stress

We investigate default probabilities and default correlations of Merton-type credit portfolio models in stress scenarios where a common risk factor is truncated. The analysis is performed in the class of elliptical distributions, a family of light-tailed to heavy-tailed distributions encompassing many distributions commonly found in financial modelling. It turns out that the asymptotic limit of default probabilities and default correlations depend on the max-domain of the elliptical distribution's mixing variable. In case the mixing variable is regularly varying, default probabilities are strictly smaller than 1 and default correlations are in (0; 1). Both can be expressed in terms of the Student t-distribution function. In the rapidly varying case, default probabilities are 1 and default correlations are 0. We compare our results to the tail dependence function and discuss implications for credit portfolio modelling

Determinants of the onshore and offshore Chinese Government yield curves

As part of its effort to internationalize the Renminbi, China's government has promoted the establishment of a regulated offshore Renminbi capital market hub in Hong Kong, where, among other activities, it issues RMB-denominated government bonds providing foreign investors access to Chinese bond markets. In a VAR model where yield curves are represented by Nelson-Siegel latent factors and which includes macroeconomic variables, we find that onshore government bond yields are primarily driven by policy-related factors such as the policy rate and money supply, whereas offshore government bond yields are additionally driven by market-related factors such as consumer confidence, GDP and FX rate expectations as well as liquidity constraints. At the current stage of market development there are virtually no spillover effects between the onshore and offshore government bond curves. Our results add quantitative evidence that China's efforts to internationalize its currency results in a simultaneous liberalization of its financial system

The funding of small and medium companies by shadow-banks in China

This paper looks at the current shadow-banking practices of Chinese SME's and the question if these practices have a positive impact on the development of those SME's. For this pur-pose, new primary data is examined: Four case studies and two supplementary sets of data. Although the data volume imposes limitations on the results, the two main findings are: First, shadow-banking does have such a positive effect. Second, interpersonal lending is by far the most important financing channel for this effect among all the shadow-banking types ob-served

Credit gap risk in a first passage time model with jumps

The payoff of many credit derivatives depends on the level of credit spreads. In particular, credit derivatives with a leverage component are subject to gap risk, a risk associated with the occurrence of jumps in the underlying credit default swaps. In the framework of first passage time models, we consider a model that addresses these issues. The principal idea is to model a credit quality process as an Itô integral with respect to a Brownian motion with a stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, one can derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. The model can be implemented efficiently using a technique called Panjer recursion. Calibration to a wide range of dynamics is supported. We illustrate the effectiveness of the model by valuing a leveraged credit-linked note

Credit dynamics in a first passage time model with jumps

The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit spreads. In the framework of first passage time models we extend the model introduced in [Overbeck and Schmidt, 2005] to address these issues. In the extended a model, a credit quality process is driven by an Itô integral with respect to a Brownian motion with stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, we derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. We show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the OS-model and the extended model and provide examples