Natalie E. Packham

Competition, Bonuses, and Risk-Taking in the Banking Industry

Remuneration systems in the banking industry, in particular bonus payments, have frequently been blamed for contributing to the buildup of risks leading to the recent financial crisis. In our model, banks compete for managerial talent that is private information. Competition for talent sets incentives to offer bonuses inducing risk-taking that is excessive not only from societys perspective but also from the viewpoint of the banks themselves. In fact, bonus payments and excessive risk-taking are increasing with competition. Thus, our model offers a rationale why bonuses are paid even when reducing the expected profits of banks. Copyright 2013, Oxford University Press.

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.

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 Ito 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 Levy-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 Ito 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 Levy-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.

Correlation Under Stress in Normal Variance Mixture Models

We investigate correlations of asset returns in stress scenarios where a common risk factor is truncated. Our analysis is performed in the class of normal variance mixture (NVM) models, which encompasses many distributions commonly used in financial modelling. For the special cases of jointly normally and t-distributed asset returns we derive closed formulas for the correlation under stress. For the NVM distribution, we calculate the asymptotic limit of the correlation under stress, which depends on whether the variables are in the maximum domain of attraction of the Frechet or Gumbel distribution. It turns out that correlations in heavy-tailed NVM models are less sensitive to stress than in medium- or light-tailed models. Our analysis sheds light on the suitability of this model class to serve as a quantitative framework for stress testing, and as such provides valuable information for risk and capital management in financial institutions, where NVM models are frequently used for assessing capital adequacy.

Model Risk of Contingent Claims

Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, P&L from model risk corresponds to P&L realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, each of which represents alternative asset price dynamics to the model used for pricing. P&L from model risk is determined relative to each of these models. Using market data, a unified loss distribution is attained by weighing models according to a likelihood criterion involving both calibration quality and model parsimony. Examples demonstrate the magnitude of model risk and corresponding capital buffers necessary to sufficiently protect trading book positions against unexpected losses from model risk. A further application of the model risk framework demonstrates the calculation of gap risk of a barrier option when employing a semi-static hedging strategy.

Determinants of the Onshore and Offshore Chinese Government Yield Curves

As part of its effort to internationalize the Renminbi, Chinas 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 in order to establish a benchmark yield curve in the market. In a VAR model where yield curves are represented by Nelson–Siegel latent factors and which includes basic macroeconomic variables, we find that market forces have a higher impact on the offshore market for government bond yields than on the corresponding onshore market. Exchange rate expectations turn out to be the main driving variable for both the onshore and the offshore market, with a significantly stronger impact on the latter. Weak spillover effects from the onshore government bond yield curve to the offshore yield curve are observed, but no spillover effects the other way round are present.

Incentive schemes, private information and the double-edged role of competition for agents

This paper examines the effect of imperfect labor market competition on the efficiency of compensation schemes in a setting with moral hazard, private information and risk-averse agents. Two vertically differentiated firms compete for agents by offering contracts with fixed and variable payments. Vertical differentiation between firms leads to endogenous, type-dependent exit options for agents. In contrast to screening models with perfect competition, we find that existence of equilibria does not depend on whether the least-cost separating allocation is interim efficient. Rather, vertical differentiation allows the inferior firm to offer (cross-)subsidizing fixed payments even above the interim efficient level. We further show that the efficiency of variable pay depends on the degree of competition for agents: For small degrees of competition, low-ability agents are under-incentivized and exert too little effort. For large degrees of competition, high-ability agents are over-incentivized and bear too much risk. For intermediate degrees of competition, however, contracts are second-best despite private information.

Asymptotic behaviour of multivariate 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. For elliptically distributed asset variables, the asymptotic limits of default probabilities and default correlations depend on the max-domain of attraction of the asset variables. In the regularly varying case, we derive an integral representation for multivariate default probabilities, which turn out to be strictly smaller than 1. Default correlations are in (0, 1). In the rapidly varying case, asymptotic multivariate default probabilities are 1 and asymptotic default correlations are 0.

CORRELATION UNDER STRESS IN NORMAL VARIANCE MIXTURE MODELS: correlation under stress

We investigate correlations of asset returns in stress scenarios where a common risk factor is truncated. Our analysis is performed in the class of normal variance mixture (NVM) models, which encompasses many distributions commonly used in financial modeling. For the special cases of jointly normally and t�?distributed asset returns we derive closed formulas for the correlation under stress. For the NVM distribution, we calculate the asymptotic limit of the correlation under stress, which depends on whether the variables are in the maximum domain of attraction of the Fréchet or Gumbel distribution. It turns out that correlations in heavy�?tailed NVM models are less sensitive to stress than in medium�? or light�?tailed models. Our analysis sheds light on the suitability of this model class to serve as a quantitative framework for stress testing, and as such provides valuable information for risk and capital management in financial institutions, where NVM models are frequently used for assessing capital adequacy. We also demonstrate how our results can be applied for more prudent stress testing.