Baeho Kim

Systemic Risk: What Defaults Are Telling Us

This paper develops dynamic measures of the systemic risk of the financial sector as a whole. It defines systemic risk as the conditional probability of failure of a sufficiently large fraction of the total population of financial institutions. This definition recognizes that the cause of systemic distress is the correlated failure of institutions to meet obligations to creditors, customers, and trading partners. The likelihood estimators of the failure probability are based on a dynamic hazard model of correlated failure timing that captures the influence on failure timing of time-varying macroeconomic and sector-specific risk factors, and of spillover effects. Tests indicate that our measures provide accurate out-of-sample forecasts of the term structure of systemic risk in the United States for the period from 1998 to 2009. This paper was accepted by Wei Xiong, finance.

Premia for Correlated Default Risk

Using data on corporate default experience in the U.S. and market rates of CDX index and tranche swaps of various maturities, we estimate reduced-form models of correlated default timing in the CDX High Yield and Investment Grade portfolios under actual and risk-neutral probabilities. The striking contrast between the estimated processes followed by the actual and risk-neutral arrival intensities of defaults, and between the parameters governing the actual and risk-neutral dynamics of the risk-neutral intensities, indicates the presence of substantial default risk premia in CDX swap market rates. The effects of risk premia on swap rates covary strongly across maturities, and depend on general stock market volatility and several measures of credit spreads. Large moves in the effects of these premia on swap rates have natural interpretations in terms of economic and financial market developments during the sample period, April 2004 to October 2007. Our results suggest that a large portion of the movements in CDX swap market rates observed during the sample period may be caused by changing attitudes toward correlated default risk rather than changes in the economic factors affecting the actual risk of clustered defaults, which ultimately governs swap payoffs.

Risk Analysis of Collateralized Debt Obligations

Collateralized debt obligations, which are securities with payoffs that are tied to the cash flows in a portfolio of defaultable assets such as corporate bonds, play a significant role in the financial crisis that has spread throughout the world. Insufficient capital provisioning due to flawed and overly optimistic risk assessments is at the center of the problem. This paper develops stochastic methods to measure the risk of positions in collateralized debt obligations and related instruments tied to an underlying portfolio of defaultable assets. It proposes an adaptive point process model of portfolio default timing, a maximum likelihood method for estimating point process models that is based on an acceptance/rejection resampling scheme, and statistical tests for model validation. To illustrate these tools, they are used to estimate the distribution of the profit or loss generated by positions in multiple tranches of a collateralized debt obligation that references the CDX High Yield portfolio and the risk capital required to support these positions.

Estimating tranche spreads by loss process simulation

A credit derivative is a path dependent contingent claim on the aggregate loss in a portfolio of credit sensitive securities. We estimate the value of a credit derivative by Monte Carlo simulation of the affine point process that models the loss. We consider two algorithms that exploit the direct specification of the loss process in terms of an intensity. One algorithm is based on the simulation of intensity paths. Here discretization introduces bias into the results. The other algorithm facilitates exact simulation of default times and generates an unbiased estimator of the derivative price. We implement the algorithms to value index and tranche swaps, and we calibrate the loss process to quotes on the CDX North America High Yield index.

Monte Carlo Algorithms for Default Timing Problems

Dynamic, intensity-based point process models are widely used to measure and price the correlated default risk in portfolios of credit-sensitive assets such as loans and corporate bonds. Monte Carlo simulation is an important tool for performing computations in these models. This paper develops, analyzes, and evaluates two simulation algorithms for intensity-based point process models. The algorithms extend the conventional thinning scheme to the case where the event intensity is unbounded, a feature common to many standard model formulations. Numerical results illustrate the performance of the algorithms for a familiar top-down model and a novel bottom-up model of correlated default risk. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Optimal Credit Swap Portfolios

This paper formulates and solves the selection problem for a portfolio of credit swaps. The problem is cast as a goal program that entails a constrained optimization of preference-weighted moments of the portfolio value at the investment horizon. The portfolio value takes account of the exact timing of protection premium and default loss payments, as well as any mark-to-market profits and losses realized at the horizon. The constraints address collateral and solvency requirements, initial capital, position limits, and other trading constraints that credit swap investors often face in practice. The multimoment formulation accommodates the complex distribution of the portfolio value, which is a nested expectation under risk-neutral and actual probabilities. It also generates computational tractability. Numerical results illustrate the features of optimal portfolios. In particular, we find that credit swap investment constraints can have a significant impact on optimal portfolios, even for simple investment objectives. Our problem formulation and solution approach extend to corporate bond portfolios and mixed portfolios of corporate bonds and credit derivatives. This paper was accepted by Wei Xiong, finance.

A Smiling Bear in the Equity Options Market and the Cross-Section of Stock Returns

We propose a measure for the convexity of an option-implied volatility curve, IV convexity, as a forward-looking measure of excess tail-risk contribution to the perceived variance of underlying equity returns. Using equity options data for individual U.S.-listed stocks during 2000-2013, we find that the average return differential between the lowest and highest IV convexity quintile portfolios exceeds 1% per month, which is both economically and statistically significant on a risk-adjusted basis. Our empirical findings indicate the contribution of informed options trading to price discovery in terms of the realization of tail-risk aversion in the stock market.