Merton Model Credit Risk Analysis: Lehman vs JP Morgan
This paper applies the Merton option pricing framework and KMV definition of debt to analyze and compare the credit risk profiles of Lehman Brothers and JP Morgan over a four-month observation window spanning 2006 to 2009. Using an equal-weighted (EW) index composed of idiosyncratic volatility, historical and option-implied default probabilities, CDS-derived default probabilities, market deviation from the S&P 500, country-specific risk, and credit ratings, the study tracks how each indicator evolves during periods of financial distress. The analysis demonstrates how distance-to-default served as a leading indicator of Lehman's collapse and highlights the divergence in credit quality between a failing institution and a solvent one.
- Methodology and Data Setup: Observation window, KMV debt definition, and model inputs
- EW Index Components and Variable Ranges: Composite EW index definition and variable range table
- Idiosyncratic Risk and Equity Returns: Volatility spikes and return drift leading to Lehman default
- Default Probability Estimation Approaches: Comparing historical, option-implied, and CDS-derived PD estimates
- Distance-to-Default as a Leading Indicator: DD declining ahead of default threshold breach
- Asset Volatility Dynamics Around Default: Noise and flattening in asset volatility near default
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What makes this paper effective
- The paper grounds its analysis in a well-established quantitative framework (Merton/KMV), giving the empirical findings theoretical credibility.
- It uses a natural experiment — comparing a failed institution (Lehman) with a solvent peer (JP Morgan) — to isolate the diagnostic value of each credit risk indicator.
- The composite EW index approach is clearly defined, with each component variable explicitly named, enabling reproducibility and transparent interpretation.
Key academic technique demonstrated
The paper demonstrates comparative case analysis within a quantitative finance framework. By applying identical estimation methods to two firms experiencing very different outcomes, it validates the predictive power of distance-to-default as a leading indicator of firm-level distress — showing that the metric signals failure 6 to 8 months in advance of default.
Structure breakdown
The paper opens by establishing the data setup and modeling assumptions (observation window, debt definition, interest rate, benchmark index). It then defines the composite EW index and presents the variable ranges in tabular form. Subsequent sections analyze each component — idiosyncratic risk, equity returns, default probability across three estimation methods, and distance-to-default — before closing with observations on asset volatility behavior around the default event.
Methodology and Data Setup
For the analysis of Lehman Brothers and JP Morgan, a four-month observation window is used, covering the years 2006 to 2009. The KMV definition of debt is applied, whereby debt is measured as short-term liabilities plus half of long-term liabilities. The risk-free interest rate is proxied by the 4-month LIBOR or swap rate; for illustration purposes, a rate of 5% is used. The benchmark index is the S&P 500. Initial asset values are computed as the sum of equity market capitalization plus total liabilities, and are subsequently derived using the Merton call option pricing framework.
EW Index Components and Variable Ranges
The equal-weighted (EW) Index score is the weighted average of the following indicators: idiosyncratic-specific volatility, default probability derived from historical equity stock prices, default probability derived from option prices, default probability derived from CDS prices, market deviation (stock return versus benchmark index return), country-specific risk, and credit rating grade.
The table below depicts the range of minimum and maximum values for the component variables across both firms during the observation period.
As illustrated above, idiosyncratic risk and default probability rise in tandem during periods of distress and drive the EW index score higher accordingly, with the index peaking at 100%. Meanwhile, market deviation from the S&P 500 may range from 0 to 100% and should be considered in complement with idiosyncratic risk to gauge entity-level fragility. For Lehman, the EW index reaches a maximum of 0.96, whereas JP Morgan's maximum EW index score of 0.171 reflects a substantially more stable credit profile throughout the same period.
Idiosyncratic Risk and Equity Returns
Idiosyncratic-specific volatility for Lehman Brothers and JP Morgan ranges from approximately 20% and 10%, respectively, up to 100%. In the case of Lehman, idiosyncratic risk shows a considerable spike within a span of three months, between January 27, 2008 and April 27, 2008, and reaches its maximum at the point of default on July 27, 2008.
Yearly returns, which denote the drift parameter in the model, trail at an approximate average of −1.2% for Lehman up until September 9, 2008, at which point they decline sharply into negative double-digit rates of return until the firm ceased to be a going concern. This downward trajectory in returns is consistent with the accelerating deterioration in asset values observed during the same period.
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