1 / 33

MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang

Summer 07, MFIN7011, Tang. Structural Models. Structural Credit Risk Models. . Objectives:Essence of structural modelsMerton (1974) model and implementationPros and cons of structural models. Summer 07, MFIN7011, Tang. Structural Models. Building Blocks: Individual Defaultable Bond. . Defau

regis
Download Presentation

MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Summer 07, MFIN7011, Tang Structural Models MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang Lecture 4 Structural Credit Risk Models Thursday, July 12, 2007 Readings: Chacko, Sjoman, Motohashi, and Dessain (2007) Chapter 3 Lando Chapter 2 & Duffie and Singleton Chapter 7

    2. Summer 07, MFIN7011, Tang Structural Models Structural Credit Risk Models

    3. Summer 07, MFIN7011, Tang Structural Models Building Blocks: Individual Defaultable Bond

    4. Summer 07, MFIN7011, Tang Structural Models Building Blocks: Portfolio of Defaultable Bonds

    5. Summer 07, MFIN7011, Tang Structural Models Modeling Credit Risk

    6. Summer 07, MFIN7011, Tang Structural Models Risk-Neutral Pricing: A Workhorse

    7. Summer 07, MFIN7011, Tang Structural Models Corporate Liabilities as Contingent Claims Bondholders and shareholders split the total value of the firm Shareholders are residual claimants Both debt value and equity value are contingent on the realization of firm value (Nobel Prize Winning) Pioneer works Black and Scholes (JPE 1973) Merton (JF 1974): On the pricing of corporate debt: the risk structure of interest rates Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.

    8. Summer 07, MFIN7011, Tang Structural Models Structural Approach to Credit Risk Modeling

    9. Summer 07, MFIN7011, Tang Structural Models Stochastic Asset Value

    10. Summer 07, MFIN7011, Tang Structural Models Option Value of Equity Intuition of Merton (1974) 1. equity’s price and volatility can be easily obtained for a public firm; plugging those into the Black-Scholes formula, one can back out the value of the firm’s asset (not accounting definition, but the economic one). One has to estimate the asset’s volatility first, using Ito’s lemma.1. equity’s price and volatility can be easily obtained for a public firm; plugging those into the Black-Scholes formula, one can back out the value of the firm’s asset (not accounting definition, but the economic one). One has to estimate the asset’s volatility first, using Ito’s lemma.

    11. Summer 07, MFIN7011, Tang Structural Models Structural Models “Structural models” in corporate finance address The valuation of corporate securities (both debt and equity); and The choice of financial structure by the firm. Valuation of corporate securities depends on their cash flows, which in turn are contingent upon the firm’s operational cash flows (or their value). Default is value based, and typically results from a decline in the value of operational cash flows Valuation and financial decisions can be jointly determined Capital structure affects securities’ cash flows and therefore values Values affect choice of capital structure Recognizing this simultaneity affects predictions of the impact of parametric changes In principle, all securities of the firm can be valued in the same model. Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.

    12. Summer 07, MFIN7011, Tang Structural Models Why Structural Models Are Important? Pricing debt, equity and other corporate securities Essential for buyers (investors), sellers (firms), and advisors Estimating default probabilities Useful to investors and policymakers The “Holy Grail” of bond ratings agencies? Determining optimal capital structure decisions Essential for firms, but need for more precise guidance Analyzing most corporate decisions that affects cash flows Determines value-maximizing decisions (e.g., investment) Determining the impact of policy changes on firms’ values and decisions (e.g. effects of changes in Treasury rates, tax policies) Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.

    13. Summer 07, MFIN7011, Tang Structural Models Structural Credit Risk Models

    14. Summer 07, MFIN7011, Tang Structural Models Structural Models Inferring the likelihood of default by observation of the buffer for default (equity) and asset volatility. A firm in a riskier business needs to have a larger proportion of total capital in equity The idea originates from Merton (1974) Equity is an call option on a firm’s assets with strike equal to total debts: S=max{V-F,0) Accordingly, debt value is D=V-S(V,F,T,t) Example: V=120, F=100, T=5, d=0.6065, volatility=0.2, then S=60.385 and D=59.615 Commercialized by KMV Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.Buffer for default: capital, as in the previous balance sheet examples. Equity is an option: this is because of the limited liability property of a corporation. Plot the payoff function of equity against the asset/debt. Then it’s obvious equity is a call option on a firm’s asset with strike being debt.

    15. Summer 07, MFIN7011, Tang Structural Models Essence of Structural Models

    16. Summer 07, MFIN7011, Tang Structural Models First structural model for credit risk modeling Treating equity as an option on the assets of the firm Caveat: default is only considered at T (maturity date for the debt) In a simple situation the equity value is ET =max(VT -F, 0) where VT is the value of the firm and F is the debt repayment required Debt value at time T is DT = VT - ET =F-max(F-VT , 0), which can be thought as long a risk-free bond with face value F and short a put option with exercise F on firm value Then value of the risky debt at time 0: D0 = V0 - E0

    17. Summer 07, MFIN7011, Tang Structural Models Merton (1974) Model: Specifics Merton model allows only two types of liabilities A single class of debt A single class of equity More complicated structures can be mapped into this simplified schedule.

    18. Summer 07, MFIN7011, Tang Structural Models Merton (1974) Model: Asset Value Process The market value of a firm’s asset follows the following stochastic process GBM GBM

    19. Summer 07, MFIN7011, Tang Structural Models Merton (1974) Model: Asset Value Process In the Merton/Black-Scholes economy, the value of a firm’s asset is described by

    20. Summer 07, MFIN7011, Tang Structural Models Merton (1974) Model: Probability of Default Probability of default is given by:

    21. Summer 07, MFIN7011, Tang Structural Models Merton (1974) Model: Probability of Default The probability of default is: which is equivalent to

    22. Summer 07, MFIN7011, Tang Structural Models Merton (1974) Model: Probability of Default Under the normality assumption for e, default probability equals

    23. Summer 07, MFIN7011, Tang Structural Models Merton’s approach (previous formula) is intuitively appealing and seems to be of easy use in practice One problem, however, is that asset value and the volatility of its dynamics are not directly observable But, market value of equity and equity volatility are easily observable if the equity and options on that equity are traded Good news: one can show that the value/volatility of equity and the value/volatility of assets are related Contribution of Merton/Black-Scholes Core of structural models Implementing Merton’s Model

    24. Summer 07, MFIN7011, Tang Structural Models Merton/BS Option Pricing Model of Equity Equity value is given by max{VA-X,0}, apply Merton/BS option pricing method we have: Equity is a residual claim on firm’s asset. It has limited liability. This is like a call option. The holder of this call option on the assets has a claim on the asset after meeting the strike price of the option. Equity is a residual claim on firm’s asset. It has limited liability. This is like a call option. The holder of this call option on the assets has a claim on the asset after meeting the strike price of the option.

    25. Summer 07, MFIN7011, Tang Structural Models Merton (1974) Model By Ito’s Lemma: => Equity volatility equals This is true only instantaneously From Ito’s lemma Volatility is percentage volatility. In practice, the market leverage moves around too much for the above formula to provide reasonable resultsFrom Ito’s lemma Volatility is percentage volatility. In practice, the market leverage moves around too much for the above formula to provide reasonable results

    26. Summer 07, MFIN7011, Tang Structural Models Implementing Merton Model Equity value and equity volatility are readily observable. Asset value and asset volatility can be backed out using previous formulas From equations (1) and (2) and estimates for VE and sE (from market prices of the stock and option on the stock), one may obtain VA and sV See Slide 17. See Slide 17.

    27. Summer 07, MFIN7011, Tang Structural Models Problem Value of company equity E0 = $4 M Volatility sE = 60% Face value of debt (1 year maturity) F = $8 M (Strike Price X) Risk-free rate: r = 5% Solve (1) and (2) Need to impose that the value of the Black-Scholes formula is equal to the value of equity E=4, subject to the constraint that N(d1)?VV0 = 4x60% = 2.4 Solution technique: recursive trial and error Assume initial ?V= ?E find V, then use V to find ?V repeat this process till convergence We obtain V0 = $11.59 M and sV = 21.08% D0 = $11.59 –$4 = $7.59 M Credit spread: = -(1/T)*ln(D/F) – r = 0.26% or 26 bps Implementing Merton Model: Example

    28. Summer 07, MFIN7011, Tang Structural Models Probability of Default

    29. Summer 07, MFIN7011, Tang Structural Models Implementing Merton Model: Practical Issue Above proposed recursive method of backing out asset value and volatility does not work well when leverage changes significantly over the sample period Remedy proposed by Vassalou and Xing (2002): Using the backed out asset value to calculate asset volatility

    30. Summer 07, MFIN7011, Tang Structural Models Structural Models: Extensions

    31. Summer 07, MFIN7011, Tang Structural Models Problems with Existing Structural Models

    32. Summer 07, MFIN7011, Tang Structural Models Pros and Cons of Structural Models

    33. Summer 07, MFIN7011, Tang Structural Models Structural Models: Application Issues Bond data can be noisy Market prices are volatile: may not be due to changes in assets or credit conditions of firm But, many credit risky assets, like loans, are not (yet) liquidly traded Hard to deal with complex debt structures Based on diffusion model: minimal credit spread for short term debt When do firms default? Firms often keep operating long after its firm value drops significantly Missed payment? How long should we wait? One week or one year? Restructuring and bankruptcy filing decision right is in management’s hand Industry models make several modifications to the original Merton model. Problems: market price volatility: i.e. price changes may not be due to changes in assets or credit conditions of the firm. Cannot deal with complex debt structures. 1. Missed payment: say loans past due 90 days. Industry models make several modifications to the original Merton model. Problems: market price volatility: i.e. price changes may not be due to changes in assets or credit conditions of the firm. Cannot deal with complex debt structures. 1. Missed payment: say loans past due 90 days.

    34. Summer 07, MFIN7011, Tang Structural Models Summary

More Related