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mertonmodel

Estimates probability of default using Merton model

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Syntax

[PD,DD,A,Sa] = mertonmodel(Equity,EquityVol,Liability,Rate)
[PD,DD,A,Sa] = mertonmodel(___，名称，值）

描述

example

[PD,DD,A,Sa] = mertonmodel（Equity,EquityVol,Liability,速度)estimates the default probability of a firm by using the Merton model.

example

[PD,DD,A,Sa] = mertonmodel（___,Name,Value)添加可选的名称值对参数。

例子

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打开实时脚本

加载数据Mertondata.mat.

loadMertondata.mat股权= mertondata.equity;EquityVol = Mertondata.Equityvol;责任= mertondata.libility;漂移= mertondata.drift;费率= mertondata.rate;Mertondata
Mertondata=5×6桌ID Equity EquityVol Liability Rate Drift __________ __________ _________ _________ ____ ______ {'Firm 1'} 2.6406e+07 0.7103 4e+07 0.05 0.0306 {'Firm 2'} 2.6817e+07 0.3929 3.5e+07 0.05 0.03 {'Firm 3'} 3.977e+07 0.3121 3.5e+07 0.05 0.031 {'Firm 4'} 2.947e+07 0.4595 3.2e+07 0.05 0.0302 {'Firm 5'} 2.528e+07 0.6181 4e+07 0.05 0.0305

使用p计算违约概率oint approach to the Merton model.

[PD,DD,A,Sa] = mertonmodel(Equity,EquityVol,Liability,Rate,'漂移',Drift)
pd =5×10.0638 0.0008 0.0000 0.0026 0.0344
DD =5×11.5237 3.1679 4.4298 2.7916 1.8196
A =5×1107×6.4210 6.0109 7.3063 5.9906 6.3231
sa =5×10.3010 0.1753 0.1699 0.2263 0.2511

Input Arguments

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公司权益的当前市场价值，被指定为正价值。

Data Types:双倍的

公司权益的波动性，指定为积极的年度标准偏差。

Data Types:双倍的

责任阈值, specified as a positive value. The liability threshold is often referred to as the default point.

Data Types:双倍的

年度无风险利率, specified as a numeric value.

Data Types:双倍的

Name-Value Arguments

将可选的参数对Name1=Value1,...,NameN=ValueN， 在哪里Nameis the argument name and价值是相应的值。名称值参数必须在其他参数之后出现，但是对的顺序并不重要。

Before R2021a, use commas to separate each name and value, and encloseNamein quotes.

例子：[PD,DD,A,Sa] = mertonmodel(Equity,EquityVol,Liability,Rate,'Maturity',4,'Drift',0.22)

到期时间对应于责任阈值的时间，指定为逗号分隔对'Maturity'和a positive value.

Data Types:双倍的

年度漂移率(expected rate of return of the firm's assets), specified as the comma-separated pair consisting of'漂移'和a numeric value.

Data Types:双倍的

Tolerance for convergence of the solver, specified as the comma-separated pair consisting of'宽容'和积极的标量值。

Data Types:双倍的

允许的最大迭代次数，指定为逗号分隔对'MaxIterations'和一个积极的整数。

Data Types:双倍的

Output Arguments

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公司在成熟时的违约概率，作为数字值返回。

Distance-to-default, defined as the number of standard deviations between the mean of the asset distribution at maturity and the liability threshold (default point), returned as a numeric value.

公司资产的当前价值，返回为数值。

年度企业的资产波动为数值。

More About

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Merton Model Using Single-Point Calibration

In the Merton model, the value of a company's equity is treated as a call option on its assets and the liability is taken as a strike price.

mertonmodelaccepts inputs for the firm's equity, equity volatility, liability threshold, and risk-free interest rate. Themertonmodel函数求解a2-经过-2未知数的非线性方程系统是公司的资产和资产波动。您可以通过在算法.

算法

Unlike the time series method (seemertonByTimeSeries），使用mertonmodel, the equity volatility (σE) is provided. Given equity (E), liability (L), risk-free interest rate (r），资产漂移（μA）和成熟度（T），您使用2-经过-2nonlinear system of equations.mertonmodel解决资产价值（A) and asset volatility (σA） 如下：

E = A N ( d 1 ) − L e − r T N ( d 2 )

σ E = A E N ( d 1 ) σ A

whereNis the cumulative normal distribution,d1和d2定义为：

d 1 = Ln ( A L ) + ( r + 0.5 σ A 2 ) T σ A T

d 2 = d 1 − σ A T

The formulae for the distance-to-default (DD) and default probability (PD) are:

D D = Ln ( A L ) + ( μ A − 0.5 σ A 2 ) T σ A T

P D = 1 − N ( D D )

参考

[1] Zielinski，T。Merton's and KMV Models In Credit Risk Management.

[2]Löffler，G。和Posch，P.N。Credit Risk Modeling Using Excel and VBA.Wiley Finance, 2011.

[3] Kim，I.J。，Byun，S.J，Hwang，S.Y。An Iterative Method for Implementing Merton.

[4] Merton, R. C. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.”Journal of Finance.Vol. 29. pp. 449 – 470.

Version History

Introduced in R2017a

See Also

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