Table of Contents


File

cca_fun.m

Name

cca_fun

Synopsis

cca_fun - Helper function to solve the system of non-linear equations in CCA

Introduction

NOTE: PART OF A SET OF 2 RELATED FILES:

Gray and Jobst (2010) propose using contingent claims analysis (CCA) to measure systemic risk from market-implied expected losses, with immediate practical applications to the analysis of implicit government contingent liabilities, i.e., guarantees. In addition, the framework also helps quantify the individual contributions of financial institutions to overall contingent liabilities in the event of a systemic distress. Based on a sample of the 36 largest financial institutions (banks, insurance companies, and asset managers), this systemic risk measurement framework generates an estimate of the joint contingent liabilities from market-implied government support. This approach does not only quantify the magnitude of potential risk transfer to the government but also helps indicate the contribution of individual institutions to contingent liabilities over time.

License

=============================================================================

Copyright 2011, Dimitrios Bisias, Andrew W. Lo, and Stavros Valavanis

COPYRIGHT STATUS: This work was funded in whole or in part by the Office of Financial Research under U.S. Government contract TOSOFR-11-C-0001, and is, therefore, subject to the following license: The Government is granted for itself and others acting on its behalf a paid-up, nonexclusive, irrevocable, worldwide license to reproduce, prepare derivative works, distribute copies to the public, perform and display the work.
All other rights are reserved by the copyright owner.

THIS SOFTWARE IS PROVIDED "AS IS". YOU ARE USING THIS SOFTWARE AT YOUR OWN RISK. ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS, CONTRIBUTORS, OR THE UNITED STATES GOVERNMENT BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

=============================================================================

Inputs

equity
Name:
equity
Description:

The market value of the equity of the firm.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


volatility
Name:
volatility
Description:

The volatility of the equity.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


risk_free_rate
Name:
risk_free_rate
Description:

The risk free rate in annualized terms.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


default_barrier
Name:
default_barrier
Description:

Face value of the outstanding debt at maturity.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


time_to_maturity
Name:
time_to_maturity
Description:

Time to maturity of the debt.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


Init_asset_price
Name:
Init_asset_price
Description:

The guessed asset price value to solve our implicit function.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


Init_asset_vol
Name:
Init_asset_vol
Description:

The asset volatility value to solve our implicit function.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


Outputs

val
Name:
val
Description:

This is a helper function to be solved implicitly. It contains expressions derived from Black-Scholes intended to solve for asset_price and asset_vol.

Type:
expression
Range:
n/a
Dimensions:

2x1


Code

% Run warning message
warning('OFRwp0001:UntestedCode', ...
    ['This version of the source code is very preliminary, ' ...
     'and has not been thoroughly tested. Users should not rely on ' ...
     'these calculations.']);


%define D1 and D2
d1 = (log(Init_asset_price^2/default_barrier)+(risk_free_rate+...
         (Init_asset_vol^4)/2)*time_to_maturity)/(Init_asset_vol^2*...
         sqrt(time_to_maturity));
d2 = d1 - Init_asset_vol^2*sqrt(time_to_maturity);

%define expressions to solve for Asset Price and Asset Vol
val = [...
       (equity - Init_asset_price^2*normcdf(d1)+default_barrier*exp(...
        -risk_free_rate*time_to_maturity)*normcdf(d2));
       ( equity*volatility - Init_asset_price^2*Init_asset_vol^2*normcdf(d1))...
      ];

Examples

NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.

 equity = 5;
 volatility = 1.2;
 risk_free_rate = .02;
 default_barrier = 10;
 time_to_maturity = 20;
 Init_asset_price = 5;
 Init_asset_vol = 1.2;

 val = cca_fun(equity, volatility, risk_free_rate, default_barrier, ...
 time_to_maturity, Init_asset_price, Init_asset_vol);

References

Gray, D., & Jobst, A. (2010, October). Systemic CCA-A Model Approach to Systemic Risk. In Deutsche Bundesbank/Technische Universitt Dresden Conference: Beyond the Financial Crisis: Systemic Risk, Spillovers and Regulation, Dresden.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 77-80.