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
Outputs
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