Systems and methods for modeling credit risks of publicly traded companies

• US 20070027786A1
• Filed: 10/05/2006
• Published: 02/01/2007
• Est. Priority Date: 07/24/2003
• Status: Active Grant

• Current Assignee: Credit Suisse Securities USA LLC (Credit Suisse)
• Original Assignee: Credit Suisse First Boston Gilts (Credit Suisse)
• Inventors: Lipton, Alexander, Lee, Shinghoi, Song, Jonathan
• Granted Patent: US 7,853,519 B2
• Time in Patent Office: Days
• US Class Current: 705/35
• CPC Class Codes: G06Q 10/10 Office automation; Time management
• CPC Class Codes: G06Q 40/00 Finance; Insurance; Tax strategies; Processing of corporate or income taxes
• CPC Class Codes: G06Q 40/03 Credit; Loans; Processing thereof

Abstract

There are provided new structural default models for modeling the likely default of publicly traded companies. In a first embodiment, the invention is straight-forward to implement and allows the capture of some important ingredients of the actual default, including positive short-term CDSs. In a second embodiment them model is somewhat more versatile and complex. Provided is a very efficient method for dealing with the timing of a default boundary, that is, jumps in the company'"'"'s value, etc. Further provided is a process using Fast Fourier Transform matrix processing for processing the structural default models in a computationally efficient manner.

Claims

1. A method for calculating the financial status of a company, comprising the steps of:

calculating the company'"'"'s value in accordance with the formula

$\frac{\mathrm{dV}}{V}=\left(r+\mathrm{\lambda <br><br>}\right)<br><br>\mathrm{dt}+\mathrm{\sigma <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{dW}-\mathrm{dN}$

 

wherein

V is the value of the company,

r is the risk neutral rate,

λ

is the intensity of jump arrivals,

σ

is the company'"'"'s volatility,

N) is the standard Poisson process,

W is the standard Wiener process,

and t is a time between 0 and T, the maturity of the debt; and

using the company value to calculate a financial metric for the company.

2. The method of claim 1 wherein the financial metric is the equity value of a company in accordance with the formula.

S=VN(d₊)−

e<sup>−

(r+λ

)T</sup>DN(d₋

)−

V(LD/V)<sup>2(r+λ

)/σ

2+1</sup>N(ƒ

₊)+e⁻

(r+λ

)TD(LD/V)<sup>2(r+λ

)/σ

2−

1</sup>N(ƒ

₋

);

wherein like variables to those defined above define the same values and wherein

d_±

=[ln(S/D)+(r+λ

±

σ

²/2)T]/σ

√

{square root over (T)}
ƒ

_±

=[ln(L²D/V)+(r+λ

±

σ

²/2)T]/σ

√

{square root over (T)}

D is the value of the debt,

T is the maturity of debt, and

L is relative level at which the company defaults.

3. The method of claim 1 wherein the financial metric is the debt value of a company in accordance with the formula

δ

=VN(d₋

)+e<sup>−

(r+λ

)T</sup>DN(d₋

)+V(LD/V)<sup>2(r+λ

)/σ

2+1</sup>N(ƒ

₊)−

e<sup>−

(r+λ

)T</sup>D(LD/V)<sup>2(r+λ

)/σ

2−

1</sup>N(ƒ

₋

);

wherein like variables to those defined above define the same values and wherein

d_±

=[ln(S/D)+(r+λ

±

σ

²/2)T]/σ

√

{square root over (T)}
ƒ

_±

=[ln(L²D/V)+(r +λ

±

σ

²/2)T]/σ

√

{square root over (T)}

D is the value of the debt,

T is the maturity of debt, and

L is relative level at which the company defaults.

4. The method of claim 1 wherein the financial metric is the survival probability of a company in accordance with the formula

Q(t)=e⁻

λ

T└

N(g₊)−

(LD/V)<sup>2r/σ

2</sup>N(g₋

)┘

,t<

T

wherein like variables to those defined above define the same values and wherein

g_±

=[±

ln(V/LD)+(r +λ

−

σ

²/2)t]/σ

√

{square root over (t)}

D is the value of the debt,

T is the maturity of debt,

L is relative level at which the company defaults.

5. A method in accordance with claim 1 and further comprising the step of calculating the credit default spread (CDS(t)) for very short maturities of the company in accordance with the formula

CDS(t)→

λ

(1−

R) when t→

0 ,

wherein R is a recovery level for a selected debt seniority.

6. A system for calculating the financial status of a company, comprising:

a processor;

a memory connected to the processor and storing instructions for controlling the operation of the processor;

the processor operative with the instructions in the memory to perform the steps of

calculating the company'"'"'s value in accordance with the formula

$\frac{\mathrm{dV}}{V}=\left(r+\mathrm{\lambda <br><br>}\right)<br><br>\mathrm{dt}+\mathrm{\sigma <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{dW}-\mathrm{dN}$

 

wherein

V is the value of the company,

r is the risk neutral rate,

λ

is the intensity of jump arrivals,

σ

ar is the company'"'"'s volatility,

N) is the standard Poisson process,

W is the standard Wiener process,

and t is a time between 0 and T, the maturity of the debt; and

using the company value to calculate a financial metric for the company.

7. The system of claim 6 wherein the financial metric is the equity value of a company in accordance with the formula

S=VN(d₊)−

e<sup>−

(r+λ

)T</sup>DN(d₋

)−

V(LD/V)<sup>2(r+λ

)/ σ

2+1</sup>N(ƒ

₊)+e<sup>−

(r+λ

)T</sup>D(LD/V)<sup>2(r+λ

)/σ

2−

1</sup>N(ƒ

₋

)

wherein like variables to those defined above define the same values and wherein

d_±

=[ln(S/D)+(r+λ

±

σ

²/2)T]/σ

√

{square root over (T)}
ƒ

_±

=[ln(L²D/V)+(r+λ

±

σ

²/2)T]/σ

√

{square root over (T)}

D is the value of the debt,

T is the maturity of debt, and

L is relative level at which the company defaults.

8. The system of claim 6 wherein the financial metric is the debt value of a company in accordance with the formula.

δ

=VN(d₋

)+e<sup>−

(r+λ

)T</sup>DN(d₋

)+V(LD/V)<sup>2(r+λ

)/σ

2+1</sup>N(ƒ

₊)−

e<sup>−

(r+λ

)T</sup>D(LD/V)<sup>2(r+λ

)/σ

2−

1</sup>N(ƒ

₋

);

wherein like variables to those defined above define the same values and wherein

d_±

=[ln(S/D)+(r+λ

±

σ

²/2)T]/σ

√

{square root over (T)}
ƒ

_±

=[ln(L²D/V)+(r+λ

±

σ

²/2)T]/σ

√

{square root over (T)}

D is the value of the debt,

T is the maturity of debt, and

L is relative level at which the company defaults.

9. The system of claim 6 wherein the financial metric is the survival probability of a company in accordance with the formula

Q(t)=e⁻

λ

T└

N(g₊)−

(LD/V)<sup>2r/σ

2</sup>N(g₋

)┘

,t<

T

wherein like variables to those defined above define the same values and wherein

g_±

=[±

ln(V/LD)+(r+λ

−

σ

²/2)t]/σ

√

{square root over (t)}

D is the value of the debt,

T is the maturity of debt,

L is relative level at which the company defaults.

10. A system in accordance with claim 6 and further comprising the step of calculating the credit default spread (CDS(t)) for very short maturities of the company in accordance with the formula

CDS(t)→

λ

(1−

R) when t→

0,

wherein R is a recovery level for a selected debt seniority.

11. A system for calculating the financial status of a company, comprising:

means for calculating the company'"'"'s value in accordance with the formula

$\frac{\mathrm{dV}}{V}=\left(r+\mathrm{\lambda <br><br>}\right)<br><br>\mathrm{dt}+\mathrm{\sigma <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{dW}-\mathrm{dN}$

 

wherein

V is the value of the company,

r is the risk neutral rate,

λ

is the intensity of jump arrivals,

σ

is the company'"'"'s volatility,

N) is the standard Poisson process,

W is the standard Wiener process,

and t is a time between 0 and T, the maturity of the debt; and

means for using the company value to calculate a financial metric for the company.

12-44. -44. (canceled)