Systems and methods for modeling credit risks of publicly traded companies

• US 7,853,519 B2
• Filed: 10/05/2006
• Issued: 12/14/2010
• Est. Priority Date: 07/24/2003
• Status: Expired due to Fees

• Current Assignee: Credit Suisse Securities USA LLC (Credit Suisse)
• Original Assignee: Credit Suisse Securities USA LLC (Credit Suisse)
• Inventors: Lipton, Alexander, Song, Jonathan Z., Lee, Shinghoi
• Primary Examiner(s): Borlinghaus; Jason M
• Application Number:
  US11/543,599
• Publication Number:
  US 20070027786A1
• Time in Patent Office: 1,531 Days
• Field of Search: None
• US Class Current: 705/38
• 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, using a computer, a value of the company in accordance with a formula

2. The method of claim 1, wherein the financial metric is an equity value of the company calculated in accordance with a 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]

D is a value of the debt,

T is the maturity of the debt, and

L is a relative level at which the company defaults.

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

δ

=VN(d₋

)+e<sup>−

(r+λ

)T</sup>DN(d₋

)+V(LD/V)<sup>2(r+λ

)/σ

2+1</sup>N(θ

₊)−

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 the debt, and

L is a relative level at which the company defaults.

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

T is the maturity of debt,

L is a relative level at which the company defaults.

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

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 a value of the company in accordance with a formula

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

T is the maturity of the debt, and

L is a relative level at which the company defaults.

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

T is the maturity of the debt, and

L is a relative level at which the company defaults.

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

T is the maturity of the debt,

L is a relative level at which the company defaults.

10. The system of claim 6, wherein the processor is further operative with the instructions in the memory to perform the step of calculating a credit default spread (CDS(t)) for very short maturities of the company in accordance with a 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 a financial status of a company, comprising:

means for calculating a value of the company in accordance with a formula

12. The system of claim 11, wherein the financial metric is an equity value of the 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 a value of the debt,

T is the maturity of the debt, and

L is a relative level at which the company defaults.

13. The system of claim 11, wherein the financial metric is a debt value of the 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 a value of the debt,

T is the maturity of the debt, and

L is a relative level at which the company defaults.

14. The system of claim 11, wherein the financial metric is a survival probability of the 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 a value of the debt,

T is the maturity of the debt,

L is a relative level at which the company defaults.

15. The system of claim 11, further comprising means for calculating a 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.