Pricing module for financial advisory system

• US 6,125,355 A
• Filed: 12/02/1997
• Issued: 09/26/2000
• Est. Priority Date: 12/02/1997
• Status: Expired due to Term

• Current Assignee: Financial Engines Incorporated (Edelman Financial Engines LLC)
• Original Assignee: Financial Engines Incorporated (Edelman Financial Engines LLC)
• Inventors: Jones, Christopher L., Watson, John G., Scott, Jason S., Bekaert, Geert, Grenadier, Steven R.
• Primary Examiner(s): Voeltz, Emanuel Todd
• Assistant Examiner(s): HAYES, JOHN W
• Application Number:
  US08/982,941
• Time in Patent Office: 1,029 Days
• Field of Search: 705/35, 705/4, 705/36, 705/1, 705/7, 705/10, 705/38
• US Class Current: 705/36.00R
• CPC Class Codes: G06Q 10/0635 Risk analysis of enterprise or organisation activities
• CPC Class Codes: G06Q 30/0201 Market modelling; Market analysis; Collecting market data
• 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
• CPC Class Codes: G06Q 40/04 Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

The pricing module of the present invention provides a single module that models both fixed-income securities and equity securities into the future in an arbitrage-free model. Because the modeling includes both fixed-income securities and equity securities that are modeled based on common input state variables and does not allow arbitrage conditions between the fixed-income securities and the equity securities (as well as no arbitrage within a security class), the present invention provides an improved pricing module as compared to those in the prior art.

Claims

1. In a computer system, a method for pricing equity securities and fixed-income securities having a no arbitrage constraint, the method comprising:

determining a fixed-income security pricing based on an inflation value, a real rate value and a term structure parameter;

determining equity security pricing based on the inflation value, the real rate value, the term structure risk parameter, a dividend growth value, and an equity correlation parameter; and

generating pricing data corresponding to the fixed-income security pricing and the equity security pricing.

2. The method of claim 1, wherein the fixed-income securities comprise:

one or more short term-bonds; and

one or more long-term bonds.

3. The method of claim 1, wherein the equity securities comprise one or more stocks, mutual funds, warrants, stock options, or derivative equity securities.

4. The method of claim 1 further comprising receiving the inflation value.

5. The method of claim 1 further comprising receiving the real rate value.

6. The method of claim 1 further comprising the step of receiving the term structure risk parameter.

7. The method of claim 1 further comprising the step of receiving the dividend growth value.

8. The method of claim 1 further comprising the step of receiving the equity correlation parameter.

9. The method of claim 1, wherein the term structure risk parameter and the equity correlation parameter are determined such that when determining fixed-income security pricing and determining equity security pricing are performed for one or more chosen historical times that the pricing approximates observed fixed-income security pricing and observed equity security pricing for the chosen historical times.

10. The method of claim 1, wherein the inflation value is determined as a heteroskedastic stochastic process.

11. The method of claim 10, wherein the inflation value at time t+1 (π

_t+1) is determined according to;

##EQU18## where μ

.sub.π

is a constant determined based on an unconditional mean for observed inflation over a period of time,

ρ

.sub.π

is a first-order autocorrelation for the observed inflation over the period of time,

π

_t is an inflation value for time t,

σ

'"'"'.sub.π

is selected such that a standard deviation of a plurality of predicted inflation values corresponding to the period of time is approximately equal to a standard deviation of the observed inflation for the period of time, and

ε

_t+1.sup.π

is a value chosen by a standard normal random deviate function.

12. The method of claim 1, wherein the real rate of interest value is determined as a heteroskedastic stochastic process.

13. The method of claim 12, wherein the real rate value at time t+1 (χ

_t+1) is determined according to;

##EQU19## where μ

.sub.χ

is a constant determined based on an unconditional mean for observed real rate over a period of time,

ρ

.sub.χ

is a first-order autocorrelation of the observed real rate of interest over the period of time,

χ

_t is a real rate value for time t,

σ

'"'"'.sub.χ

is selected such that a standard deviation of a plurality of predicted real rate values corresponding to the period of time is approximately equal to a standard deviation of the observed real rate of interest over the period of time, and

ε

_t+1.sup.χ

is a value chosen by a standard normal random deviate function.

14. The method of claim 13, wherein the estimated real rate of interest is determined based on a short-term nominal rate of interest and a value of inflation is based on expected inflation and the nominal short-term rate of interest.

15. The method of claim 14, wherein the short-term nominal rate of interest is determined according to:

##EQU20## where μ

.sub.π

is a constant determined based on an unconditional mean of observed inflation over a period of time,

ρ

.sub.π

is a first-order autocorrelation for inflation over the period of time,

π

_t is an inflation value for time t, and

σ

'"'"'.sub.π

² is a variance of the innovations in the inflation process over the period of time.

16. The method of claim 1, wherein the dividend growth value is determined as a homoskedastic stochastic process.

17. The method of claim 16, wherein the dividend growth value at time t+1 (Δ

d_t+1) determined according to;

space="preserve" listing-type="equation">Δ

d.sub.t+1 =μ

.sub.d +ρ

.sub.d Δ

d.sub.t +σ

'"'"'.sub.d ε

.sub.t+1.sup.Δ

d

where

μ

_d is a constant determined based on an unconditional mean for observed dividend growth over a period of time,

ρ

_d is a first-order autocorrelation for the observed dividend growth over the period of time,

χ

_d is a dividend growth value for time t,

σ

'"'"'_d is selected such that a standard deviation of a plurality of predicted dividend growth values corresponding to the period of time approximately equal to a standard deviation of observed dividend growth for the period of time, and

ε

_t+1.sup.Δ

d is a value chosen by a standard normal random deviate function.

18. The method of claim 1, wherein the term structure risk (λ

) value is approximately equal to a slope of a yield curve at a particular time for a representative investor.

19. The method of claim 1, wherein the equity correlation (β

) value is determined based on observed equity behavior with respect to observed bond behavior.

20. The method of claim 1, wherein the step of determining fixed-income security pricing comprises the step of determining an n-period yield (y_nt) according to:

##EQU21## where p_nt is a logarithm of a time, t, of a default-free bond paying one dollar in n years.

21. The method of claim 20, wherein p_nt is:

space="preserve" listing-type="equation">p.sub.nt =A.sub.n +B.sub.n χ

.sub.t +C.sub.n π

.sub.t

where

space="preserve" listing-type="equation">A.sub.n =A.sub.n-1 =μ

.sub.π

+B.sub.n-1 μ

.sub.χ

+C.sub.n-1 μ

.sub.π

##EQU22## and

space="preserve" listing-type="equation">A.sub.0 =B.sub.0 =C.sub.0 =0

and where

χ

_t is a real rate value for time t,

π

_t is an inflation value for time t,

μ

.sub.π

is a constant determined based on an unconditional mean for observed inflation over a period of time,

μ

.sub.χ

is a constant determined based on an unconditional mean for observed real rate over the period of time,

ρ

.sub.χ

is a first order autocorrelation of the observed real rate of interest over the period of time,

λ

is approximately equal to a slope of a yield curve at a particular time,

σ

'"'"'.sub.π

is selected such that a standard deviation of a plurality of predicted inflation values corresponding to the period of time is approximately equal to a standard deviation of the observed inflation for the period of time,

ρ

.sub.π

is a first order autocorrelation for the observed inflation over the period of time, and

σ

.sub.π

² is a variance of the observed inflation over the period of time.

22. The method of claim 1, wherein determining equity security pricing comprises determining a price to dividend ratio at a time, t, (pd_t) according to:

##EQU23## where ##EQU24##

space="preserve" listing-type="equation">ƒ

.sub.i+1 =ƒ

+ƒ

.sub.i ρ

.sub.d

and

space="preserve" listing-type="equation">a.sub.0 =b.sub.0 =c.sub.0 =ƒ

.sub.0 =0

and where

χ

_t is a real rate value at time t,

π

_t is an inflation value at time t,

Δ

d_t is a dividend growth value at time t,

μ

.sub.π

is a constant determined based on a mean for observed inflation over a period of time,

ρ

.sub.π

is a first-order autocorrelation for the observed inflation over the period of time,

σ

'"'"'.sub.π

² is a variance of the observed inflation over the period of time,

μ

.sub.χ

is a constant determined based on a mean for observed real rate over the period of time,

ρ

.sub.χ

is a first-order autocorrelation of the observed real rate of interest over the period of time,

σ

'"'"'.sub.χ

is selected such that the variance of an inflation process is approximately equal to observed inflation over the period of time,

μ

_d is a constant determined based on a mean for observed dividend growth over the period of time,

ρ

_d is a first-order autocorrelation for dividend growth over the period of time,

σ

'"'"'_d is selected such that a standard deviation of a plurality of dividend growth values corresponding to the period of time is approximately equal to a standard deviation of observed dividend growth for the period of time, and

β

is the equity correlation parameter.

23. The method of claim 22, wherein equity security returns are determined according to:

##EQU25## where V is a value of a stock market.

24. In a computer system, a method for pricing equity securities and fixed-income securities having a no arbitrage constraint, the method comprising:

determining a term structure risk parameter based on observed term structure data;

determining an equity correlation parameter based on a correlation between equity dividends and fixed-income securities;

determining a heteroskedastic inflation value;

determining a heteroskedastic real rate value;

determining a homoskedastic dividend growth value;

pricing fixed-income securities based on the term structure risk parameter, the inflation value and the real rate value; and

pricing equity securities based on the term structure risk parameter, the inflation value, the real rate value, the dividend growth value, and the equity correlation parameter; and

generating pricing data corresponding to the fixed-income security pricing and the equity security pricing.

25. A system for analyzing asset portfolios comprising:

a value module that provides one or more values;

a pricing kernel communicably coupled to the value module, the pricing kernel to generate prices for fixed-income securities based on a term structure risk parameter, an inflation value and a real rate value and to generate prices for equity securities based on the term structure risk parameter, the inflation value, the real rate value, a dividend growth value, and an equity correlation parameter, wherein the pricing of fixed-income securities and the pricing of equity securities are subject to a no arbitrage constraint; and

a simulation module communicatively coupled to the pricing kernel, the simulation module to estimate future asset worth based on the prices generated by the pricing kernel, the simulation module to generate pricing data corresponding to the fixed-income security pricing and the equity security pricing.

26. The system of claim 25, wherein the fixed-income securities comprise:

one or more short term-bonds; and

one or more long-term bonds.

27. The system of claim 25, wherein the equity securities comprise one or more stocks.

28. The system of claim 25 wherein the parameter module provides the inflation value.

29. The system of claim 25 wherein the parameter module provides the real rate value.

30. The system of claim 25 wherein the parameter module provides the term structure risk parameter.

31. The system of claim 25 wherein the parameter module provides the dividend growth value.

32. The system of claim 25 wherein the parameter module provides the equity correlation parameter.

33. The system of claim 25, wherein the inflation value is determined as a heteroskedastic stochastic process.

34. The system of claim 25, wherein the real rate value is determined as a heteroskedastic stochastic process.

35. The system of claim 25, wherein the dividend growth value is determined as a homoskedastic stochastic process.

36. An apparatus for pricing fixed-income securities and equity securities having a no arbitrage constraint, comprising:

an input device;

an output device; and

a processor coupled to the input device and to the output device to output pricing of fixed-income securities and equity securities, wherein fixed-income securities are priced based on a term structure risk parameter, an inflation value and a real rate value, and further wherein equity securities are priced based on the term structure risk parameter, the inflation value, the real rate value, a dividend growth value and an equity correlation parameter.

37. The apparatus of claim 36, wherein the term structure risk parameter is determined based on a slope of an observed yield curve relevant to a representative investor.

38. The apparatus of claim 36, wherein the equity correlation parameter is determined based on observed dividend behavior and with respect to observed bond behavior.

39. The apparatus of claim 36, wherein the term structure risk parameter and the equity correlation parameter are determined such that when fixed-income securities and equity securities are priced for one or more chosen historical times that the prices approximate observed fixed-income security prices and observed equity security prices, respectively, for the one or more chosen historical times.

40. A machine readable medium having stored thereon sequences of instructions, which when executed by one or more processors, cause one or more electronic devices to:

determine a term structure risk parameter based on evaluation of a user;

determine an equity correlation parameter based on a correlation between equity dividends and fixed-income securities;

n equity correlation parameter based on a correlation between equity dividends and fixed-income securities;

determine a heteroskedastic inflation value;

determine a hetroskedastic real rate value;

determine a homoskedastic dividend growth rate;

price fixed-income securities based on the term structure risk parameter, the inflation value and the real rate value;

price a equity securities based on the term structure risk parameter, the inflation value, the real rate value, the dividend growth value, and the equity correlation parameter; and

generate pricing data corresponding to the fixed-income security pricing and the equity security pricing;

wherein pricing fixed-income securities and pricing equity securities are subject to a no arbitrage constraint.

41. The machine readable medium of claim 40 wherein the fixed-income securities comprise:

one or more short-term bonds; and

one or more long-term bonds.

42. The machine readable medium of claim 40 wherein the equity securities comprise one or more stocks, mutual funds, warrants, stock options, or derivative equity securities.

43. The machine readable medium of claim 40, wherein the term structure risk parameter and the equity correlation parameter are determined such that when determining fixed-income security pricing and determining equity security pricing are performed for one or more chosen historical times that the pricing approximates observed fixed-income security pricing and observed equity security pricing for the chosen historical times.

44. The machine readable medium of claim 40, wherein the term structure risk (λ

) value is approximately equal to a slope of a yield curve at a particular time for a representative investor.

45. The machine readable medium of claim 40, wherein the equity correlation (β

) value is determined based on observed equity behavior with respect to observed bond behavior.

46. A machine readable medium having stored thereon sequences of instructions, which when executed by one or more processors, cause one or more electronic devices to:

determine a fixed-income security pricing based on an inflation value, a real rate value and a term structure parameter;

determine equity security pricing based on the inflation value, the real rate value, the term structure risk parameter, a dividend growth value, and an equity correlation parameter; and

generate pricing data corresponding to the fixed-income security pricing and the equity security pricing.

47. The machine readable medium of claim 46 wherein the fixed-income securities comprise:

one or more short-term bonds; and

one or more long-term bonds.

48. The machine readable medium of claim 46 wherein the equity securities comprise one or more stocks, mutual funds, warrants, stock options, or derivative equity securities.

49. The machine readable medium of claim 46, wherein the term structure risk parameter and the equity correlation parameter are determined such that when determining fixed-income security pricing and determining equity security pricing are performed for one or more chosen historical times that the pricing approximates observed fixed-income security pricing and observed equity security pricing for the chosen historical times.

50. The machine readable medium of claim 46, wherein the term structure risk (λ

) value is approximately equal to a slope of a yield curve at a particular time for a representative investor.

51. The machine readable medium of claim 46, wherein the equity correlation (β

) value is determined based on observed equity behavior with respect to observed bond behavior.