Methods for determining value at risk

• US 20020019803A1
• Filed: 04/26/2001
• Published: 02/14/2002
• Est. Priority Date: 05/01/2000
• Status: Active Grant

• Current Assignee: OANDA Corp.
• Original Assignee: Olsen Data Limited
• Inventors: Muller, Ulrich A.
• Granted Patent: US 7,356,504 B2
• Time in Patent Office: Days
• US Class Current: 705/38
• CPC Class Codes: G06Q 20/10 specially adapted for electronic funds transfer [EFT] systems; specially adapted for home banking systems
• CPC Class Codes: G06Q 20/102 Bill distribution or payments
• 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 40/08 Insurance

Abstract

A preferred embodiment comprises a method for determining value-at-risk based on tick-by-tick financial data. Major steps of the method comprise the following: (1) financial market transaction data is electronically received by a computer; (2) the received financial market transaction data is electronically; (3) a time series z is constructed that models the received financial market transaction data; (4) an exponential moving average operator is constructed; (5) an operator is constructed that is based on the exponential moving average operator; (6) a causal operator Ω[z] is constructed that is based on the iterated exponential moving average operator; (7) values of predictive factors are calculated; (8) the values calculated by the computer are stored in a computer readable medium, and (9) value-at-risk is calculated from the values stored in step (8).

Claims

1. A method of determining value-at-risk, comprising the steps of:

electronically receiving financial market transaction data over an electronic network;

electronically storing in a computer-readable medium said received financial market transaction data;

constructing an inhomogeneous time series z that represents said received financial market transaction data;

constructing an exponential moving average operator;

constructing an iterated exponential moving average operator based on said exponential moving average operator;

constructing a time-translation-invariant, causal operator Ω

[z] that is a convolution operator with kernel ω and

that is based on said iterated exponential moving average operator;

electronically calculating values of one or more predictive factors relating to said time series z, wherein said one or more predictive factors are defined in terms of said operator Ω

[z];

electronically storing in a computer readable medium said calculated values of one or more predictive factors; and

electronically calculating value-at-risk from said calculated values.

2. The method of claim 1, wherein said operator Ω

[z] has the form;

Ω

[z](t)=∫

<sub>−

∞</sub>

^t dt′

ω

(t−

t′

)z(t′

) =∫

₀^∞

dt′

ω

(t′

)z(t−

t′

)

.

3. The method of claim 1, wherein said exponential moving average operator EMA[τ

;

z] has the form;

4. The method of claim 1, wherein said operator Ω

[z] is a differential operator Δ

[τ

] that has the form;

Δ

[τ

]=γ

(EMA[α

τ

, 1]+EMA[α

τ

2]−

2 EMA[α

β

τ

, 4]),

where γ

is fixed so that the integral of the kernel of the differential operator from the origin to the first zero is 1;

α

is fixed by a normalization condition that requires Δ

[τ

;

c]=0 for a constant c; and

β

is chosen in order to get a short tail for the kernel of the differential operator Δ

[τ

].

5. The method of claim 4 wherein said one or more predictive factors comprises a return of the form r[τ

]=Δ

[τ

;

x], where x represents a logarithmic price.

6. The method of claim 1 wherein said one or more predictive factors comprises a momentum of the form x−

EMA[τ

;

x], where x represents a logarithmic price.

7. The method of claim 1 wherein said one or more predictive factors comprises a volatility.

8. The method of claim 7 wherein said volatility is of the form:

Volatility[τ

,τ

′

, p;

z]=MNorm [τ

/2,p;

Δ

[τ

′

;

z]], where

MNorm[τ

,p;

z]=MA[τ

;

|z|^p]^1/p, and

$\mathrm{MA}<br><br>\left[\mathrm{\tau <br><br>},n\right]=\frac{1}{n}<br><br>\underset{k=1}{\overset{n}{\sum <br><br>}}<br><br>\mathrm{EMA}<br><br>\text{\hspace{1em}<br><br>}\left[{\mathrm{\tau <br><br>}}^{\mathrm{\prime <br><br>}},k\right],\text{\hspace{1em}<br><br>}<br><br>\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\tau <br><br>}}^{\mathrm{\prime <br><br>}}=\frac{2<br><br>\mathrm{\tau <br><br>}}{n+1},$

and where p satisfies 0<

p≦

2, and τ

′

is a time horizon of a return r[τ

]=Δ

[τ

;

x], where x represents a logarithmic price.