Method and system for simulating risk factors in parametric models using risk neutral historical bootstrapping
First Claim
1. A method for simulating the value of an attribute of a financial instrument comprising the steps of:
- providing a parametric model for the attribute having at least one noise-varying parameter an with a corresponding noise component ε
n;
determining values for the at least one parameter and the attribute at various time indices i using historical data;
deriving a set of historical residual values ε
n,i for each noise component ε
n the historical residual value ε
n,i at index i, when applied to the model with the determined parameter values at index i, at least substantially reproducing the determined attribute value at index i;
standardizing each set of historical residual values 6n; and
using values selected from the set of standardized historical residual values ε
n as the noise component during a simulation of the attribute value via the model.
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Abstract
An improved method for simulating noise-varying risk factor values in a parametric simulation comprises analyzing historical data to determine the actual value of the risk factors and other attributes in the model and using this data to generate historical residual values which reproduces the historical price when used in the model with corresponding historical attribute values. The set of historical residual values is standardized and can be bootstrapped to increase the number of members in the set or vary the sets properties. Values of the historical residuals are then selected, e.g., at random, and used in place of the random noise components to produce simulated risk factor values which are used in the parametric model to simulate the evolution of the instrument price.
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Citations
20 Claims
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1. A method for simulating the value of an attribute of a financial instrument comprising the steps of:
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providing a parametric model for the attribute having at least one noise-varying parameter an with a corresponding noise component ε
n;
determining values for the at least one parameter and the attribute at various time indices i using historical data;
deriving a set of historical residual values ε
n,i for each noise component ε
n the historical residual value ε
n,i at index i, when applied to the model with the determined parameter values at index i, at least substantially reproducing the determined attribute value at index i;
standardizing each set of historical residual values 6n; and
using values selected from the set of standardized historical residual values ε
n as the noise component during a simulation of the attribute value via the model. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 18)
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9. A method for simulating the price of a financial instrument comprising the steps of:
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providing a parametric pricing model having at least one parameter an with a corresponding noise component ε
n;
determining values for the parameters at various time indices i using historical data;
deriving a set of historical residual values ε
n,i for each noise component ε
n, the historical residual value ε
n,i at index i, when applied to the model with the determined parameter values at index i, at least substantially reproducing the attribute price at index i;
standardizing each set of historical residual values ε
n;
applying a multi-day bootstrap procedure to each set of historical residual values to increase the quantity of historical residual values in each set; and
using values selected from the set of historical residual values as the noise component for the corresponding parameter during a simulation of the instrument price. - View Dependent Claims (10)
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11. A system for simulating an attribute of a financial instrument comprising:
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a computer system having a processor and at least one data store, the data store having a parametric model for the attribute stored therein, the parametric model having at least one noise-varying parameter an with a corresponding noise component ε
n;
the data store further having a computer program stored therein to configure the processor to;
determine values for the at least one parameter and the attribute at various time indices i using historical data;
derive a set of historical residual values ε
n,i for each noise component ε
n, the historical residual value ε
n,i at index i, when applied to the model with the determined parameter values at index i, at least substantially reproducing the determined attribute value at index i;
standardize each set of historical residual values ε
n; and
use values selected from the set of standardized historical residual values ε
n, as the noise component during a simulation of the attribute value via the model. - View Dependent Claims (12, 13, 14, 15, 16, 17, 20)
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19. A system for simulating the price of a financial instrument comprising:
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a computer system having a processor and at least one data store, the data store having a parametric model for the attribute stored therein, the parametric model having at least one noise-varying parameter an with a corresponding noise component ε
n;
the data store further having a computer program stored therein to configure the processor to;
determine values for the parameters at various time indices i using historical data;
derive a set of historical residual values ε
n,i for each noise component ε
n, the historical residual value ε
n,i at index i, when applied to the model with the determined parameter values at index i, at least substantially reproducing the attribute price at index i;
standardize each set of historical residual values ε
n;
apply a multi-day bootstrap procedure to each set of historical residual values to increase the quantity of historical residual values in each set; and
use values selected from the set of historical residual values as the noise component for the corresponding parameter during a simulation of the instrument price.
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Specification