US 7,599,871 B1 · Method and system for non-Gaussian pricing of options and other derivatives

Abstract

In preferred embodiments, a method and system for pricing a derivative (e.g., a stock option) based on a non-Gaussian price model assuming statistical feedback. The dynamics of the underlying financial instrument (e.g., stock) are assumed to follow a stochastic process with anomalous nonlinear diffusion, phenomenologically modeled as a statistical feedback process within the framework of a generalized thermostatistics. Preferred embodiments implement solutions to a generalized form of the Black-Scholes differential equation, using risk-free asset valuation techniques in some cases.

Claims46

Dependent claims

A method for determining price, f(S), of a derivative having an underlying financial instrument, said method including the steps of:

(a) determining a non-Gaussian model of price, S, of the underlying financial instrument, said model assuming statistical feedback,
where the price S is S=S(t+τ)=S(τ)eY(t), where t denotes a time delay, time interval, or timescale, τ is an initial time value, τ=0 without loss of generality, Y(t) is a value that evolves across timescale t, and the underlying financial instrument has a return;
and
(b) by operating a computer system, determining as price f, a derivative price value consistent with the model determined in step (a), including by generating data indicative of the derivative price value.

1 more element

A computer system, comprising:

a processor programmed to generate data indicative of price, f(S), of a derivative having an underlying financial instrument whose price is S=S(t+τ)=S(τ)eY(t), where t denotes a time delay, time interval, or timescale, T is an initial time value, τ=0 without loss of generality, Y(t) is a value that evolves across timescale t, and the underlying financial instrument has a return, including by implementing a non-Gaussian model of the price S, said model assuming statistical feedback, and determining as the price, f, a value consistent with the model;
and
a display device coupled to the processor for displaying a result of the determination of the price, f(S), of the derivative.

A computer readable medium which is a tangible object and which stores code for programming a processor to generate data indicative of the price, f(S), of a derivative having an underlying financial instrument whose price is S=S(t+τ)=S(τ)eY(t), where t denotes a time delay, time interval, or timescale, T is an initial time value, τ=0 without loss of generality, Y(t) is a value that evolves across timescale t, and the underlying financial instrument has a return, including by implementing a non-Gaussian model of the price, S, said model assuming statistical feedback, and determining, as the price f, a value consistent with the model.

Dependencies are inferred from the claim text.

Abstract

Claims46

Dependent claims

A method for determining price, f(S), of a derivative having an underlying financial instrument, said method including the steps of:

(a) determining a non-Gaussian model of price, S, of the underlying financial instrument, said model assuming statistical feedback,
where the price S is S=S(t+τ)=S(τ)eY(t), where t denotes a time delay, time interval, or timescale, τ is an initial time value, τ=0 without loss of generality, Y(t) is a value that evolves across timescale t, and the underlying financial instrument has a return;
and
(b) by operating a computer system, determining as price f, a derivative price value consistent with the model determined in step (a), including by generating data indicative of the derivative price value.

1 more element

A computer system, comprising:

a processor programmed to generate data indicative of price, f(S), of a derivative having an underlying financial instrument whose price is S=S(t+τ)=S(τ)eY(t), where t denotes a time delay, time interval, or timescale, T is an initial time value, τ=0 without loss of generality, Y(t) is a value that evolves across timescale t, and the underlying financial instrument has a return, including by implementing a non-Gaussian model of the price S, said model assuming statistical feedback, and determining as the price, f, a value consistent with the model;
and
a display device coupled to the processor for displaying a result of the determination of the price, f(S), of the derivative.

Dependencies are inferred from the claim text.

Method and system for non-Gaussian pricing of options and other derivatives

Life of this patent

Abstract

Claims46

Method and system for non-Gaussian pricing of options and other derivatives

Life of this patent

Abstract

Claims46