Method and system for pricing and risk analysis of options

A method to determine the value of an option, the option dependent upon a stochastic variable, the method comprising:

• generating on a processor a specification of permissible error for the determination;
• generating on the processor a function indicating the weight to be assigned in measuring error of the determination (error weight function);
• generating on the processor a specification of the evolution of the stochastic variable among a plurality of time periods;
• generating on the processor a specification of the dependency of the option on the stochastic variable;
• transmitting by the processor the specification of permissible error, the error weight function, the specification of the evolution of the stochastic variable, and the specification of the dependency of the option on the stochastic variable;
• and
• receiving on the processor a determination of the value of the option within the permissible error for the determination, wherein the determination apportioned the specification of permissible error among the plurality of time periods.

An apparatus to determine a value of an option, the option dependent upon a stochastic variable, the apparatus comprising:

• memory;
• one or more processors;
• a receiver to receive a specification of permissible error, of a function indicating the weight to be assigned in measuring error of the determination (error weight function), of an evolution of the stochastic variable, and of a relationship between the option and the stochastic variable, wherein evolving the weight function from one time period to the next is determining the weight function at the next time period based upon the weight function at the previous time period and upon the evolution of the stochastic variable;
• an apportioner to apportion the specification of permissible error among a plurality of time periods;
• a forward sweep module to evolve the error weight function through the plurality of time periods;
• and
• a backward sweep module to determine values of the stochastic variable at the plurality of time periods, wherein the determination of a value for one or more of the time periods is within the permissible error apportioned for the time period and the backward sweep module is to determine the permissible error by weighting an estimate of an error of a determination of a value of the stochastic variable by the error weighting function;
• and to determine the value of the option, responsive to the determination of the values of the stochastic variable at the plurality of time periods.

A computer program product comprising a computer useable medium having a computer readable program, wherein the computer readable program when executed on a computer causes the computer to:

• receive a specification of permissible error for the determination;
• receive a function indicating the weight to be assigned in measuring error of the determination (error weight function);
• receive a specification of an evolution of the stochastic variable;
• receive a specification of the relationship between the option and the stochastic variable;
• apportion the specification of permissible error among a plurality of time periods;
• evolve the error weight function through the plurality of time periods, wherein evolving the weight function from one time period to the next is determining the weight function at the next time period based upon the weight function at the previous time period and upon the evolution of the stochastic variable;
• determine values of the stochastic variable at the plurality of time periods, wherein the determination of a value for one of the plurality of time periods is within the permissible error apportioned for the one of the plurality of time periods;
• and
• the determining values comprises weighting an estimate of an error of the determination of the value for the one of the plurality of time periods by the error weighting function;
• determine the value of the stochastic variable, responsive to the determination of the values of the option at the plurality of time periods;
• and
• store the value of the option in a buffer.

The claim of method 1, wherein the error is calculated by the formula:

• error
• =
• ∫
• ⅆ
• ψ
• ⁡
• (
• x
• )
• ⁢
• 
• δ
• 0
• ⁡
• (
• x
• )
• 
• ,
• where
• ψ is the error weight function;
• v0 (x) is a discounted value of the option at time t=0,
• δ0 (x) is an error of v0 (x), and
• v0 (x)={circumflex over (v)}0 (x)+δ0 (x), with {circumflex over (v)}0 (x) denoting a determination of the discounted value of the option.