A computer-implemented method of determining an approximated value of a parameter in a first domain is described. The parameter is dependent on one or more variables which vary in a second domain, and the parameter is determined by a function which relates sets of values of the one or more variables in the second domain to corresponding values in the first domain. The method is implemented on a computer system including a processor, and the method comprises: determining a plurality of anchor points in the second domain, wherein each anchor point comprises a set of values of the one or more variables in the second domain; evaluating, at each anchor point, the function to generate corresponding values of the parameter in the first domain; generating an approximation function to the function by fitting a series of orthogonal functions or an approximation to a series of orthogonal functions to the corresponding values of the parameter in the first domain; and using the approximation function to generate the approximated value of the parameter in the first domain.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method of determining an approximated value of a parameter in a first domain, the parameter being dependent on one or more variables which vary in a second domain, and the parameter being determined by a function which relates sets of values of the one or more variables in the second domain to corresponding values in the first domain, the method being implemented on a computer system including a processor, and the method comprising: determining a plurality of anchor points in the second domain, wherein each anchor point comprises a set of values of the one or more variables in the second domain; evaluating, at each anchor point, the function to generate corresponding values of the parameter in the first domain; generating an approximation function to the function by fitting a series of orthogonal functions or an approximation to a series of orthogonal functions to the corresponding values of the parameter in the first domain; and using the approximation function to generate the approximated value of the parameter in the first domain. 2. The computer-implemented method of claim 1, further comprising: transforming the function into an intermediary function before the generating step, wherein the intermediary function is a linear transformation of the function, and wherein the generating step comprises approximating the intermediary function. 3. The computer-implemented method of claim 2, wherein the transforming step comprises linearly transforming the function into a predetermined range. 4. The computer-implemented method of claim 1, wherein the series of orthogonal functions is one of the group comprising: sines, cosines, sines and cosines, Bessel functions, Gegenbauer polynomials, Hermite polynomials, Laguerre polynomials, Chebyshev polynomials, Jacobi polynomials, Spherical harmonics, Walsh functions, Legendre polynomials, Zernike polynomials, Wilson polynomials, Meixner-Pollaczek polynomials, continuous Hahn polynomials, continuous dual Hahn polynomials, a classical polynomials described by the Askey scheme, Askey-Wilson polynomials, Racah polynomials, dual Hahn polynomials, Meixner polynomials, piecewise constant interpolants, linear interpolants, polynomial interpolants, gaussian process based interpolants, spline interpolants, barycentric interpolants, Krawtchouk polynomials, Charlier polynomials, sieved ultraspherical polynomials, sieved Jacobi polynomials, sieved Pollaczek polynomials, Rational interpolants, Trigonometric interpolants, Hermite interpolants, Cubic interpolants, and Rogers-Szegö polynomials. 5. The computer-implemented method of claim 1, wherein the series of orthogonal functions is a series of orthogonal polynomials. 6. The computer-implemented method of claim 1, wherein the approximation to a series of orthogonal functions is an approximation to a series of orthogonal polynomials. 7. The computer-implemented method of claim 1, further comprising: selecting a series of orthogonal functions or an approximation to a series of orthogonal functions before the generating step, and wherein the generating step comprises using the selected series of orthogonal functions or the approximation to the series of orthogonal functions. 8. The computer-implemented method of claim 1, wherein the number of anchor points, NE, is so that: N S · T N E · T + N S · t > 1 wherein NS is the number of scenarios, t is the time taken to run the approximation function, and T is the time taken to run the function. 9. The computer-implemented method of claim 1, further comprising: holding the values of all but one variable in the set to be constant in the evaluating step. 10. The computer-implemented method of claim 1, further comprising using the approximated values of the parameter to generate standard metrics. 11. The computer-implemented method of claim 1, wherein the values of the variables vary stochastically. 12. The computer-implemented method of claim 1, wherein the using step comprises using the approximation function a plurality of times to generate at least one scenario or one time step, each scenario or each time step comprising a plurality of approximated values. 13. The computer-implemented method of claim 12, wherein the number of scenarios or time steps is significantly greater than the number of anchor points. 14. The computer-implemented method of claim 1, wherein an output of the function is a parameter of a financial product. 15. The computer-implemented method of claim 14, wherein the financial product is a financial derivative including one or more of a group comprising: an option pricing function, a swap pricing function and a combination thereof. 16. The computer-implemented method of claim 1, wherein the function is one of the group comprising: a Black-Scholes model, a Longstaff-Schwartz model, a binomial options pricing model, a Black model, a Garman-Kohlhagen model, a Vanna-Volga method, a Chen model, a Merton's model, a Vasicek model, a Rendleman-Bartter model, a Cox-Ingersoll-Ross model, a Ho-Lee model, a Hull-White model, a Black-Derman-Toy model, a Black-Karasinski model, a Heston model, a Monte Carlo based pricing model, a binomial pricing model, a trinomial pricing model, a tree based pricing model, a finite-difference based pricing model, a Heath-Jarrow-Morton model, a variance gamma model, a Fuzzy pay-off method, a Single-index model, a Chepakovich valuation model, a Markov switching multifractal, a Datar Mathews method, and a Kalotay-Williams-Fabozzi model. 17. The computer-implemented method of claim 1, wherein the anchor points are the zeros or extrema of each orthogonal function, or a subset of the zeros or extrema. 18. The computer-implemented method of claim 17, wherein the approximating function is generated using an interpolation scheme. 19. The computer-implemented method of claim 18, wherein the interpolation scheme is one from the group comprising: piecewise constant interpolants, linear interpolants, polynomial interpolants, gaussian process based interpolants, spline interpolants, barycentric interpolants, Rational interpolants, Trigonometric interpolants, Hermite interpolants and Cubic interpolants. 20. The computer-implemented method of claim 1, wherein the anchor points are integration points of a numerical integration scheme. 21. The computer-implemented method of claim 20, wherein the numerical integration scheme is one from the group comprising: Newton-Cotes methods, a trapezoidal method, a Simpson's method, a Boole's method, a Romberg integration method, Gaussian quadrature methods, Chenshaw-Curtis methods, a Fejer method, a Gaus-Kronrod method, Fourier Transform methods, an Adaptive quadrature method, a Richardson extrapolation, a Monte Carlo and Quasi Monte Carlo method, a Markov chain Monte Carlo, a Metropolis Hastings algorithm, a Gibbs Sampling, and Fast Fourier Transform methods. 22. The computer-implemented method of claim 1, wherein the speed of the calculation is increased with no loss of accuracy in the standard metrics, and/or the accuracy of the standard metrics increase with no decrease in the speed of the calculation when using the approximation function. 23. The computer-implemented method of claim 1, wherein there is a difference between the approximated value of the parameter and the parameter in the 2nd significant figure when compared at the same point in the first domain. 24. The computer-implemented method of claim 1, wherein there is a difference between the approximated value of the parameter and the parameter in between the 4th and the 6th significant figure when compared at the same point in the first domain. 25. The computer-implemented method of claim 1, wherein there is a difference between the approximated value of the parameter and the parameter in the 15th significant figure when compared at the same point in the first domain. 26. A financial derivative comprising a parameter, wherein a value of the parameter is determined using the computer-implemented method of claim 1. 27. A computer system comprising a processor configured to determine an approximated value of a parameter in a first domain, the parameter being dependent on one or more variables which vary in a second domain, and the parameter being determined by a function which relates sets of values of the one or more variables in the second domain to corresponding values in the first domain, the computer system comprising: a determination module arranged to determine a plurality of anchor points in the second domain, wherein each anchor point comprises a set of values of the one or more variables in the second domain; an evaluation module arranged to evaluate, at each anchor point, the function to generate corresponding values of the parameter in the first domain; a generation module arranged to generate an approximation function to the function by fitting a series of orthogonal functions or an approximation to a series of orthogonal functions to the corresponding values of the parameter in the first domain; and an approximation module arranged to use the approximation function to generate the approximated value of the parameter in the first domain. 28. A computer-implemented method of determining an approximated value of a parameter in a first domain, the parameter being dependent on one or more variables which vary in a second domain, and the parameter being determined by a function which relates sets of values of the one or more variables in the second domain to corresponding values in the first domain, the method using a series of orthogonal functions or an approximation to a series of orthogonal functions to approximate the function. 29. The computer-implemented method of claim 17, wherein the series of orthogonal functions used to generate the approximation function is a first series of orthogonal functions and the series of orthogonal functions used to determine the plurality of anchor points is a second series of orthogonal functions different from the first series of orthogonal functions. 30. The computer-implemented method of claim 29, wherein the first series of orthogonal functions is the Lagrange polynomials and second series of orthogonal functions is the Chebyshev polynomials. 31. The computer-implemented method of claim 4, wherein the series of orthogonal functions is the Chebyshev polynomials, and the method comprises applying a Clenshaw algorithm to the approximation function to obtain a Clenshaw approximation function before the using step, wherein the using step comprises using the Clenshaw approximation function to generate the approximated value of the parameter. 32. The computer-implemented method of claim 4, wherein the series of orthogonal functions is the Lagrange polynomials, and the method comprises applying a Barycentric algorithm to the approximation function to obtain a Barycentric approximation function before the using step, wherein the using step comprises using the Barycentric approximation function to generate the approximated value of the parameter. 33. The computer-implemented method of claim 1, wherein the determining step comprises determining a plurality of anchor points in a sub-domain of the second domain, wherein each anchor point comprises a set of values of the one or more variables in the sub-domain of the second domain, and the generating step comprises generating the approximation function to the function in the sub-domain. 34. The computer-implemented method of claim 1, wherein using the approximation function comprises applying a transform to the approximation function, and using the transformed approximation function to generate the approximated value of the parameter. 35. The computer-implemented method of claim 34, wherein the transform is a derivative of the approximation function with respect to at least one of the variables in the second domain. 36. A computer-implemented method of determining an approximated value of a parameter in a first domain, the parameter being dependent on one or more variables which vary in a second domain, and the parameter being determined via a function which relates sets of values of the one or more variables in the second domain to corresponding values in the first domain, the method being implemented on a computer system including a processor, and the method comprising: determining a plurality of anchor points in the second domain, wherein each anchor point comprises a set of values of the one or more variables in the second domain; evaluating, at each anchor point, the function to generate corresponding values of the parameter in the first domain; applying a transform to the corresponding values of the parameter in the first domain; generating an approximation function by fitting a series of orthogonal functions or an approximation to a series of orthogonal functions to the transformed corresponding values of the parameter in the first domain; and using the approximation function to generate the approximated value of the parameter in the first domain. 37. A computer-implemented method of determining an approximated value of a parameter in a first domain, the parameter being dependent on one or more variables which vary in a second domain, and the parameter being determined by a function which relates sets of values of the one or more variables in the second domain to corresponding values in the first domain, the method being implemented on a computer system including a processor, and the method comprising: receiving a plurality of given values of the parameter in the first domain corresponding to a plurality of given sets of values of the one or more variables in the second domain; determining a plurality of anchor points in the second domain, wherein each anchor point comprises a set of values of the one or more variables in the second domain; transforming the given sets of values of the one or more variables in the second domain to correspond to the plurality of anchor points; generating an approximation function to the function by fitting a series of orthogonal functions or an approximation to a series of orthogonal functions to the given values of the parameter in the first domain at the plurality of anchor points; and using the approximation function to generate the approximated value of the parameter in the first domain.