Patent Document ID: 7630931
Application ID: 11378675
Patent Status: 1

Claim One:
1. A computer-implemented system for determining prices of derivatives, comprising: a memory comprising a database configured to store historical prices of underlying assets and historical prices of derivatives of the underlying assets; a processor configured to execute computer executable code stored in program modules, comprising: a stochastic process modeling module, comprising: a time series module configured to generate a time series process describing risk factors comprising returns for the underlying assets; a smooth truncation module configured to generate a smoothly truncated heavy tailed asymmetric probability distribution and by replacing the left and right heavy tails of a Stable distribution based on the time series process by a first and second normal distribution, respectively, in accordance with the equation: τ 1 2 = ( φ ⁡ ( Φ - 1 ⁡ ( G ⁡ ( a ) ) ) 2 ⁢ ⁢ π ⁢ g ⁡ ( a ) ) 2 , v 1 = a - τ 1 ⁢ Φ - 1 ⁡ ( G ⁡ ( a ) ) ⁢ ⁢ and τ 2 2 = ( φ ⁡ ( Φ - 1 ⁡ ( G ⁡ ( b ) ) ) 2 ⁢ ⁢ π ⁢ g ⁡ ( b ) ) 2 , v 2 = b + τ 2 ⁢ Φ - 1 ⁡ ( 1 - G ⁡ ( b ) ) where ν and τ 2 comprise parameters (ν i , τ i 2 ), i=1,2 of the normal distributions, ν further comprises mean of the normal distribution, τ 2 further comprises variance of the normal distribution, φ comprises the density of the normal distribution, Φ −1 comprises the inverse of the cumulative distribution function of the normal distribution, g comprises the density of the Stable distribution, G comprises the cumulative distribution function of the Stable distribution, a comprises the lower truncation point and b comprises the upper truncation point of the Stable distribution by the first and second normal distribution; and an innovation module configured to determine an innovation process, wherein marginals of the probability distribution of the innovation process comprise the smoothly truncated heavy tailed and asymmetric probability distribution; a calibrator module configured to set parameters for the innovation process to match the historical prices, in accordance with the equation: log S t −log S t-1 =r t −d t −log g(σ t )+σ t ε t , wherein conditional variance of volatility of the underlying asset changes over time in accordance with the equation: σ t 2 = α 0 + ∑ k = 1 q ⁢ ⁢ α k ⁢ σ t - k 2 ⁡ ( ɛ t - k - λ ) 2 + ∑ k = 1 p ⁢ ⁢ β k ⁢ σ t - k 2 where S t comprises the price of the underlying asset at time t, r t comprises risk free rate of return, d t comprises dividend rate at time t of the underlying asset, log g comprises the logarithmic moment generating function of the smooth truncated heavy tailed asymmetric probability distribution, σ t comprises volatility of the underlying asset, σ t 2 comprises conditional variance of the underlying asset, α k comprises coefficients of the lag-squared innovations, ε t comprises the innovation process, λ comprises market price of risk, t comprises discrete time, k comprises an index parameter where k is an integer from one 1 to q in the first summation and 1 to p in the second summation, p comprises the number of lags of the conditional variance terms, q comprises the number of terms of the lag-squared innovations, and β k comprises the coefficients of the lagged conditional variances; a derivative pricing calculator module configured to determine future prices of derivatives comprising options and swaps by executing the innovation process on the parameters; an output device configured to provide future prices of the derivatives, and a network to operatively couple and provide communication between the database, the output device, and the computer processor.