Patent Document ID: 7813979
Application ID: 11031079
Patent Flag: 1

Claim One:
1. A computer-implemented method of determining a net present value of one of a call and a put (“V call ” and “V put ,” respectively) of an average spot basket option as a function of an evaluation date, comprising: reading, by a processor, an evaluation date; reading, by the processor, contract data for a set of assets belonging to a basket; reading, by the processor, market data, as a function of the evaluation date, for the set of assets belonging to the basket; calculating, by the processor, the net present value according to the following equations: V call ⁡ ( t E ) = ⅇ - r ⁡ ( t E , T ) ⁢ ( T - t E ) ⁡ [ + F ~ ⁢ N ⁡ ( + d ~ 1 ) - K ~ ⁢ N ⁡ ( + d ~ 2 ) ] V put ⁡ ( t E ) = ⅇ - r ⁡ ( t E , T ) ⁢ ( T - t E ) ⁡ [ - F ~ ⁢ N ⁡ ( - d ~ 1 ) + K ~ ⁢ N ⁡ ( - d ~ 2 ) ] } for ⁢ ⁢ t E ≤ T ⁢ ⁢ and K ~ > 0 ⁢ V call ⁡ ( t E ) = ⅇ - r ⁡ ( t E , T ) ⁢ ( T - t E ) ⁡ [ + F ~ - K ~ ] V put ⁡ ( t E ) = 0 } for ⁢ ⁢ t E ≤ T ⁢ ⁢ and K ~ ≤ 0 ⁢ V call / put ⁡ ( t E ) = 0 , for ⁢ ⁢ t E > T } where d ~ 1 = ln ⁢ ⁢ F ~ K ~ v + v 2 , d ~ 2 = d ~ 1 - v K ~ = K - ∑ j = 1 N A ⁢ ∑ i = 1 N j ⁢ ( 1 - δ i ( j ) ) × w i ( j ) ⁢ S j ⁡ ( t i ( j ) ) where ⁢ ⁢ δ i ( j ) = { 0 , if ⁢ ⁢ S j ⁡ ( t i ( j ) ) ⁢ ⁢ is  already  fixed 1 , if ⁢ ⁢ S j ⁡ ( t i ( j ) ) ⁢ ⁢ is  not  yet  fixed F ~ = 〈 M 〉 v 2 = ln ⁢ 〈 M 2 〉 - 2 ⁢ ⁢ ln ⁢ 〈 M 〉 〈 M 〉 = ∑ j = 1 N A ⁢ S j ⁡ ( t E ) ⁢ ∑ i = 1 N j ⁢ δ i ( j ) × w i ( j ) ⁢ ⅇ g j ⁡ ( t i ( j ) - t E ) 〈 M 2 〉 = ∑ j = 1 N A ⁢ ∑ j ′ = 1 N A ⁢ S j ⁡ ( t E ) ⁢ S j ′ ⁡ ( t E ) ⁢ ∑ jj ′ ∑ jj ′ ⁢ = ∑ i = 1 N i ⁢ δ i ( j ) × w i ( j ) ⁢ ⅇ g j ⁡ ( t i ( j ) - t E ) × ∑ i ′ = 1 N i ′ ⁢ δ i ′ ( j ′ ) × w i ′ ( j ′ ) ⁢ ⅇ g j ′ ⁡ ( t i ′ ( j ′ ) - t E ) × ⅇ ρ jj ′ ⁢ σ j ⁢ σ j ′ ⁢ τ ii ′ ( jj ′ ) g j = r ⁡ ( t E , T ) - q j ⁡ ( t E , T ) , j = 1 , … ⁢ , N A τ ii ′ ( jj ′ ) = { 0 , if ⁢ ⁢ ( t i ( j ) - t E ) × ( t i ′ ( j ′ ) - t E ) < 0 Min ⁢ { Abs ⁡ ( t i ( j ) - t E ) , Abs ⁡ ( t i ′ ( j ′ ) - t E ) } , else where N(x) represents a normal cumulative distribution r(t 1 ,t 2 ) represents a riskless domestic currency interest rate for the time span t 1. .. t 2 q j (t 1 ,t 2 ) represents a dividend rate, or foreign currency interest rate for the time span t 1. .. t 2 S j (t) represents a spot price of the j-th underlying asset, j=1,. .. , N A σ j represents a volatility of the j-th underlying asset ρ jj′ represents a correlation coefficient between the assets j and j′ (the correlation is related to the logarithm of the asset prices) K represents a strike price t E represents an evaluation date (unit of measure is year) T = Max i , j ⁢ { t i ( j ) } represents a latest fixing instant, i.e., the maturity at option w i (j) represents an i-th weighting factor of j-th asset; and displaying the calculated net present value on a display device.