Method and System for Creating and Trading Derivative Investment Products Based on a Statistical Property Reflecting the Variance of an Underlying Asset

Abstract

A system and method for creating a limited risk derivative based on a realized variance of an underlying equity is disclosed. In one implementation, a limited risk derivative product includes a capped value for a statistical property reflecting a variance of the underlying equity is calculated based on a pari-mutuel action. The capped value comprises a dynamic value and a cap. The dynamic value reflects an average volatility of prices returns of the underlying equity over a predefined period of time and the cap reflects a maximum value of the dynamic value. The limited risk derivative product additionally includes an average of a summation of each squared daily return of the underlying equity included in the value for the statistical property reflecting the variance of the underlying equity.

1 . A limited risk derivative product based on a realized variance of an underlying equity, comprising:
 a capped value for a statistical property reflecting the variance of the underlying equity, the capped value for the statistical property comprising a dynamic value and a cap, the dynamic value reflecting an average volatility of price returns of the underlying equity over a predefined time period and the cap reflecting a maximum value of the dynamic value; and   an average of a summation of each squared daily return of the underlying equity included in the value for the statistical property reflecting the variance of the underlying equity;   wherein the value of the statistical property is calculated according to the formula:   
       
         
           
             
               
                 Realized 
                  
                 
                     
                 
                  
                 Variance 
               
               = 
               
                 AF 
                 × 
                 
                   ( 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         
                           N 
                           a 
                         
                         - 
                         1 
                       
                     
                      
                     
                         
                     
                      
                     
                       
                         R 
                         i 
                         2 
                       
                        
                       
                         / 
                       
                        
                       
                         ( 
                         
                           
                             N 
                             e 
                           
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       wherein: 
       
         
           
             
               
                 
                   R 
                   i 
                 
                 = 
                 
                   ln 
                    
                   
                       
                   
                    
                   
                     
                       P 
                       
                         i 
                         + 
                         1 
                       
                     
                     
                       P 
                       i 
                     
                   
                 
               
               , 
             
           
         
       
       P i  is an initial value of the underlying equity used to calculate a daily return, P i+1  is a final value of the underlying equity used to calculate the daily return, N e  is a number of expected underlying equity values needed to calculate daily returns during a variance calculation period, N a  is an actual number of underlying equity values used to calculate daily returns during the variance calculation period; and AF is an annualization factor.