Method And System For Simulating Implied Volatility Surfaces For Basket Option Pricing

Abstract

A method and system for simulating changes in volatility for a price of a particular option on an underlying financial instrument is disclosed. A volatility surface model having at least one surface parameter is provided along with a set of volatilities for a plurality of options on the underlying financial instrument. The set of volatilities is analyzed to determine an initial value for each surface parameter which, when used in the surface model, defines a surface approximating the set of volatilities. The values of the surface parameters are then evolved using an appropriate evolution function. A volatility value for a particular option is extracted from the volatility surface defined by the evolved surface parameter values. The extracted volatility value can then be used in an option pricing model to provide a price of the particular option. The volatility of a basket options valued relative to the performance of multiple components can be simulated by determining the value of surface parameters for options on the component securities and then combining the component surface parameters to determine surface parameters for a volatility surface of the basket.

1 - 14 . (canceled) 
     
     
         15 . A computer-implemented method for simulating volatility of a basket of individual derivative instruments comprising:
 receiving historical financial data related to a plurality of individual derivative instruments;   deriving an individual surface parameter for each the plurality of individual derivative instruments from the historical financial data, wherein each of the individual surface parameters represents a measure of volatility for each of the individual derivative instruments;   determining surface parameters for a surface volatility model of the basket of individual derivative instruments by combining the individual surface parameters; and   simulating, using a processor, changes in prices of the basket of individual derivatives instruments by evolving the surface parameters for the surface volatility model of the basket of individual derivative instruments.   
     
     
         16 . The computer-implemented method of  claim 15 , further comprising determining an implied volatility for one of the plurality of individual derivative instruments by referencing the changes simulated. 
     
     
         17 . The computer-implemented method of  claim 16 , wherein the plurality of individual derivative instruments includes options. 
     
     
         18 . The computer-implemented method of  claim 17 , wherein determining the implied volatility includes using a price of the option and a time before the option expires. 
     
     
         19 . The computer-implemented method of  claim 15 , wherein deriving the individual surface parameter for each of the plurality of individual derivative instruments includes using a regression analysis. 
     
     
         20 . The computer-implemented method of  claim 19 , wherein deriving the individual surface parameter for each of the plurality of individual derivative instruments includes translating the historical data before using the regression analysis. 
     
     
         21 . The computer-implemented method of  claim 19 , wherein deriving the individual surface parameter for each of the plurality of individual derivative instruments includes using a set of predefined guidelines to determine values form the historical financial data that will be used in the regression analysis. 
     
     
         22 . The computer-implemented method of  claim 15 , wherein evolving the surface parameters includes a mean-reversion process. 
     
     
         23 . The computer-implemented method of  claim 22 , wherein the mean-reversion process includes a simulated time series for each of the surface parameters. 
     
     
         24 . The computer-implemented method of  claim 22 , further comprising determining a set of reversion parameters for the mean-reversion process. 
     
     
         25 . The computer-implemented method of  claim 24 , wherein set of reversion parameters are determined empirically. 
     
     
         26 . A system for simulating volatility of a basket of individual derivative instruments comprising:
 a data store containing having stored thereon individual surface parameters defining an individual volatility surface for each of the individual derivative instruments; and   a processor being configured via computer software to:
 determine values for a plurality of surface parameters defining a volatility surface for the basket of the individual derivative instruments using the individual surface parameters associated with each of the individual derivative instruments; 
 generate initial values for the volatility surface of the basket by regressing a set of initial volatility data; 
 determine, from historical financial data having source point values, a set of calibration residual values representing the difference between the source point values and the initial values; 
 simulate, using a processor, changes in prices of the basket of individual derivatives instruments by evolving the volatility surface using a mean-reversion process with the set of calibration residual values. 
   
     
     
         27 . The system  claim 26 , wherein the mean-reversion process includes a simulated time series for each of the surface parameters defining the volatility surface. 
     
     
         28 . The system  claim 26 , wherein the processor is further configured via computer software to determine a set of reversion parameters for the mean-reversion process. 
     
     
         29 . The system  claim 28 , wherein the set of reversion parameters are determined empirically. 
     
     
         30 . A computer-implemented method for simulating volatility of a basket of individual derivative instruments comprising:
 selecting a parametric model for each of the individual derivative instruments based on historical financial data having source point data;   determining surface parameters for a surface volatility model of the basket of individual derivative instruments by combining the parametric models of each of the individual derivative instruments;   generating initial values for the surface volatility model by regressing initial volatility data;   determining, from the historical financial data, a set of calibration residual values representing the difference between the source point data and the initial values; and   simulating, using a processor, changes in prices of the basket of individual derivatives instruments by evolving the surface volatility model defined by the surface parameters and the set of calibration residual values.   
     
     
         31 . The computer-implemented method of  claim 30 , wherein the surface parameters account for a number of shares of each individual derivative instrument in the basket, a price of each individual derivative instruments of the basket, and an exchange rate between a native currency and a currency in which the basket of individual derivative instruments is priced. 
     
     
         32 . The computer-implemented method of  claim 30 , further comprising determining an implied volatility for one of the individual derivative instruments by referencing the changes simulated. 
     
     
         33 . The computer-implemented method of  claim 32 , wherein the basket of individual derivative instruments includes options. 
     
     
         34 . The computer-implemented method of  claim 33 , wherein determining the implied volatility includes using a price of the option and a time before the option expires.