Patent ID: 7287006

Claim:
A risk-adjusted pricing method for calculating the value of a derivative: a. determining an underlying security; b. determining the type of derivative; c. determining risks associated with said derivative; d. determining trading costs associated with said derivative; e. formulating a risk-adjusted pricing (RAP) equation with multiple parameters of the format: Expected ⁢ ⁢ Return On Investment = Return on Government ⁢ ⁢ Bonds + Rate ⁢ ⁢ of ⁢ ⁢ Expected Investment Cost + Rate ⁢ ⁢ of ⁢ ⁢ Expected Risk Premium for said derivative comprising one of the following formulas E[dO−δdS]=[r ( O−δS ) dt]+[r TC dt+r B δSdt+r D δSdt]+[r VAR dt+r σ dt+r GAP dt] (i) or E[dO−δdS]=[rOdt]+[r TC dt]+[r VAR dt+r σ dt+r GAP dt] (ii) where E[dO−δdS] represents Expected Return On Investment comprising the derivative O hedged with δ units of the underlying security S over a time interval dt; [r(O−δS)dt] and [rOdt] represent Return On Government Bonds with rate r; [r TC dt+r B δSdt+r D δSdt] and [r TC dt] represent Rate of Expected Investment Cost comprising average rate of trading costs r TC , borrowing fees r B , and dividend rate r D ; and [r VAR dt+r σ dt+r GAP dt] represents Rate of Expected Risk Premium comprising average positive variance risk premium rate r VAR , volatility risk premium rate r σ , and underlying price gap risk premium rate r GAP ; f. inputting said parameters of the RAP equation into a computer and solving said RAP equation with said computer for said derivative using numerical methods; and g. outputting a value for said derivative based on said solving of said RAP equation.