Development
The concept of a local volatility was developed when Bruno Dupire and Emanuel Derman and Iraj Kani noted that there is a unique diffusion process consistent with the risk neutral densities derived from the market prices of European options.
Derman and Kani described and implemented a local volatility function to model instantaneous volatility. They used this function at each node in a binomial options pricing model. The tree successfully produced option valuations consistent with all market prices across strikes and expirations. The Derman-Kani model was thus formulated with discrete time and stock-price steps. The key continuous-time equations used in local volatility models were developed by Bruno Dupire in 1994. Dupire's equation states
Read more about this topic: Local Volatility
Famous quotes containing the word development:
“Dissonance between family and school, therefore, is not only inevitable in a changing society; it also helps to make children more malleable and responsive to a changing world. By the same token, one could say that absolute homogeneity between family and school would reflect a static, authoritarian society and discourage creative, adaptive development in children.”
—Sara Lawrence Lightfoot (20th century)
“I can see ... only one safe rule for the historian: that he should recognize in the development of human destinies the play of the contingent and the unforeseen.”
—H.A.L. (Herbert Albert Laurens)
“Somehow we have been taught to believe that the experiences of girls and women are not important in the study and understanding of human behavior. If we know men, then we know all of humankind. These prevalent cultural attitudes totally deny the uniqueness of the female experience, limiting the development of girls and women and depriving a needy world of the gifts, talents, and resources our daughters have to offer.”
—Jeanne Elium (20th century)