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:
“Ultimately, it is the receiving of the child and hearing what he or she has to say that develops the child’s mind and personhood.... Parents who enter into a dialogue with their children, who draw out and respect their opinions, are more likely to have children whose intellectual and ethical development proceeds rapidly and surely.”
—Mary Field Belenky (20th century)
“Understanding child development takes the emphasis away from the child’s character—looking at the child as good or bad. The emphasis is put on behavior as communication. Discipline is thus seen as problem-solving. The child is helped to learn a more acceptable manner of communication.”
—Ellen Galinsky (20th century)
“America is a country that seems forever to be toddler or teenager, at those two stages of human development characterized by conflict between autonomy and security.”
—Anna Quindlen (b. 1952)