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:
“There are two things which cannot be attacked in front: ignorance and narrow-mindedness. They can only be shaken by the simple development of the contrary qualities. They will not bear discussion.”
—John Emerich Edward Dalberg, 1st Baron Acton (1834–1902)
“Other nations have tried to check ... the fulfillment of our manifest destiny to overspread the continent allotted by Providence for the free development of our yearly multiplying millions.”
—John Louis O’Sullivan (1813–1895)
“The American has dwindled into an Odd Fellow—one who may be known by the development of his organ of gregariousness.”
—Henry David Thoreau (1817–1862)