Black-Scholes-Merton equation
Ecuación de Black-Scholes-Merton
- Date
- 1973 · confidence high
- Place
- Chicago and Cambridge (MIT), United States
- Credited to
- Fischer Black, Myron Scholes and Robert Merton
- People
- 👤 Fischer Black1938–1995👤 Myron Scholes1941–👤 Robert C. Merton1944–
- Field
- Knowledge & symbols
What was discovered
A partial differential equation, derived from Itô calculus and the no-arbitrage hedging argument, that gives the price of an option. It created financial mathematics and transformed derivatives markets.
Scholes and Merton received the Nobel Prize in Economics in 1997; the assumption that returns are normally distributed is its weak point, criticised by Mandelbrot.
What it led to
- financial engineering
- volatility models
- quantitative risk management
Built on
- Heat equation1822
- Itô stochastic calculus1944
- Itô calculus
- Bachelier (1900)
Made possible
- options markets (CBOE, 1973)
- derivatives (financial)