Chapter 1


In Théorie de la Speculation (1900), Louis Bachelier made the first attempt to model the inherent randomness in stock prices using a continuous-time counterpart of white noise, the Brownian Motion. For many years this modelling approach was of purely academic interest as financial institutions used less mathematically demanding methods. More than 70 years later the ideas proposed by Bachelier were used in two seminal papers by Robert Merton on continuous-time finance in general and Fischer Black and Myron Scholes on the pricing of options and corporate liabilities. Contrary to their own expectations, this area has expanded enormously during the last decades, and Merton and Scholes received the Nobel Prize in economics in ...

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