Options and partial differential equations
CitationKor, A. ve Can, M. (2009). Options and partial differential equations. International Conference on Mathematical Sciences, Maltepe Üniversitesi. s. 42-43.
The aim of this paper is to show how partial differential equations appear in financial models and to present briefly analytical and numerical methods used for effective computations of prices and hedging of options. In his thesis defended in 1900 in the Sorbonne, Louis Bachelier proposed a probabilistic modeling of the time evolution of the price of a share. In terms of what he calls the 'radiation of probability', he was able to relate the distribution of probability to the heat equation, which describes the evolution of temperature in a given media. In the first section, the reasoning of Louis Bachelier is used to bring out a relationship between the heat equation and a modeling of the evolution of share prices. In the second section, the equations satisfied by options prices are introduced. In the third section certain class of solutions to the Black, Scholes and Merton Equation are introduced.
SourceInternational Conference on Mathematical Sciences
- Makale Koleksiyonu 
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