Tonight I went to a very interesting Sydney Financial Maths Workshop:
Path Integral Methods and their Application to Finance and the Black-Scholes World
Dr Debashis Gangopadhyay (Reader, Bose National Centre for Basic Sciences, Kolkata, India)
Abstract A pedagogical demonstration is given of how the Feynman path integral (or functional integral) formalism can be used to obtain the pricing kernel in Black-Scholes theory. First, a brief introduction is given of the relevant area of quantum mechanics and the Heisenberg Uncertainty Principle. Next, the conceptual foundations of fluctuations are discussed both from the operator viewpoint and also from the Least Action Principle. After this the path integral formalism is set up in a way suitable for explicit calculations. Finally, the pricing kernel in option pricing for the Black-Scholes process is derived using the path integral formalism.
The page advertising the seminar is here and includes a link to material used in the talk. Some handwritten notes were handed out – I’m sure you could e-mail the workshop’s organiser and ask for a photocopy of the notes.
Something very interesting is that the speaker discussed calculating path integrals, and it sounded at the end that if the volatility of a stock (?) could be determined, the theory outlined in the talk could, in principle, be used to do asymptotically converging calculations of quantities of interest.