PHYSICS OF OUR DAYS: Collectively fluctuating assets in the presence of arbitrage opportunities, and option pricing
Abstract
Methods of functional analysis are applied to describe collectively fluctuating default-free pure discount bonds subject to trading-related noise which generates arbitrage opportunities. Two key elements of the model are: (i) the naturally incorporated fixed bond price at maturity which is achieved by making use of only those fluctuating paths of price motion which terminate at a specified final condition, and (ii) the most attractive arbitrage opportunities between bonds with close maturities, with modeled a local linear approximation. The model can be written in different closed forms as a stochastic partial differential equation. The functional Black-Scholes equation for contingent claims is derived, and a connection with the conventional methods of option valuation is indicated.
- Publication:
-
Physics Uspekhi
- Pub Date:
- December 1997
- DOI:
- 10.1070/PU1997v040n12ABEH000319
- Bibcode:
- 1997PhyU...40.1239A