27,982 research outputs found
Black-Scholes option pricing within Ito and Stratonovich conventions
Options financial instruments designed to protect investors from the stock
market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton
proposed a very popular option pricing method using stochastic differential
equations within the Ito interpretation. Herein, we derive the Black-Scholes
equation for the option price using the Stratonovich calculus along with a
comprehensive review, aimed to physicists, of the classical option pricing
method based on the Ito calculus. We show, as can be expected, that the
Black-Scholes equation is independent of the interpretation chosen. We
nonetheless point out the many subtleties underlying Black-Scholes option
pricing method.Comment: 14 page
Relativistic Black-Scholes model
Black-Scholes equation, after a certain coordinate transformation, is
equivalent to the heat equation. On the other hand the relativistic extension
of the latter, the telegraphers equation, can be derived from the Euclidean
version of the Dirac equation. Therefore the relativistic extension of the
Black-Scholes model follows from relativistic quantum mechanics quite
naturally. We investigate this particular model for the case of European
vanilla options. Due to the notion of locality incorporated in this way one
finds that the volatility frown-like effect appears when comparing to the
original Black-Scholes model.Comment: 18 pages, publishe
The Quantum Black-Scholes Equation
Motivated by the work of Segal and Segal on the Black-Scholes pricing formula
in the quantum context, we study a quantum extension of the Black-Scholes
equation within the context of Hudson-Parthasarathy quantum stochastic
calculus. Our model includes stock markets described by quantum Brownian motion
and Poisson process.Comment: Has appeared in GJPAM, vol. 2, no. 2, pp. 155-170 (2006
Option Pricing in a Fractional Brownian Motion Environment
The purpose of this paper is to obtain a fractional Black-Scholes formula for the price of an option for every t in [0,T], a fractional Black-Scholes equation and a risk-neutral valuation theorem if the underlying is driven by a fractional Brownian motion BH (t), 1/2fractional Brownian motion, fractional Black-Scholes market, quasiconditional expectation
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