City Research Online

Finance Without Brownian Motions: An Introduction To Simplified Stochastic Calculus

Černý, A. and Ruf, J. Finance Without Brownian Motions: An Introduction To Simplified Stochastic Calculus. .

Abstract

The paper introduces a simple way of recording and manipulating stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The new calculus is thus intuitive and compact. The calculus is also fail-safe in that, under minimal assumptions, all formal calculations are guaranteed to yield mathematically well-defined stochastic processes. Several illustrative examples of the new concept are given, among them a novel result on the Margrabe option to exchange one defaultable asset for another.

Publication Type: Monograph (Working Paper)
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Q Science > QA Mathematics
Departments: Business School > Finance
Date Deposited: 13 Mar 2020 16:55
URI: https://openaccess.city.ac.uk/id/eprint/23389
[img]
Preview
Text - Pre-print
Download (814kB) | Preview

Export

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login