1999/07/13 by Jiri Hoogland, Hoogland, Jiri, Dimitri Neumann +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Complex Systems and Time Series Analysis #Condensed Matter (cond-mat) #FOS: Mathematics #FOS: Physical sciences #Financial Markets and Investment Strategies #Stochastic processes and financial applications #cond-mat #math.AP
paper · pdf · doi:10.48550/arxiv.cond-mat/9907185
26 pages, Latex2e, amsmath
arxiv created 1999/07/13 · openalex publication_date 1999/07/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects only, and which completely avoids the use of martingale techniques. In this article we show the use of the formalism in the context of path-dependent options. We derive compact and intuitive formulae for the prices of a whole range of well known options such as arithmetic and geometric average options, barriers, rebates and lookback options. Some of these have not appeared in the literature before. For example, we find rather elegant formulae for double barrier options with moving barriers, continuous dividends and all possible configurations of the barriers. The strength of the formalism reveals itself in the ease with which these prices can be derived. This allowed us to pinpoint some mistakes regarding geometric mean options, which frequently appear in the literature. Furthermore, symmetries such as put-call transformations appear in a natural way within the framework.