The Wiener Stock Price Model and the Basic Principles of Black-Scholes Theory

Gerhard Larcher
Additional contact information
Gerhard Larcher: Johannes Kepler University of Linz

Chapter 4 in The Art of Quantitative Finance Vol.1, 2023, pp 273-516 from Springer

Abstract: Abstract We give basic tools for the statistical analysis of financial data. Especially we introduce the basic parameters trend, volatility, and correlation for stocks. Then we motivate and derive the Wiener stock price model (geometric Brownian motion). Thereby we discuss the goals and the meaning of mathematical modeling in general. We then show that—if parameters are chosen in a suitable way—the binomial N-step-model converges to the Wiener model. As a consequence we derive the Black-Scholes formula, i.e. the formula for the fair price of derivatives over an underlying which follows a Wiener model. We extensively discuss this pricing formula for plain vanilla call and put options and for strategies built by combinations of these options. We define the “Greeks” (i.e., the derivations of the fair prices with respect to different parameters), and we discuss the Greeks for various examples in detail. Finally we explain how hedging derivatives in a Wiener model is carried out.

Keywords: Trend; Volatility; Distribution of stock returns; Heavy-tail phenomenon; Correlations; Basic tools from statistics of financial markets; The role of mathematical modeling; The Wiener stock price model; Simulation of stock price developments; Brownian motion; Geometric Brownian motion; The Black Scholes formula; Hedging in the Wiener model; Discussion of pricing formulas for puts; Calls and option combinations; The Greeks; Delta/gamma hedging (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-031-23873-4_4

Ordering information: This item can be ordered from
http://www.springer.com/9783031238734

DOI: 10.1007/978-3-031-23873-4_4

Access Statistics for this chapter

More chapters in Springer Texts in Business and Economics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().