Lecture

Black-Scholes Formula: Risk-neutral Pricing and Option Pricing

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In course

MGT-301: Foundations in financial economics

The aim of this course is to expose EPFL bachelor students to some of the main areas in financial economics. The course will be organized around six themes. Students will obtain both practical insights through real-world examples and understand how one can ...

Description

This lecture covers the Black-Scholes formula in financial economics, focusing on risk-neutral pricing and option pricing. The instructor explains the model assumptions, risk-neutrality constraint, and the derivation of the Black-Scholes formula. Topics include implied volatility, option pricing, and pricing by replication.

Instructors (3)

Rüdiger Fahlenbrach

RUEDIGER FAHLENBRACH is Full Professor at Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. Formerly on the faculty of the Fisher College of Business of the Ohio State University (USA), he holds a Ph.D. in Finance from the University of Pennsylvania (Wharton). He holds a senior research chair from the Swiss Finance Institute, and is research member at the European Corporate Governance Institute (ECGI). He has research interests in empirical corporate finance, in particular corporate governance and entrepreneurship. Ruediger Fahlenbrach has published in the leading academic journals in finance, including the Journal of Finance, the Journal of Financial Economics, the Review of Financial Studies and the Journal of Financial and Quantitative Analysis. Ruediger currently serves a three year term as elected director of the European Finance Association (2018-2020). He is Associate Editor of the Review of Finance, and former associate editor of the Review of Financial Studies and Financial Management. His research has been reported in many large-circulation newspapers such as The New York Times, The Wall Street Journal, The Economist, Le Temps, NZZ, Handelsblatt, Forbes Magazine, USA Today, and Fortune Magazine.

Julien Hugonnier

Expertise Asset pricing theory, incomplete markets and financial frictions, general equilibrium theory, decision making under uncertainty Teaching & PhD PhD Students Luca Pagliuca, Darius Nik Nejad Past EPFL PhD Students Rodolfo Javier Prieto Katunaric, Michael Hasler, Giuliano Antonio Curatola, Julien Cujean, Thomas Antonius Geelen, Nicolas Gauderon, Benoit Vincent Sylvain Cornet Past EPFL PhD Students as codirector Rémy Praz, Cagil Kocyigit, Alexis Marchal Courses Derivatives FIN-404 Thi

Pierre Collin-Dufresne

Official source

Ontological neighbourhood

Economics

Microeconomics: Financial economics

Related concepts (32)

Binomial options pricing model

In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting. The binomial model was first proposed by William Sharpe in the 1978 edition of Investments (), and formalized by Cox, Ross and Rubinstein in 1979 and by Rendleman and Bartter in that same year.

Option (finance)

In finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction.

Local volatility

A local volatility model, in mathematical finance and financial engineering, is an option pricing model that treats volatility as a function of both the current asset level and of time . As such, it is a generalisation of the Black–Scholes model, where the volatility is a constant (i.e. a trivial function of and ). Local volatility models are often compared with stochastic volatility models, where the instantaneous volatility is not just a function of the asset level but depends also on a new "global" randomness coming from an additional random component.

Valuation of options

In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: for discussion of the mathematics; Financial engineering for the implementation; as well as generally. This price can be split into two components: intrinsic value, and time value (also called "extrinsic value"). The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder.

Lattice model (finance)

In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date.

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