Theory and practice of option pricing

obligatory courses

Master's level course.

The main goal of the course is to deepen the knowledge of Black-Scholes-Merton option pricing theory in its formal, intuitive and purely practical dimension. During the course, students learn the exact assumptions of the model and its theoretical and practical limitations (transaction costs, the price discontinuity of the process, discrete adjustment of hedging positions), and reflect on pricing biases occurring when individual assumptions are not satisfied. Students will also learn how the market value options and what is required of a good valuation model. In this light, we will discuss possible improvements to the BSM theory, which should facilitate greater understanding of actual option prices quoted by the market. Theoretical considerations will be illustrated using practical examples and C ++ /VBA codes.

The detailed content of the course is presented below.

• Review of option pricing

• Theory and practice of dynamic replication: implied and realized volatility

• P&L of a delta-hedged portfolio

• Practical limitations of replication: transaction costs and discrete time steps

• Volatility smile – causes and consequences

• Volatility smile and pricing vanilla and exotic options

• Calibration and model risk

• Pricing models accounting for volatility smile

Derman, E.; I. Kani (1994): “Riding on a smile”, Risk, 7, 32-39.

Derman, E.; N.N. Taleb (2005): The illusions of dynamic replication, Quantitative Finance, Vol. 5, No. 4, August 2005, 323–326.

Dupire, B. (1993): “Pricing and hedging with smiles”, Discussion paper, Paribas Capital

Gatheral, J. (2006): The Volatility Surface - A Practitioner's Guide. John Wiley & Sons Ltd.

Haug, E.G. oraz N.N. Taleb (2011): Option Traders Use (very) Sophisticated Heuristics, Never the Black–Scholes–Merton Formula, Journal of Economic Behavior and Organization, Vol. 77, No. 2, 2011.

Hull, J. C. (2008): Options, Futures & Other Derivatives. Prentice Hall, 7 edn.

Neftci, S. N. (2008): Principles of Financial Engineering. Elsevier.

Sinclair, E. (2008): Volatility Trading. Wiley Trading.

Taleb, N.N. (1997): Dynamic Hedging: Managing Vanilla and Exotic Options, Wiley

Wilmott, P. (2006): Paul Wilmott On Quantitative Finance. John Wiley & Sons Ltd.

Upon completion of the course the student:

- knows how to price call and put options within the Black-Scholes framework, and understands the main assumptions underlying the theory

- knows basic conventions used in option markets, as well as knows and understands the concept of implied volatility

- correctly identifies the main risk factors underlying investment in options

- knows how to analyze theoretically and model quantitatively the results of the main option trading strategies, including dynamic hedging/replication

- is familiar with the main numerical techniques used for pricing and analyzing options (Monte Carlo simulation, finite different schemes)

KW01, KW02, KU01, KU02

Zasady zaliczenia: egzamin pisemny na zakończenie kursu (75%), zadanie domowe (25%)