1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
To explain mathematics of the fundamental Black-Scholes model and pricing within that model.

COURSE DESCRIPTION AND SYLLABUS:
1. Brownian motion and Ito calculus. Brownian motion. Continuous time martingales. Ito integral. Ito formula. Stochastic differential equations.
2. Black-Scholes model. Model description. Change of measure, martngale representation. Pricing and hedging of European securities. American options in Black - Scholes model. Partial differential equations in Black - Scholes model. Bonds, forrwards and futures.

1. W. A. Baxter, A.Rennie: Financial Calculus
2. D. Lamberton, B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance
3. T. Bjork: Arbitrage Theory in Continuous Time
4. J. Cvitanić, F. Zapatero: Introduction to the Economics and Mathematics of Financial Markets
5. J. C. Hull: Options, Futures, and Other Derivative Securities, 5th edition
6. I. Karatzas, S. Shreve: Brownian Motion and Stochastic Calculus, 2nd edition
7. B. Oksendal: Stochastic Differential Equations, 6th edition
8. N. H. Bingham, R. Kiesel: Risk - Neutral Valuation: Pricing and Hedging of Financial Derivatives
9. M. Musiela, M. Rutkowski: Martingale Methods in Financial Modelling
10. T. Mikosch: Elementary Stochastic Calculus -- With Finance in View

Enrollment :
Passed : Financial modelling 1

Mandatory course - Regular study - Financial and Business Mathematics