The main derivatives traded on the market, their precise definitions and the modeling of the underlying assets in discrete time. Simulation of price processes. Random walks and their importance in simulating market assets. Introduction to Monte Carlo methods. Review of probability and stochastic processes in discrete time. Arbitrage and hedging strategies. Practical examples. Deltahedging.

The one-period model. Calculating European options and contingent contracts. Complete and incomplete markets. The pricing of derivatives and its relationship with the expected value in the risk-neutral measure. The multi-period model. The binomial case and the Gaussian limit. A brief introduction to the consequences of the Central Limit Theorem. The example of the Black-Scholes formula. The concept of implied volatility and the calculation of Greeks. Delta-Gamma hedging.

The binomial model in practice: Calibration and Pricing. The Feynman-Kac formula in discrete time and its applications. Process simulations and Monte Carlo methods. Options with optimal exercise time. Stop times and calculation of American options. The Longstaff-Schwarz algorithm. Applications to the domestic derivatives market.


References:
SHREVE, S. – Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer Finance, 2005.
DUFFIE, D. – Dynamic Asset Pricing Theory, Princeton University Press, Princeton, 1992.
KORN & KORN. – Option Prices and Portfolio Optimization. AMS, 2000.
SHIRYAYEV, A. N. – Essentials of Stochastic Finance: facts, models, theory. World Scientific, New Jersey, 1999.
HULL, J. – Options, Futures, and Other Derivatives. Prentice Hall (9th Edition) 2014