Sumários
Black-Scholes model
27 Novembro 2017, 11:30 • João Guerra
The Black-Scholes model: advantages of the martingale approach.
How to deduce the Balck-Scholes PDE from the martingale approach.
The Black-Scholes formulas with dividends.
The Black-Scholes model
23 Novembro 2017, 11:30 • João Guerra
The Black-Scholes model: the martingale approach.
The risk-neutral valuation formula and the sketch of its proof using the 5 step method.
The pricing of a call option using the risk-neutral valuation formula: the derivation of the Black-Scholes formula.
The Dynamics of S_{t} under the risk-neutral measure or equivalent martingale measure Q.
The replicating or hedging portfolio. The Delta of an option or financial derivative. How to calculate the Delta and the importance of the Delta in the risk management of a portfolio.
Black-Scholes model
20 Novembro 2017, 11:30 • João Guerra
The Black-Scholes model: assumptions and basic ideas.
The Black-Scholes partial differential equation (PDE) and boundary conditions. The PDE approach.
The Black-Scholes formulas for call ooptions and put options.
Binomial method for american options, Girsanov Theorem and the Martingale representation Theorem
16 Novembro 2017, 11:30 • João Guerra
The Binomial method for pricing american options: an example.
Continuous time models for option pricing: some preliminary results.
The Cameron-Martin-Girsanov (or Girsanov) Theorem and the Martingale Representation Theore,
How to apply the Girsanov Theorem to a Brownian motion with drift, in order to obtain a risk-neutral measure Q, such that the discounted price of a risky asset is a martingale.
The Binomial model
13 Novembro 2017, 11:30 • João Guerra
The state-price deflator approach or the Stochastic discount factor approach to the option pricing problem in the Binomial model.
The recombining Binomial model: how to estimate the parameters u, d from the volatility.
How to price american options with the Binomial model: example.