The martingale approach: delta hedging. The greeks.

26 Novembro 2018, 11:30 • João Guerra

Advantages of the martingale approach. 

Some exotic options examples: Asian options and Barrier options.

Brief summary of the state-price deflator approach. 

Portfolio risk management: Delta hedging. Delta zero porfolios. 

The greeks: Delta, Gamma, Vega, Rho, Lambda, Theta. 

The Black-Scholes PDE with greeks. 

 

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Black-Scholes model: the martingale or risk neutral approach

22 Novembro 2018, 11:30 • João Guerra

Black-Scholes model: replicating portfolio with shares and cash and the Black-Scholes PDE. 

The Feynman-Kac representation formula and the Girsanov theorem applied to Black-Scholes PDE. 

The Risk-neutral valuation formula under the equivalent martingale measure Q. 

Examples and exercises of application of the Risk-neutral valuation formula.

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Black-Scholes PDE and Black-Scholes formula

19 Novembro 2018, 11:30 • João Guerra

Black-Scholes PDE and Black-Scholes formula.

The replicating porfolio in the Black-Scholes model. 

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Preliminary concepts for continuous time financial models

15 Novembro 2018, 11:30 • João Guerra

Complete markets: concept

Girsanov Theorem applied to Geometric Brownian motion

Martingale representation theorem. 

Black-Scholes model assumptions. 

Black-Scholes formulas: briwf discussion. 

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Recombining binomial model

12 Novembro 2018, 11:30 • João Guerra

Recombining binomial model: pricing formulas and examples. 

Pricing american options with the binomial model: example. 

Calibrating the binomial model using the volatility and equalizing the mean and variance of the binomial model and the lognormal model. 

 

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