Properties of option prices

22 Outubro 2020, 11:30 • João Guerra

Option prices properties. The intrinsic value and time value of an option price. 

How the following factors affect prices: Underlying asset price, strike, time until maturity, volatility of the underlying asset, interest rate and dividends. 

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R examples and Introduction to financial derivatives and options

20 Outubro 2020, 11:30 • João Guerra

Examples of R code scripts on Brownian motion and geometric Brownian motion simulations. 

Introduction to financial derivatives and options. No-arbitrage and law of one price. 

American and European options: basic definitions.

Long and short positions in options. 

Put and call European options: examples. 

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Exercises

15 Outubro 2020, 11:30 • João Guerra

Discussion of exercises on Brownian motion, martingales, Ito formula and stochastic differential equations. 

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Stochastic differential equations

13 Outubro 2020, 11:30 • João Guerra

Deterministic ordinary differential equations and stochastic differential equations - motivation. 

"Explosion" of solutions example and non uniqueness of solutions example. Linear growth condition and Lipschitz condition. 

Examples: solutions for the geometric Brownian motion SDE, the Langevin SDE and the Ornstein-Uhlenbeck with mean reversion SDE. 

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Itô formula or Itô Lemma

1 Outubro 2020, 11:30 • João Guerra

Motivation for Itô formula: the square of an infinitesimal increment of Brownian motion, the 2nd. order Taylor formula and the chain rule.

Itô process. Definition and example. 

One-dimensional Itô formula in integral form and in differential form. Examples. 

Multidimensional standard Brownian motion, multidimensional Itô process and multidimensional Itô formula. Example. 

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