Stochastic Interest Rates

22 Outubro 2019, 11:00 • João Guerra

Stochastic interest rates: the non independent yields case - a example. 

Stochastic interest rates with independent log-normal annual rates of return. 

Examples and exercises. 

---

Stochastic Interest rate models

17 Outubro 2019, 11:30 • João Guerra

Introduction to deterministic and stochastic interest rates

Probability distribution and moments of the accumulated amount of a series of annual investments.

Particular case of independent annual rates of return (discrete or continuous random variables).

---

Exercises and the lognormal model

15 Outubro 2019, 11:00 • João Guerra

Exercises on Brownian motion, Itô formula and stochastic differential equations. 

The lognormal model: properties, emopirical tests and weaknesses of the model. 

---

Stochastic Differential Equations.

8 Outubro 2019, 11:00 • João Guerra

Stochastic Differential Equations. 

The geometric Brownian motion SDE and how to solve it. 

The Langevin equation and its solution: the Ornstein-Uhlenbeck process. 

The mean-reverting Ornstein-Uhlenbeck process. 

 

---

Itô formula or Itô lemma

3 Outubro 2019, 11:30 • João Guerra

Itô formula and Taylor formula of second order and chain rule. 

Itô formula or one dimensional Itô processes. 

Motivation and Examples. 

Itô formula for multidimensional Itô processes. Examples. 

 

 

---