Sumários
18 Novembro 2024, 12:00
•
João Guerra
Interest rate models: Vasicek, CIR, Hull-White (Vasicek), Hull-Whte (CIR)
Limitations of one-factor models.
An example of a two-factor model: the 2-factor Vasicek model.
4 Novembro 2024, 12:00
•
João Guerra
Definitions and relationships between: Bond prices, Spot rate, Forward rate, instantneous forward rate, short (instantaneous) interest rate and cash account.
Desirable properties of a term structure model.
The market price of risk definition. All bonds have the same market price of risk (does not depend on maturity).
Bond prices as discounted expected payoff under the measure Q.
The dynamics of B(t,T) and of r(t) under Q.
The Vasicek model.
29 Outubro 2024, 11:30
•
João Guerra
Discussion of implied volatility and implied volatility smiles using the R Package fOptions.
Discussion of exercises about the Black-Scholes model.
28 Outubro 2024, 12:00
•
João Guerra
Use of R and the R Package fOptions to:
1) Calculate call option and put option prices under the B-S model
2) Calculate financial derivatives and option prices by Monte-Carlo simulation
3) Calculate the greeks useing fOptions and estimate the greeks numerically by finite differences using the Monte-Carlo simulation.
4) Implied volatility and Implied volatility smiles
22 Outubro 2024, 11:30
•
João Guerra
Risk neutral valuation in the Black-Scholes model. Example: the binary option.
Black-Scholes formulas with dividends.
Replicating portfolios and delta hedging.
The delta of a portfolio. Zero delta Portfolio.
The greeks: Delta, Gamma, Vega, Rho, Lambda and Theta.
The greeks and portfolio management.