Lecturer

prof. Flavio Pressacco flavio.pressacco@uniud.it

Credits

9 CFU

Department

Department of Economics and Statistics

Summary

• Recall of probability theory
• Recall of stochastic processes
• Introduction to stochastic differential equations
• Single period binomial financial markets
• Arbitrage free pricing on single period binomial financial markets
• Price risk and interest rate risk on financial markets
• Theory of plain vanilla options
• Arbitrage free options pricing
• Introduction to interest rate options

Detailed programme

- Recall of stochastic processes

Binomial processes
Sum of binomial random variables (additive binomial process)
Multiplicative binomial process
Continuous time processes
Wiener process
Diffusion process
Log-normal process

- Introduction to stochastic differential equations

Stochastic differential equations
Total stochastic differential
Ito’s Lemma

- Single period binomial financial markets

The single period asset return on binomial markets
Portfolios of assets on binomial market
Dominance between assets and portfolios on binomial markets
Arbitrage free markets
Risk neutral probability
Characteristic line of a single period market

- Arbitrage free pricing on single period binomial financial markets

Price as the present value of the risk neutral expectation

- Price risk and interest rate risk on financial markets

Multiperiod markets (big markets) and arbitrage free pricing
Big markets of the I, II, III type
Arbitrage free pricing of risky assets in big markets of the I and II type
Arbitrage free pricing of interest rate sensitive asset in big markets of the III type

- Theory of plain vanilla options

Put, Call, European and American options
The payoff at maturity of an option
Fundamental equation of option theory
Put-Call parity for European options
Support and intrinsic value for Put and Call options
Components of European options value
The time value
Interest premium or interest toll
American options
Early exercise on American options

- Arbitrage free options pricing

Arbitrage free pricing of European options on binomial market of the I type
Arbitrage free pricing of American options on binomial market of the I type
The backward induction
Early exercise opportunity
Hedging portfolio
Black-Scholes formula

- Introduction to interest rate options

Cap, Floor, Swap, Collar

Binomial trees for interest rate in multiperiod markets of the III type
Introduction to the pricing of an interest rate sensitive asset
Options on interest rates in multiperiod markets of the III type

Bibliography

• F. Pressacco, P. Stucchi, Lezioni di Matematica Finanziaria, FORUM, chapter 4
• J. Hull, Options, futures and other derivatives, Prentice Hall, 2000

Notes by the professor available on line