•GUIDA ECONOMIA 07-08 - Università degli studi di Udine

prospectus udine
203
Exam
During the course seminar attendance
and written tests will be assessed.
The final exam is an oral exam.
Further information
The lecturer is available to answer student
queries at the end of each lesson and
once a week at the Department of Legal
Sciences (Udine, via Treppo 18); for
times, consult http://www.sindy.
uniud.it/asp/CercaOrariDocente.asp or send
him an e-mail (guglielmo.
cevolin@dsg.uniud.it).
FINANCIAL MATHEMATICS
ADVANCED COURSE
Prof. Flavio Pressacco
Contents
- Review 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
Single period asset return on binomial
markets.
Portfolios of assets on binomial markets.
Dominance between assets and portfolios
on binomial markets.
Arbitrage free markets.
Risk neutral probability.
Characteristic line of a single period market.
The choice of the numeraire.
Martingale probabilities.
- 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
assets 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 the theory of
options.
Put-Call parity for European options.
Support and intrinsic value for Put and
Call options.
Components of the value of European
options.
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 a binomial market of the I
type.
Arbitrage-free pricing of American
options on a binomial market of the I
type.
Backward induction.
Early exercise opportunity.
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.