Foreign students graduate courses

elena.degiuli@unipv.it

The course aims to explain the major methodologies and techniques used for the quantitative pricing of derivative contracts.

Basic concepts of stochastic calculus: Wiener process, Itô integral, martingale, Ito's lemma for scalar and vector processes, geometric Brownian motion, Feynman-Kac theorem, equations of Kolmogorov (backward and forward). European options and their wallets, pathdependent simple and exotic derivatives, American options, forward contracts and futures, derivatives as underlying, currencies and commodities. Evaluation of derivatives in complete markets: The discrete-time model of Cox, Ross, Rubinstein and continuous-time models . The model of Black and Scholes (neutral to risk assessment, the principle of linearity of evaluations, historical volatility and implied volatility). The Black-Scholes and Black. Hedging and risk management: report of a tie, delta and gamma hedging. Extensions of the Black-Scholes model and its limitations. Incomplete market models: evaluation and risk-neutral pricing equations. Evaluation of bond (fixed coupon bonds, floating rate bonds), and Interest Rate Swaps. Short rate models. Martingale for the short rate models (models of Vasicek, Ho-Lee, CIR, Hull-White). Introduction to models for the yield curves: the model of Heath-Jarrow-Morton. Work with a dynamic portfolio optimization in continuous time: formalization of the problem of consumption-investment good, the theorem of the two funds (with risky assets and risk-free asset). The course also provides a series of seminars on specific topics (on stochastic volatility models to financial data, commodity derivatives, risk measures for portfolio optimization) and 12 hours of classroom exercises for the presentation of computer numerical methods commonly used in the evaluation of derivatives.

T. Bjork, Arbitrage Theory in Continuos Time (second edition), Oxford University Press, 2004.

M.E. De Giuli, M.A. Maggi, U. Magnani, E. Rossi, Derivati: teoria e applicazioni, Giappichelli, Torino, 2002.

Paul Wilmott, Sam Howison, Jeff De Wynne, The Mathematics of Financial Derivatives, A Student’s Introduction, Cambridge University Press, 1995.

W. Paul and J. Baschnagel - Stochastic Processes from Physics to Finance, Springer, 2000
ASSESSMENT

Written test with exercises and theoretical questions supplemented by an oral test..

Pietro Previtali

Claudia Dossena

E-MAIL

gabriele.cioccarelli@unipv.it