Teacher
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CATTANI Carlo
(syllabus)
Elements of probability calculus: discrete and continuous random variables (v.a.). Distribution function and probability density of a v.a. Expected value (average) and variance of a v.a. discreet and continuous. Discrete and continuous probability distributions. Bernouilli distribution, binomial, Poisson distribution, uniform, exponential, Gaussian, standard normal. Moment generating function.
Derivative securities. Arbitrage, risk and risk protection. Regulated markets and OTC. Perfect market. Cox Binomial Model Ross Rubinstein (CRR). Forward contracts, futures, floaters, swaps. Put and call options. Derivatives payoff. Profitability of an option. Put-call parity.
Option pricing: discrete model. Cox Monoperiodal Binomial Model Ross Rubinstein: detailed derivation. Absence of arbitrage. Arbitrage theorem. Delta-hedging. Risk neutral assessment. Binomial model with n periods: detailed derivation. Backward method. Generalized formula. Difference between the pricing of European and American options Stochastic process. Markov process. Wiener process. Generalized Wiener process. Ito process. Brownian Motion. Ito lemma: detailed derivation. Stochastic differential equations. Log-normal property. Option pricing: continuous model. Model Black Scholes (BS): detailed derivation. Heat equation. BS solution. Cumulative distribution N (x). Formula for the approximate calculation of N (x). Greek letters, delta, gamma, vega, theta, rho. Relationship between the Greek letters. Hedging strategies.
Volatility. Implied volatility. Volatility smile. Stochastic volatility models: Hull-White, Scott and Stein-Stein (Ornstein-Uhlenbeck process), Ball-Rome. Cox-Ingersoll-Ross process. Heston model. Girsanov's theorem. Covariance matrix. Cholesky decomposition. Derivation of Heston equations. Solution of the Heston equations. Introduction to numerical calculation methods. Simulations in Matlab / GNU Octave. Implementations for calculating CRR, BS and Heston model solutions
(reference books)
Opzioni, Futures e altri Derivati, J. Hull, Ed. Pearson, Prentice-Hall.
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