1. SDE & Statistics MiniCourse Topics List for the Exam
Università di Verona, 2015 may 25 Michele Bonollo
Esempio di Apertura 1

2. Topics (until may 25th) Stochastic processes Black&Scholes Model
The Ito Formula
Meaning of the second order term
Basic Properties of the Brownian motion
Black&Scholes Model
The context
Parameters practical meaning
The SDE and the log normal solution
ITO proof of the solution
Options pricing
Call & Put options
PayOff concept
Fair value & mark to market concept. B&S formula. Call-Put Parity
Greeks. Delta, Gamma, Vega for the call option
Montecarlo Pricing and the variance estimation (inf & SUP)

3. Topics (until may 25th) Option Risk measurement
The Leverage of an Option and Portfolio of Options
The general VaR (quantile) definition
The Delta VaR vs the “full evaluation” VaR for one options
Portfolio volatility and DeltaVaR of an options portfolio
Practical Applications (select 1 of them or a mixed recipe)
The Brownian motion and lognormal simulation. Exercise: To generate for a lognormal diffusion St at different time steps ti N paths and to estimate at any time step the average, the standard deviation and the quantile (alfa level) of St. Improvement: to make it for two diffusions S1 & S2 with a given correlation r
Montecarlo estimation of the fair value & Montecarlo volatility. Upper and lower bound for the price (portfolio of options). Exercise: improve what we did in the course. Improvement: Calculate the MtM of a portfolio of 2 options with the same underlying diffusion St.
What If analysis. Greeks accuracy vs. Full evaluation approach. Exercise: as in the course . Improve it with a grid of M different scenarios at the same time and try to plot in a graph the dependence of the MtM from the Underlying price. Scenarios could be ± 1% ±2%, … ± 10% in the underlying level St
Delta impact in practical cases. Exercise: as in the course calculate the Profits & Loss effect with the delta approximation and the VaR of the option. Estimate the volatility s by an actual stock price time series, choice an index (MIB, DAX, S&P500) or a share (UNICREDIT, TELECOM, FINMECCANICA, ..) as you prefer