SDE & Statistics MiniCourse Topics List for the Exam

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Presentation transcript:

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

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)

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