Degree Course: CONSULENZA E CONTROLLO AZIENDALE (LM-77) Syllabus for A.Y. 2011/2012  

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PLAIN VANILLA OPTIONS. Plain vanilla options, definitional aspects. The opening of long and short positions in options (long and short call, long and short put). The Building Block. Lego Approach. Intrinsic value and time value. The intrinsic value and moneyness of the option. The factors that determine the time value. The American-style option and early exercise. The put-call parity. The put-call parity for European-style options. The put-call parity for American-style options.

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MODELS OF OPTION VALUATION. Introduction. The dynamics of stock prices. The formula of Black and Scholes with and without the presence of dividends. Estimation of volatility. The historical volatility. Empirical rules on volatility. Implied volatility. The volatility smile. The relationship between the distribution of returns and the smile. The binomial model with n steps. The hypotheses at the base of the model. The Monte Carlo simulation. Definition of the number of run of the simulation. The generation of random numbers. The method of the inverse transformation.

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THE GREEKS AND THE DELTA HEDGING. The Greeks. The delta. The gamma. The vega. The rho. Theta. Use of the Greeks: a summary example. The Greeks of a portfolio of options. Option book hedging. Dynamic delta hedging. Delta-gamma hedging. Delta-vega hedging. Delta-gamma-vega hedging. Higher order greeks. The Vanna. The Volga. Vomma (or gamma-vega. volgamma). The delta bleed (charm). The calculation of sensitivities using Monte Carlo simulation: finite difference method.

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COMPLEX STRATEGIES. The Building Block Approach. The bull spread (call spread, bullish vertical spread). The collar. The straddle. The strangle. The butterfly.

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ASIAN OPTIONS. Asian options (or average options). The put-call parity for Asian options. The factors affecting the payoff (and price). The type of average. The sampling frequency. The period of calculation of the average. The weight attributed to the individual surveys. The evaluation of average price options with geometric average. Geometric mean and continuous monitoring of the mean (Kemna and Vorst). Geometric average and discrete monitoring of the average (Haug, Haug and Margrabe). The case of non-constant periodicity between successive fixings. The evaluation of options with arithmetic mean. Arithmetic mean and continuous monitoring of the mean (Turnbull Wakeman model). Arithmetic mean and continuous monitoring of the mean (Levy approximation).

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ASIAN OPTIONS. Vorst's model. Arithmetic mean and discrete mean monitoring (Levy modified by HHM). Curran's approximation. Asian options pricing and the volatility term structure. The binomial model and Asian options. The Monte Carlo simulation. The payoff and the sensitivities of the Asian option. The delta hedging of the Asian options. Delta hedging of average price options. Delta hedging of the average strike options. Static hedging of the Asian option. Use of Asian options.



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BINARY OPTIONS. Binary options: cash or nothing, asset or nothing, gap. Binary options: European and American style. Use of binary options. The analytical evaluation of European binary options. Asset or nothing pricing. Cash or nothing pricing. The gap option pricing.

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BINARY OPTIONS. The analytical evaluation of the American binary options (one touch deferred binary). Payoffs and sensitivities of digital options. Hedging techniques for European binary options. Payoffs and sensitivities of American digital options. The hedging of one touch options. One touch digital delta hedging. The static replication of digital one touch.

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BARRIER OPTIONS. Types of barrier options. Barrier parity. Use of barrier options. Valuation of European barrier options The closed formula of Rubinstein and Reiner. Evaluation of knock-in barriers. Valuation of knock-out barriers. The binomial model and barrier options. Evaluation of barrier options with Monte Carlo. Valuation of American barrier options The closed formula of Haug. The risks of barrier options. Payoffs and sensitivities of regular barrier options. Greeks of down and in call. Greeks of up and in put. Greeks of the down and out call. Greeks of the up and out put.

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BARRIER OPTIONS. Hedging regular barrier options: static replication techniques. The replication of the knock-down & in option. The replica of the knock-down & out option. Static replication and put-call symmetry. Static replication - Overcoming the basic assumptions. The payoffs and sensitivities of barrier-reverse options. The greeks of the up and in call (HK). Greeks of the up and out call (HK). The methodologies of risk mitigation of the reverse knock out. The choice of the volatility parameter. The coverage of the reverse knock in/out.

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FORWARD START AND CLIQUET OPTIONS. Forward start options. Forward start options: the valuation in closed formula. The pricing of forward start options: some key factors. The calculation of the forward implied volatility. The payoff and the sensitivity of the forward start option. Cliquet options. The valuation of the closed formula cliquet. The binomial model. The payoff and sensitivity of the cliquet options. Types of cliquet structures. The simple cliquet bond. Cliquet bond with barrier. The pure digital cliquet bond. The reverse cliquet bond. The protected reverse cliquet bond. Structured Napoleon. Reverse cliquet and Napoleon: critical aspects.




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LOOKBACK OPTIONS. Fixed and floating strike lookback options. The pricing of the lookback options. The valuation of floating strike lookback calls. The analytical formula of Goldman, Sosin & Gatto. The valuation of fixed strike lookback calls. Payoff and sensitivity of lookback options. Static replication of lookback options. The use of lookback options.

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OPTIONS ON TWO UNDERLYINGS AND MULTI-ASSET OPTIONS. Types of multi-asset options. Mountain Range Options. Multiasset options Pricing issues. Exchange-one-asset-for-another options. The variables that affect the value of the option. Analytical valuation. Spread options. Variables affecting the value of the option. Analytical valuation. Use of spread options. Best of and worst of options (or min-max options). Min-max options The analytical valuation. The role of correlation in the value of best of and worst of options. Correlation risk in best of options. Correlation risk in worst of options.

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THE VOLATILITY SURFACE FOR FX OPTIONS- Criteria for efficient and convenient representation of the volatility surface; approaches to constructing the surface, interpolation of the smile between strikes: the Vanna-Volga approach, calculation of Vanna-Volga weights and option pricing, construction of the volatility matrix in practice; extensions of the Vanna-Volga model.

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VOLATILITY TRADING Options and trading, Call overwriting; Hedging strategies with options, complex options; Volatility trading with options; Variance and volatility; volatility, variance and gamma swaps; options on variance; the relationship between IV and realized volatility; Forward Start products and vol indices; Light exotics. Relative value & correlation trading: trades on earnings announcements/jumps; Skew & Term Structure trades: the relationship between skew and term structure; the "Square root of time" rule; Term structure trading; Measurement of skew and smile; skew trading.

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STOCHASTIC VOLATILITY OPTION VALUATION MODELS.
The model of Heston The SABR model and the volatility surfaces
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Interest rates: valuation of interest rate derivatives. Curve estimation with pre-2008 and dual method. Interest rate hedging for corporate clients
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FX derivatives: valuation of FX derivatives. Curve estimation with Vanna Volga . FX hedging for corporate clients

Teaching materials available on the course site
Academic and Professional Articles
Exotic Options and Hybrids: A Guide to Structuring, Pricing and Trading (The Wiley Finance Series Book 507) (English Edition) 1st Edition, English Edition by Mohamed Bouzoubaa , Adel Osseiran