New York Day 3 - Wednesday October 5

Advanced analytical tools for pricing and hedging in a volatile world

with Marcello Minenna and Paolo Verzella

08.30 Registration and coffee

09.00 Stylised facts on the real world as guidelines to build robust models beyond Black Scholes

• The "anormality" of the returns normality assumption
• Real probability distributions for asset prices: asymmetry, Kurtosis and fat tails
• An extended framework for pricing and hedging in the real world
• Multifactorial diffusive models, jump diffusion and pure jump
• Models: an overview

10.30 Morning break

11.00 Advanced mathematical tools for the real world

• Multifactorial stochastic calculus
• Lévy processes
• The Fourier and Laplace transforms
• The mathematics of the complex plane

12.30 Lunch

13.30 Extending the Black-Scholes framework: multifactorial models

• Stochastic interest rates models: a Martingale derivation
• Stochastic volatility models: PDE derivation via Fourier transform
• Solving the pricing problem via numerical algorithms in Excel and MATLAB
• Calibrating multifactorial models: procedures and solutions in Excel and MATLAB, with extensive evaluation tests
• Moving from Vanilla Derivatives to Exotics in a multifactorial setting: Monte Carlo solutions

14.30 Afternoon break

15.00 Extending the Black-Scholes Framework: Jump Models

• Jump diffusion models: replicating and quasi-replicating portfolios
• Pure jump models: the stochastic time hypothesis and mixtures of probabilities densities
• Solving the pricing problem via numerical algorithms in Excel and MATLAB
• Calibrating jump models: procedures and solutions in Excel and MATLAB with extensive evaluation tests
• Moving from Vanilla Derivatives to Exotics in jump setting: Monte Carlo solutions

17:00 Q&A - opportunity for further technical questions