Modern Option Pricing
Led by Julien Guyon, Senior Quant, Bloomberg L.P.
Friday 6 November 2020
Your 2020 workshop leader
Julien is a senior quantitative analyst in the Quantitative Research group at Bloomberg L.P., New York. He is also an adjunct professor in the Department of Mathematics at Columbia University and at the Courant Institute of Mathematical Sciences, NYU.
Before joining Bloomberg, Julien worked in the Global Markets Quantitative Research team at Societe Generale in Paris for six years (2006-2012), and was an adjunct professor at Universite Paris 7 and Ecole des ponts.
He co-authored the book Nonlinear Option Pricing (Chapman & Hall, CRC Financial Mathematics Series, 2014) with Pierre Henry-Labordere. His main research interests include nonlinear option pricing, volatility and correlation modelling, and numerical probabilistic methods. Julien holds a Ph.D. in Probability Theory and Statistics from Ecole des ponts.
Your 2020 workshop highlights
In this workshop we will address various aspects and techniques of modern option pricing. We will introduce mathematical tools, old and new, and explain how they can be used to solve modern quantitative finance problems.
The tools include McKean stochastic differential equations, backward stochastic differential equations (BSDEs), branching diffusions, machine learning techniques, linear programming, and optimal transport. They will be applied to a variety of challenging issues that are crucial for risk-management and model risk assessment: the exact calibration of models to market smiles; the valuation of derivatives under parameter uncertainty; the computation of the credit valuation adjustment (CVA) and initial margin (IM) of a large book of derivatives; the valuation of VIX derivatives,;and the derivation of model-independent bounds for option prices, given the prices of vanilla options. Implementation details will be provided, together with illustrative examples.
The particle method for smile calibration
- Introductory example: Stochastic local volatility
- McKean stochastic differential equations
- The particle method
- Adding stochastic rates and stochastic repo/dividend yield
- Path-dependent volatility
- Local correlation
- Cross-dependent volatility
Stochastic control techniques and applications
- Backward Stochastic Differential Equations
- Uncertain volatility model, uncertain default rate model
- Different rates for borrowing and lending
- Portfolio optimization
- Marked branching diffusions
Machine Learning Techniques For Option Pricing
- ML techniques for the estimation of conditional expectations
- Nonparametric regression: nearest neighbours, kernel regression
- Parametric regression: neural networks, kernel trick, random forests
- Application to American option pricing; smile calibration; VIX derivatives pricing
- Solving stochastic control problems with neural networks
- Application to CVA and IM computations
Model-free bounds for option prices
- Primal problem: Linear programming formulation
- Dual problem: Optimal transport
- Martingale optimal transport
- Example: Bounds for VIX futures and VIX options given S&P 500 smiles