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Il giorno 14 aprile alle ore 14.30 in aula Caldirola si terrà il seminario
Option pricing, hedges and deep learning
Simona Sheit and Matthias Blank (d-fine GmbH, Frankfürt)
Pricing and hedging of options (and other derivatives) are at the core of mathematical finance. These are financial contracts that can be bought and sold and give its owner the right to buy or sell a certain asset at a future point in time. Under ideal market assumptions, options and their underlying assets can be modelled using (continuous) stochastic processes whose dynamic can be described by stochastic differential equations. A classical solution to pricing and hedging options in such a setting is the Black-Scholes model, for which its authors received a Nobel Prize in 1997.
In incomplete markets we can, by their very definition, no longer hedge every claim, and techniques that are based on the possibility of perfect hedging, like the Black-Scholes ansatz, can no longer be used for pricing derivatives.
On the other hand, over the last decade or so, deep learning algorithms have been successfully able to tackle many problems in machine learning that were previously thought to be extremely difficult, and neural networks are at the forefront of the current boom in machine learning applications. Areas where neural networks have accomplished stunning results range from image and speech recognition to the outright spectacular generation of art.
Using these techniques in quantitative finance is intriguing, and one recent seminal paper here has been the Deep Hedging framework of Bu ̈hler et al. (Deep Hedging, 2019), applying deep neural networks to the problem of optimal hedging in incomplete markets.
In this presentation, we will give an overview of the basic concepts in mathematical finance and show how financial assets can be modelled and simulated in a rigorously math- ematical framework. We then briefly introduce neural networks and discuss how they can be trained on simulated data of this type to find (model-dependent) trading strategies. In the last years, these techniques have been the focus both of active scientific research and heightened industry interest.
Keywords: Option pricing, SDEs, Black-Scholes, deep learning, (recurrent) neural networks
