HEDGING · Hedging under Friction and Uncertainty: Theory and Numerics
FP7 — People (Marie Curie Actions)
- Duration
- 2013-11-01 → 2017-10-31
- EU contribution
- €100,000
- Participants
- 1
- Scheme
- MC-CIG
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Results in brief
Hedging under Friction and Uncertainty: Theory and Numerics
My goal in this project is to deal with a class of hedging and pricing problems arising in modern Mathematical Finance. These problems are not only interesting from the point of view of applications, but also provide a good source for new mathematical questions which require new tools in the area of Probability Theory. I focused on three main topics: i. Hedging with Friction. ii. Robust Hedging. iii. Numerical Schemes. All the above topics are related to theory of Pricing and Hedging of Derivative Securities. In real Market conditions, it is very difficult to provide an accurate probabilistic model for the behaviour of stock prices. Furthermore, trading of assets is subject to transaction costs, i.e. there is a gap between the bid price and the ask price. These two facts raise the natural question of understanding hedging in markets with friction and model uncertainty. During this project I wrote 9 papers, 8 already accepted/published and one more paper is under review. The accepted/published papers appeared/will appear in top journals in mathematical finance such as Annals of Applied Probability, Finance and Stochastics , Mathematical Finance and Mathematics of Operation Research. In the written papers we (coauthors and me) developed a probabilistic theory for hedging problems in a non standard framework, which includes model uncertainty and non continuous transaction costs. The written papers settled important questions and opened new research horizons in mathematical finance, in the direction of hedging under price impact and model uncertainty. The impact of this project was an establishment (at the Hebrew University) of a research in the area of mathematical finance. Moreover, my collaboration relations with leading researchers will make an essential contribution to the scientific community in Israel, and will strengthen the position of the Hebrew University in the field of mathematical finance. Currently my research group contains, in addition to myself, two PhD students Benjamin Gotessman and Jonathan Zouari, So far I had three Master Students that already graduated: Maxim Bocharenko, Chen Michael and Niv Nayman. Moreover, I established several sources and seminars in mathematical finance. Based on the described above achievements I received tenure and was promoted to Associate Professor.
Data: CORDIS, © European Union
Project objective
In this project our goal is to deal with a class of hedging and pricing problems whicharise in modern Mathematical Finance.These problems are not only interesting fromthe applications point of viewbut also provide a good source for new mathematical questions which requirenew tools in the area of probability theory.We will focus on three main topics:(i) Hedging with Friction.(ii) Robust Hedging.(iii) Numerical Schemes.All the above topics are related to the theory ofpricing and hedging of derivative securities.In the last 35 years there was great progress in this direction.By now there is quite a good understanding of pricing and hedgingin frictionless financial markets with a known probabilistic structure.This understanding was achieved by developing the machinery of stochastic calculus,stochastic control, martingale theory,hypothesis testing, etc.In real market conditions,it is very difficult to providea correct probabilistic model for the behaviorof stock prices.Furthermore, trading of assets is subject to transaction costs,i.e. there is a gap between an ask price and the bid price.These two factsraise the natural questionof understanding hedging in markets with friction and model uncertainty.Usually, when dealing with complex models of financial markets, explicitformulas for option prices and the corresponding super--replication strategiesare not available. This is the motivation to study numerical schemesfor several stochastic control problems which are related to hedging under volatility uncertainty.In the current project we are interested not only in providing the algorithms of numerical schemes,but also in implementing them.In summary,the proposed questions are not only crucial for the understandingof pricing andhedging in financial markets, but also a great source of new mathematical problems.These problems require new tools and also attract the attention of world class mathematicians.
Original text from CORDIS.
Participants
- THE HEBREW UNIVERSITY OF JERUSALEM · JerusalemCoordinatorIsrael
Links
Data: CORDIS, © European Union