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Stochastic Models Forpricing And Hedging Derivatives İn Incomplete Makets: Structure, Calibration, Dynamical Programming, Risk Optimization
Date
2009-09-30
Author
Tezcan, Cihangir
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THE PURPOSE AND THE RATIONALE (AMAÇ VE GEREKÇE) The common standard pricing methods of financial assets and derivative instruments determine the price as the fair value. The latter is defined as a unique arbitrage free price in a complete market. It is determined as expected value of the corresponding discounted payoff w.r.t. to a unique equivalent martingale measure (EMM). This method essentially relies on the assumption that that the market is complete, such that the buyer price and seller price match exactly each other at the unique arbitrage free price. In practice, when the bid-ask spread is small, the market may be approximately complete, and the fair value pricing and hedging methods may be applied. In an incomplete market the standard fair value pricing method can not be applied. For incomplete markets the bid-ask spread, i.e. the difference between buyer and seller prices, is no longer negligible. In such a situation the market state is no longer characterized by the elementary risk factors related to basic assets, such as stock prices, bond prices and currency prices. The market state will depend on further variables. The calibration of these variables will be essential in order to select the pricing EMM among infinitely many possible arbitrage-free EMMs. This project is aimed to develop the pricing and hedging methods for essentially incomplete markets. Commodity markets are usually incomplete. But also more traditional markets such as the interest and credit markets have turned out to be incomplete during the recent financial crisis. The development of consistent methods and algorithms for pricing and hedging of the assets and financial instruments of these incomplete markets is therefore a high priority task. The technical framework for incomplete market pricing and hedging distinguishes essentially 3 different settings: - sub/super hedging and pricing - utility based hedging and pricing - risk measure based hedging and pricing THE KNOWLEDGE AND/OR THE TECHNOLOGY THAT WILL BE PRODUCED AT THE END OF THE PROJECT A coherent theoretical framework for pricing and hedging of derivatives in incomplete markets will be developed during the project. A conceptual clarification of the requirements on pricing, hedging, and model calibration will result from this project. Furthermore the relation to risk measures and risk premiums will be clarified. The project sets the foundation for practically applicable algorithms for pricing of derivatives in commodity markets, and for an incomplete credit- related interest market.
URI
https://hdl.handle.net/11511/61660
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Graduate School of Applied Mathematics, Project and Design
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C. Tezcan, “Stochastic Models Forpricing And Hedging Derivatives İn Incomplete Makets: Structure, Calibration, Dynamical Programming, Risk Optimization,” 2009. Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/61660.