Stochastic Models Forpricing And Hedging Derivatives İn Incomplete Makets: Structure, Calibration, Dynamical Programming, Risk Optimization

Date

2009-09-30

Author

Tezcan, Cihangir

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

128
views

0
downloads

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

Collections

Graduate School of Applied Mathematics, Project and Design

Suggestions

OpenMETU
Core

Calibration of stochastic models for interest rate derivatives Rainer, Martin (Informa UK Limited, 2009-01-01) For the pricing of interest rate derivatives various stochastic interest rate models are used. The shape of such a model can take very different forms, such as direct modelling of the probability distribution (e.g. a generalized beta function of second kind), a short-rate model (e.g. a Hull-White model) or a forward rate model (e.g. a LIBOR market model). This article describes the general structure of optimization in the context of interest rate derivatives. Optimization in finance finds its particular app...
On forward interest rate models : via random fields and Markov jump processes Altay, Sühan; Körezlioğlu, Hayri; Department of Financial Mathematics (2007) The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, instantaneous forward interest rates are modeled using random fields and Markov Jump processes and the drift conditions of the forward rate dynamics are given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country...
Stochastic optimization applied to self-financing portfolio: does bequest matter? Gazioglu, Saziye; Bastiyali-Hayfavi, Azize (Informa UK Limited, 2010-01-01) The article studies stochastic optimization of an intertemporal consumption model to allocate financial assets between risky and risk-free assets. We use a stochastic optimization technique, in which utility is maximized subject to a self-financing portfolio constraint. The papers in literature have estimated the errors of Euler equations using data from financial markets. It has been shown that it is sufficient to test the first order Euler equation implied by the model. However, they all assume a constant...
Uncertainty assessment for the evaluation of net present value of a mineral deposit Erdem, Ömer; Güyagüler, Tevfik; Department of Mining Engineering (2008) The profitability of a mineral deposit can be concluded by the comparison of net present values (NPV) of all revenues and expenditures. In the estimation of NPV of a mineral deposit, many parameters are used. The parameters are uncertain. More accurate and reliable NPV estimation can be done with considering the related uncertainties. This study investigates the probability distributions of uncertain variables in estimation of NPV and evaluation of NPV using Monte Carlo simulation. @Risk 4.5.7 software pack...
Stochastic volatility, a new approach for vasicek model with stochastic volatility Zeytun, Serkan; Hayfavi, Azize; Department of Financial Mathematics (2005) In the original Vasicek model interest rates are calculated assuming that volatility remains constant over the period of analysis. In this study, we constructed a stochastic volatility model for interest rates. In our model we assumed not only that interest rate process but also the volatility process for interest rates follows the mean-reverting Vasicek model. We derived the density function for the stochastic element of the interest rate process and reduced this density function to a series form. The para...

Citation Formats

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.