Dynamic complex hedging and portfolio optimization in additive markets

Download

index.pdf

Date

2009

Author

Polat, Onur

Metadata

Show full item record

Item Usage Stats

241
views

81
downloads

In this study, the geometric Additive market models are considered. In general, these market models are incomplete, that means: the perfect replication of derivatives, in the usual sense, is not possible. In this study, it is shown that the market can be completed by new artificial assets which are called “power-jump assets” based on the power-jump processes of the underlying Additive process. Then, the hedging portfolio for claims whose payoff function depends on the prices of the stock and the power-jump assets at maturity is derived. In addition to the previous completion strategy, it is also shown that, using a static hedging formula, the market can also be completed by considering portfolios with a continuum of call options with different strikes and the same maturity. What is more, the portfolio optimization problem is considered in the enlarged market. The optimization problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. For particular choices of the equivalent martingale measure, it is shown that the optimal portfolio consists only of bonds and stocks.

Subject Keywords

Finance.

URI

http://etd.lib.metu.edu.tr/upload/2/12610441/index.pdf
https://hdl.handle.net/11511/18430

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Completion of a levy market model and portfolio optimization Türkvatan, Aysun; Hayfavi, Azize; Department of Financial Mathematics (2008) In this study, general geometric Levy market models are considered. Since these models are, in general, incomplete, that is, all contingent claims cannot be replicated by a self-financing portfolio consisting of investments in a risk-free bond and in the stock, it is suggested that the market should be enlarged by artificial assets based on the power-jump processes of the underlying Levy process. Then it is shown that the enlarged market is complete and the explicit hedging portfolios for claims whose payof...
Jump detection with power and bipower variation processes Dursun, Havva Özlem; Hayfavi, Azize; Department of Financial Mathematics (2007) In this study, we show that realized bipower variation which is an extension of realized power variation is an alternative method that estimates integrated variance like realized variance. It is seen that realized bipower variation is robust to rare jumps. Robustness means that if we add rare jumps to a stochastic volatility process, realized bipower variation process continues to estimate integrated variance although realized variance estimates integrated variance plus the quadratic variation of the jump c...
Credit risk modeling and credit default swap pricing under variance gamma process Anar, Hatice; Uğur, Ömür; Department of Financial Mathematics (2008) In this thesis, the structural model in credit risk and the credit derivatives is studied under both Black-Scholes setting and Variance Gamma (VG) setting. Using a Variance Gamma process, the distribution of the firm value process becomes asymmetric and leptokurtic. Also, the jump structure of VG processes allows random default times of the reference entities. Among structural models, the most emphasis is made on the Black-Cox model by building a relation between the survival probabilities of the Black-Cox ...
Additional factor in asset-pricing: Institutional ownership Uğurlu-Yıldırım, Ecenur; Şendeniz Yüncü, İlkay (Elsevier BV, 2020-01-01) In this paper, we hypothesize that institutional investor variable is a proxy for some systematic risk factors, which should be incorporated into the asset-pricing model. Mimicking portfolio for institutional ownership, called IMI (Institutional minus Individual), is constructed. Including IMI to the Carhart's 4-factor model captures the common variations in returns better than all other models that are tested. Consistent with the literature, the new 5-factor model improves mispricing mostly in portfolios i...
Asset pricing models : stochastic volatility and information-based approaches Çalışkan, Nilüfer; Hayfavi, Azize; Department of Financial Mathematics (2007) We present two option pricing models, both different from the classical Black-Scholes-Merton model. The first model, suggested by Heston, considers the case where the asset price volatility is stochastic. For this model we study the asset price process and give in detail the derivation of the European call option price process. The second model, suggested by Brody-Hughston-Macrina, describes the observation of certain information about the claim perturbed by a noise represented by a Brownian bridge. Here we...

Citation Formats

O. Polat, “Dynamic complex hedging and portfolio optimization in additive markets,” M.S. - Master of Science, Middle East Technical University, 2009.