Asset pricing models : stochastic volatility and information-based approaches

Download

index.pdf

Date

2007

Author

Çalışkan, Nilüfer

Metadata

Show full item record

Item Usage Stats

137
views

68
downloads

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 also study in detail the properties of this noisy information process and give the derivations of both asset price dynamics and the European call option price process.

Subject Keywords

Finance.

URI

http://etd.lib.metu.edu.tr/upload/12608213/index.pdf
https://hdl.handle.net/11511/16790

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Dynamic complex hedging and portfolio optimization in additive markets Polat, Onur; Hayfavi, Azize; Department of Financial Mathematics (2009) 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 ...
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...
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...
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...
Credit risk modeling with stochastic volatility, jumps and stochastic interest rates Yüksel, Ayhan; Akyıldız, Ersan; Department of Financial Mathematics (2007) This thesis presents the modeling of credit risk by using structural approach. Three fundamental questions of credit risk literature are analyzed throughout the research: modeling single firm credit risk, modeling portfolio credit risk and credit risk pricing. First we analyze these questions under the assumptions that firm value follows a geometric Brownian motion and the interest rates are constant. We discuss the weaknesses of the geometric brownian motion assumption in explaining empirical properties of...

Citation Formats

N. Çalışkan, “ Asset pricing models : stochastic volatility and information-based approaches,” M.S. - Master of Science, Middle East Technical University, 2007.