Comparative analysis of the SVJJ and the Hyperbolic models on the Swedish market

University essay from Högskolan i Halmstad/Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE); Högskolan i Halmstad/Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE)

Abstract:

In this thesis we investigate and compare two recently developed models of the option valuation according to the Swedish market. The first model is the Stochastic Volatility model with jumps in the stock price and the volatility (SVJJ) and the second is the Hyperbolic model. First of all we make brief introduction about the valuation of derivatives and considered models. Then we introduce methods for the estimation of parameters for each model. To solve this problem for the SVJJ model we use the Empirical Characteristic Function Estimation and for the Hyperbolic we use the Maximum Likelihood Method. Before explicit calculations (with estimated parameters) we describe the derivation of the pricing formula which is based on characteristic functions and densities. In conclusion we made numerical valuations of the call option prices for the OMXS30 index on the Swedish Stock Exchange. The main idea of this thesis is to compare 2 different models using numerical methods and the real data sets. To achieve this goal we firstly, compare the empirical characteristic function obtained from the market and the analytical ones for estimated parameters in case of both models. Secondly, we make a comparison of calculated call option prices and produce the summary.

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