• The Korean Journal of Financial Management
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• v.24 no.4
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• pp.1-43
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• 2007

The traditional Black-Scholes model for option pricing is based on the assumption that the log-return of the underlying asset follows a Brownian motion. But this assumption has been criticized for being unrealistic. Thus, for the last 20 years, many attempts have been made to adopt different stochastic processes to derive new option pricing models. The option pricing models based on L$\acute{e}$vy processes are being actively studied originating from the Gerber-Shiu model driven by H. U. Gerber and E. S. W. Shiu in 1994. In 2004, G. H. L. Cheang derived an option pricing model under multiple L$\acute{e}$vy processes, enabling us to adopt drift and jumps to the Gerber-Shiu model, while Gerber and Shiu derived their model under one L$\acute{e}$vy process. We derive the Gerber-Shiu model which includes drift and jumps under L$\acute{e}$vy processes. By adopting a Gamma distribution, we expand the Heston model which was driven in 1993 to include jumps. Then, using KOSPI200 index option data, we analyze the price-fitting performance of our model compared to that of the Black-Scholes model. It shows that our model shows a better price-fitting performance.

• Journal of Powder Materials
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• v.17 no.4
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• pp.276-280
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• 2010

In the present work, ethylene glycol-based (EG) copper oxide nanofluids were synthesized by pulsed wire evaporation method. In order to explode the pure copper wire, high voltage of 23 kV was applied to the both ends of wire and argon/oxygen gas mixture was used as reactant gas. EG-based copper oxide nanofluids with different volume fraction were prepared by controlling explosion number of copper wire. From the transmission electron microscope (TEM) image, it was found that the copper oxide nanoparticles exhibited an average diameter about 100 nm with the oxide layer of 2~3 nm. The synthesized copper oxide consists of CuO/$Cu_2O$ phases and the Brunauer Emmett Teller (BET) surface area was estimated to be $6.86\;m^2\;g^{-1}$. From the analyses of thermal properties, it is suggested that viscosity and thermal conductivity of EG-based copper oxide nanofluids do not show temperature-dependent behavior over the range of 20 to $90^{\circ}C$. On the other hand, the viscosity and thermal conductivity of EG-based copper oxide nanofluids increase with volume fraction due to the active Brownian motion of the nanoparticles, i.e., nanoconvection.