• The Korean Journal of Applied Statistics
• /
• v.29 no.1
• /
• pp.181-192
• /
• 2016

We consider several methods to approximate option prices with correction terms to the Black-Scholes option price. These methods are able to compute option prices from various risk-neutral distributions using relatively small data and simple computation. In this paper, we compare the performance of Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method of using Normal inverse gaussian distribution, and an asymptotic method of using nonlinear regression through simulation experiments and real KOSPI200 option data. We assume the variance gamma model in the simulation experiment, which has a closed-form solution for the option price among the pure jump $L{\acute{e}}vy$ processes. As a result, we found that methods to approximate an option price directly from the approximate price formula are better than methods to approximate option prices through the approximate risk-neutral density function. The method to approximate option prices by nonlinear regression showed relatively better performance among those compared.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.36 no.5A
• /
• pp.511-520
• /
• 2011

In this paper, we introduce a multiuser (MU) scheduling method for multiuser amplify-and-forward relay systems, which selects both the transmission mode, i.e., either one- or two-hop transmission, and the desired user via two steps. A closed-form expression for the average achievable rate of the proposed scheduling is derived under two transmission modes with MU scheduling, and its asymptotic solution is also analyzed in the limit of large number of mobile stations. Based on the analysis, we perform our two-step scheduling algorithm: the transmission mode selection followed by the user selection that needs partial feedback for instantaneous signal-to-noise ratios (SNRs) to the base station. We also analyze the average SNR condition such that the MU diversity gain is fully exploited. In addition, it is examined how to further reduce a quantity of feedback under certain conditions. The proposed algorithm shows the comparable achievable rate to that of the optimal one using full feedback information, while its required feedback overhead is reduced below half of the optimal one.