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½ÇÁõÀû Ãß°èÇÒÀÎÀ²¿¡ ´ëÇÑ ¿¬±¸ : KOSPI 200 ¿É¼Ç ½ÃÀåÀ» Áß½ÉÀ¸·Î

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º» ¿¬±¸´Â KOSPI 200 ¿É¼Ç°¡°ÝÀÌ ÇÔÀÇÇÏ´Â ½ÇÁõÀû Ãß°èÇÒÀÎÀ²(empirical pricing kernel)À» Rosenberg and Engle(2002)ÀÇ ¿ª °øÇбâ¹ý(reverse engineering)À» ÀÌ¿ëÇÏ¿© ÃßÁ¤ÇÑ´Ù. ³í¹®ÀÇ ÁÖ¿ä ½ÇÁõºÐ¼® °á°ú´Â ¾Æ·¡¿Í °°´Ù. ù°, S&P 500 ¿É¼Ç ÀڷḦ ÀÌ¿ëÇÑ Rosenberg and Engle(2002)ÀÇ °á°ú¿Í´Â ´Þ¸® ¸èÇÔ¼ö ÇüÅÂÀÇ Ãß°èÇÒÀÎÀ²¿¡ ºñÇØ º¸´Ù º¹ÀâÇÏ°í ÀϹÝÀûÀÎ ÇÔ¼öÇüŸ¦ °®´Â ´ÙÇ×½Ä ÇüÅÂÀÇ Ãß°èÇÒÀÎÀ²ÀÇ ÇìÁö ¼º°ú°¡ ¿ì¼öÇßÀ¸¸ç, ³»Ç¥º» °¡°Ý°áÁ¤·Â°ú ¿ÜÇ¥º» ¿¹Ãø·Â ¿ª½Ã ¿ì¿ùÇß´Ù. µÑ°, ¿É¼Ç°¡°Ý°ú º¸¼ö¸¦ °í·ÁÇÏ´Â °Í ÀÌ¿Ü¿¡ ´Ü±â ä±Ç°¡°ÝÀ» Á¤È®È÷ °¡°Ý°áÁ¤Çϵµ·Ï Á¦¾àÇÏ´Â °æ¿ì, ½ÇÁõÀû Ãß°èÇÒÀÎÀ²ÀÇ °¡°Ý°áÁ¤·Â°ú ¿¹Ãø·ÂÀÌ »ó´ëÀûÀ¸·Î ¿­µîÇØ Á³´Ù. ´Ü, ¸èÇÔ¼ö ÇüÅÂÀÇ Ãß°èÇÒÀÎÀ²ÀÇ °æ¿ì ¿­µîÇØÁø Á¤µµ°¡ Å« ¹Ý¸é, ´ÙÇ×½Ä ÇüÅÂÀÇ Ãß°èÇÒÀÎÀ²ÀÇ °æ¿ì ¿É¼Ç°¡°Ý¸¸À» ÀÌ¿ëÇÏ¿© ÃßÁ¤ÇÑ °æ¿ì¿Í ±× Â÷ÀÌ°¡ Å©Áö ¾Ê´Ù. ÇìÁö ¼º°úÀÇ °æ¿ì, ä±Ç°¡°ÝÀ» °í·ÁÇÏ°í ½ÇÁõÀû Ãß°èÇÒÀÎÀ²À» ÃßÁ¤ÇÏ¿©µµ ÇìÁö ¼º°ú°¡ Å©°Ô ´Þ¶óÁöÁö ¾Ê¾ÒÀ¸¸ç ÇìÁö ¹æ¹ý¿¡ µû¶ó ¿ÀÈ÷·Á ´õ ÇìÁö ¼º°ú°¡ ÁÁ¾Æ Áö´Â °æ¿ìµµ ¹ß°ßµÇ¾ú´Ù. ¼Â°, ½Ã°£¿¡ µû¶ó º¯ÇÏÁö ¾Ê´Â Ãß°èÇÒÀÎÀ²À» »ç¿ëÇϸé, °¡°Ý°áÁ¤·Â°ú ¿¹Ãø·ÂÀº Å©°Ô ³ªºüÁö¸ç, ´ÙÇ×½Ä ÇüÅÂÀÇ ½ÇÁõÀû Ãß°èÇÒÀÎÀ²ÀÇ °æ¿ì¿¡¼­ ÀÌ Â÷ÀÌ°¡ ´õ µÎµå·¯Áø´Ù. ÇìÁö ¼º°ú ¶ÇÇÑ ½Ã°£¿¡ µû¶ó º¯ÇÏ´Â ½ÇÁõÀû Ãß°èÇÒÀÎ À²À» ÀÌ¿ëÇßÀ» ¶§º¸´Ù »ó´ëÀûÀ¸·Î ¿­µîÇØ Áø´Ù. ´Ü, ¸èÇÔ¼ö ÇüÅÂÀÇ ½ÇÁõÀû Ãß°èÇÒÀÎÀ²ÀÇ °æ¿ì, ƯÁ¤ ÇìÁö ¹æ¹ý À» »ç¿ëÇßÀ» ¶§´Â ¿ÀÈ÷·Á ½Ã°£¿¡ µû¶ó º¯ÇÏÁö ¾Ê´Â Æò±ÕÀûÀÎ °³³äÀÇ Ãß°èÇÒÀÎÀ²ÀÇ ÇìÁö ¼º°ú°¡ ´õ ÁÁ¾Ò´Ù. ³Ý°, ´ÙÇ×½Ä Ãß°èÇÒÀÎÀ²Àº ±âÃÊÀÚ»êÀÇ ¼öÀÍ·ü º¯È­¿¡ µû¸¥ º¯µ¿ÀÇ ÆøÀÌ ¸èÇÔ¼ö Ãß°èÇÒÀÎÀ² º¸´Ù Å©¸ç, ½Ã°£ÀÌ Áö³²¿¡ µû¶ó ±âÃÊÀÚ»êÀÇ ¼öÀÍ·ü°úÀÇ °ü°è ¶ÇÇÑ Å« ÆøÀ¸·Î º¯È­ÇÑ´Ù. ¸èÇÔ¼ö Ãß°èÇÒÀÎÀ²Àº ±âÃÊÀÚ»êÀÇ ¼öÀÍ·üÀÌ Áõ°¡ÇÔ¿¡ µû¶ó ´ëü·Î °¨¼ÒÇÏ´Â °æÇâÀ» º¸À̴µ¥ ÀÌ´Â ÅõÀÚÀÚµéÀÇ ÇÑ°èÈ¿¿ëÀÌ °¨¼ÒÇÔÀ» ÀǹÌÇÑ´Ù. ´Ù¼¸Â°, ½ÇÁõÀû Ãß°èÇÒÀÎÀ²·ÎºÎÅÍ À¯µµµÈ À§ÇèȸÇǵµ´Â ½Ã°£ÀÌ Áö³²¿¡ µû¶ó º¯ÇÏ¿´À¸¸ç, °æÁ¦ »óȲÀ» Àâ¾Æ³»´Â º¯¼öµé Áß ¿ÀÁ÷ ±âÃÊÀÚ»êÀÇ ¼öÀÍ·ü°ú À§ÇèȸÇǵµÀÇ ·¡±×(lag) °ª¸¸ÀÌ Åë°èÀûÀ¸·Î À¯ÀÇÇÑ °ü°è¸¦ º¸¿´´Ù.
½ÇÁõÀû Ãß°èÇÒÀÎÀ²,ÇìÁö ¼º°ú,À§ÇèȸÇǵµ,KOSPI 200 ¿É¼Ç,¿ª °øÇбâ¹ý

A Study on Empirical Pricing Kernels£ºA Case of the KOSPI 200 options

  • Jangkoo Kang
  • Byung Chun Kim
  • Doojin Ryu
  • Jaesun Yun
This paper estimates the empirical pricing kernels (EPK) implied by the KOSPI 200 options using the reverse engineering technique suggested by Rosenberg and Engle (2002). The empirical pricing kernels are estimated as a power function as well as a polynomial function of the returns of the underlying index. The empirical results documented in this paper are as follows£º First, the empirical performance of the power pricing kernel is worse than that of the polynomial pricing kernel that contains more parameters and so is more flexible than the power pricing kernel. This contrasts to the results of Rosenberg and Engle (2002), which investigate the S&P 500 options market. Second, the pricing and forecasting ability of the EPK deteriorate if we estimate the EPK by imposing the restriction that the EPK prices the short term bond exactly. While the amount of the deterioration is large in the case of the power pricing kernel, it is relatively small in the case of the polynomial pricing kernel. The hedging performance with the restriction is almost the same as or sometimes better than the one without the restriction, depending on the hedging method. Third, the empirical performance of time-invariant EPKs is generally poor. The difference in the empirical performance between the time-invariant EPK and the time varying EPK is more prominent in the case of polynomial EPK. The hedging performance of time-invariant EPKs is sometimes better than that of the time-varying EPKs in the case of power EPK. Fourth, the polynomial EPK is more sensitive to the underlying return state compared to the power EPK. The shape of the polynomial EPK that is a function of the underlying return state fluctuates more and reflects the non-linearity of the pricing kernel better than the power EPK. The estimated power EPKs tend to decrease as the underlying return increase. This implies the marginal utilities of investors decrease with the underlying return. Fifth, the risk aversion implied by the EPK is time varying and it has a statistically significant relation with the KOSPI 200 index return and the lag value of the risk aversion.
Empirical Pricking Kernel,Hedging Performance,Risk Aversion,KOSPI 200 Options,Reverse Engineering