Korean Management Science Review (경영과학)

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지

Conditional Value-at-Risk Optimization for Conversion of Convertible Bonds

전환사채 주식전환을 위한 조건부 VaR 최적화

  • 박구현 (홍익대학교 산업공학과) ;
  • 심은택 (홍익대학교 산업공학과)
  • Received : 2011.03.16
  • Accepted : 2011.05.19
  • Published : 2011.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this study we suggested two optimization models to answer a question from an investor standpoint : how many convertible bonds should one convert, and how many keep? One model minimizes certain risk to the minimum required expected return, the other maximizes the expected return subject to the maximum acceptable risk. In comparison with Markowitz portfolio models, which use the variance of return, our models used Conditional Value-at-Risk(CVaR) for risk measurement. As a coherent measurement, CVaR overcomes the shortcomings of Value-at-Risk(VaR). But there are still difficulties in solving CVaR including optimization models. For this reason, we adopted Rockafellar and Uryasev's[18, 19] approach. Then we could approximate the models as linear programming problems with scenarios. We also suggested to extend the models with credit risk, and applied examples of our models to Hynix 207CB, a convertible bond issued by the global semiconductor company Hynix.

Keywords

Acknowledgement

Supported by : 홍익대학교

References

  1. 김동석, 김인준, 이용, "전환가격 재조정이 포함된 전환사채의 가치평가에 관한 실증연구", 선물연구, 제9권, 제2호(2001), pp.1-23.
  2. 김동언, "전환사채 가격 평가에 관한 실증연구", 증권예탁 , 제52호(2005), pp.43-63.
  3. 이성효, "전환확률을 고려한 전환사채 주식비중의 추정", 증권학회지, 제25권(1999), pp.161-187.
  4. 지홍민, 신지숙, "조건부 VaR를 이용한 배당부 생명보험계약의 위험관리", 리스크관리연구, 제16권, 제2호(2005), pp.163-193.
  5. 윤평식, 박경욱, 김철중 역, 선물․옵션 투자의 이론과 전략, 7판, 교보문고, 2009(원서：Hull, J.C., Options, Futures, and Other Derivatives, 7th edition, Pearson, 2009).
  6. 이건희, "Part 6：전환사채", 채권투자 교과서, 북클래스, (2011), pp.186-208.
  7. Anderson, F., H. Mausser, D. Rosen, and S. Uryasev, "Credit risk optimization with value- at-risk criterion," Mathematical Programming Series B, Vol.89(2001), pp.273-291. https://doi.org/10.1007/PL00011399
  8. Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath, "Coherent measures of risk," Mathematical Finance, Vol.9(1999), pp.203-228. https://doi.org/10.1111/1467-9965.00068
  9. Ayache, E., P.A. Forsyth, and K.R. Vetzal, "The valuation of convertible bonds with credit risk," Journal of Derivatives, Vol.11 (2003), pp.9-29.
  10. Benati, S. and A. Rizzi, "A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem," European Journal of Operational Research, Vol.176(2007), pp.423-434. https://doi.org/10.1016/j.ejor.2005.07.020
  11. Brennan M.J. and E.S. Schwartz, "Convertible bonds：Valuation and optimal strategies for call and conversion," Journal of Finance, Vol.32(1977), pp.1699-1715. https://doi.org/10.1111/j.1540-6261.1977.tb03364.x
  12. Gotoh, J. and Y. Takano, "Newsvendor solutions via conditional value-at-risk minimization," European Journal of Operational Research, Vol.179(2007), pp.80-96. https://doi.org/10.1016/j.ejor.2006.03.022
  13. Habian, C.I., "Handling CVaR objectives and constraints in two-stage stochastic models," European Journal of Operational Research, Vol.191(2008), pp.888-911. https://doi.org/10.1016/j.ejor.2007.02.052
  14. Huang, D., S. Zhu, F.J. Fabozzi, and M. Fukushima, "Portfolio selection under distributional uncertainty:A relative roburst CVaR approach," European Journal of Operational Research, Vol.203(2010), pp.185-194. https://doi.org/10.1016/j.ejor.2009.07.010
  15. Ingersoll, J.E., "A contingent-claims valuation of convertible securities," Journal of Financial Economics, Vol.4(1977), pp.289-322. https://doi.org/10.1016/0304-405X(77)90004-6
  16. Kunzi-Bay, A. and J. Mayer, "Computational aspects of minimizing conditional valueat- risk," Computational Management Science, Vol.3(2006), pp.3-27. https://doi.org/10.1007/s10287-005-0042-0
  17. Markowitz, H., "Portfolio selection," The Journal of Finance, Vol.7(1952), pp.77-91.
  18. Rockafellar, R.T. and S. Uryasev, "Optimization of conditional value-at-risk," The Journal of Risk, Vol.2(2000), pp.21-41. https://doi.org/10.21314/JOR.2000.038
  19. Rockafellar, R.T. and S. Uryasev, "Conditional value-at-risk for general loss distributions," The Journal of Banking and Finance, Vol.26(2002), pp.1443-1471. https://doi.org/10.1016/S0378-4266(02)00271-6
  20. Tsai, J.T., J.L. Wang, and L.Y. Tzeng, "On the optimal product mix in life insurance companies using conditional value at risk," Insurance:Mathematics and Economics, Vol.46(2010), pp.235-241.
  21. Tsiveriotis, K. and C. Fernandes, "Valuing convertible bonds with credit risk," Journal of Fixed Income, Vol.8(1998), pp.95-102. https://doi.org/10.3905/jfi.1998.408243
  22. Zhang, D., H. Xu, and Y. Wu, "Single and multi-period optimal inventory control models with risk-averse constraints," European Journal of Operational Research, Vol.199 (2009), pp.420-434. https://doi.org/10.1016/j.ejor.2008.11.047