Pricing an Equity-Linked Security with Non-Guaranteed Principal

  • Cho, Jae-Koang (Department of Statistics and Actuarial Science, Soongsil University) ;
  • Lee, Hang-Suck (Department of Statistics and Actuarial Science, Soongsil University)
  • Published : 2007.08.31


Equity-linked securities (ELS) provide their customers with the return linked to the underlying equity (or equities). Equity-linked products in Korea have recently gained popularity due to relatively low interest rates. This paper discusses an equity-linked security whose principal is not guaranteed. The payoff of the ELS depends on the returns of two underlying assets. This paper presents numerical prices of the proposed product by using Monte-Carlo simulation method. It assumes that the log-returns of two stocks follow either Brownian motion or variance gamma process. Finally, the comparison of the two approaches is discussed.


  1. Bates, D. S. (1995). Post-crash moneyness biases in S&P 500 futures options. Rodney, L. White Center working paper, Wharton School, University of Pennsylvania, Philadelpia, PA
  2. Berman, M. B. (1971). Generating gamma distribution variates for computer simulation models. Technical Report, R-641-PR, Rand Corporation
  3. Black: F. (1975). Fact and fantasy in the use of option. Financial Analyst Journal, 31, 36-72
  4. Black: F. and Scholes, M. (1973). The pricing of options and other corporate liabilities. Journal of Political Economy, 81, 637-659
  5. De Jong, F., Kemna, A. and Kloeck, T. (1990). The Impact of Option Expirations on the Dutch Stock Market. Erasmus University
  6. Engle, R. F. and Gloria, G.-R. (1989). Semiparametric ARCH Models. Economics Working Paper Series, Department of Economics, University of California, San Diego
  7. Gerber, H. U. and Shiu, E. S. W. (1996). Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics, 18, 183-218
  8. Heston, S. L. (1993). Invisible parameters in option prices. The Journal of Finance, 48, 933-947
  9. Jaimungal, S. (2004). Pricing and hedging equity indexed annuities with variancegamma deviates. Working Paper, Department of Statistics, University of Toronto
  10. Madan, D. B., Carr, P. P. and Chang, E. C. (1998). The variance gamma process and option pricing. European Finance Review, 2, 79-105
  11. Madan D. B. and Milne, F. (1991). Option pricing with VG martingale components. Mathematical Finance, 1, 39-55
  12. Papaioannou, M. G. and Temel, T. (1993). Portfolio performance of the SDR and reserve currencies: Tests using the ARCH methodology. International Monetary Fund, Staff Papers - International Monetary Fund, Washington
  13. Wilmott, P. (2001). Paul Wilmott on Quantitative Finance. John Wiley & Sons, New York