Optimal Reset Ratio for Reset Options with Liquidity Cost

10.29973/JCSA.200606.0002

Chien-Hung Chang；Hui-Chun Tien；Min-Teh Yu

Reset Options ； Liquidity Cost ； Reset Ratio ； Moneyness

中國統計學報

44卷2期（2006 / 06 / 01）

130 - 144

英文

This study sets up a framework that specifies liquidity cost as a power function of moneyness for traded reset options in order to demonstrate how to locate the optimal reset ratio that provides the most liquid contract. We first derive the closed-form solutions for the expected values of these power functions that are necessary for finding the optimal reset ratio and then adopt the empirical parameter values of liquidity cost estimated for S&P100 and S&P500 options to locate the optimal reset ratio. Numerical results show how the optimal reset ratios are related to asset volatility and expected return. Though this study demonstrates the procedures and feasibility to locate the optimal reset ratios for a power function of liquidity, the linear property of integrals allows us to generalize these power functions to be more complicated polynomial functions.

1. Bollen, N. P. B.,Smith, T.,Whaley, R. E.(2003).Optimal contract design: for whom?.Journal of Futures Markets,23,719-750.
2. Boyle, P.,Kolkiewicz, A.,Tan, K. S.(2001).Valuing the rest option embedded in some equity-linked insurance products.North American Actuarial Journal,5(3),1-18.
3. Brenner, M.,Sundaram, R. K.,Yermack, D.(2000).Altering the terms of executive stock options.Journal of Financial Economics,57,103-128.
4. Chan, H. W.,Pinder, S. M.(2000).The value of liquidity: Evidence from the derivatives market.Pacific-Basin Finance Journal,8,483-503.
5. Chang, C. C.,Chung, S. L.,Shackleton M. B.(2004).Pricing options with American-style average reset features.Quantitative Finance,4,292-300.
6. Dai, M.,Kwok, Y. K.,Wu, L. X.(2003).Options with multiple reset rights.Internal Journal of Theoretical and Applied Finance,6,637-653.
7. Etling, C.,Miller, T.W.(2000).The relationship between index option moneyness and relative liquidity.Journal of Futures Markets,20,971-987.
8. Gerber, H. U.,Shiu, E. S. W.(1999).From ruin theory to pricing reset guarantees and perpetual put options.Insurance: Mathematics and Economics,24,3-14.
9. Gray, S. F.,Whaley, R. E.(1999).Reset put options: valuation, risk characteristics, and application.Australian Journal of Management,24(1)
10. Grossman, S. J.,Miller, M. H.(1986).Economic costs and benefits of the proposed one-minute time breaking regulation.Journal of Futures Markets,6,141-166.
11. Hsueh, L. P.,Liu, Y. A.(2001).Step-reset options: design and valuation.Journal of Futures Markets,22,155-171.
12. Karatzas, I.,Shreve, S. E.(1988).Brownian Motion and Stochastic Calculus.Springer-Verlag.
13. Liao, S. L.,Wang, C. W.(2003).The valuation of reset options with multiple strike resets and reset dates.Journal of Futures Markets,23(1),87-107.
14. Vijh, A. M.(1990).Liquidity of the CBOE Equity Options.Journal of Finance,45(4),1157-1179.