We value moving-average reset warrant under liquidity costs by using simulation approach. Some numerical analyses concerning the changes on the reset period; reset frequencies; reset ratio; and number of days in the moving average, which affect the values of warrants and reset probabilities, will be explored. We also set up a liquidity cost model which can determine the optimal reset ratio and thus minimize the liquidity cost of warrant. Finally, the delta jump inherent in the reset warrant was discussed in this study.

1.Introduction…………………………………………………………………….……1
2. Literature Review
2.1 The Monte Carlo Simulation and its applications…………………………2
2.2 The impact of liquidity on option pricing…………………………………4
3. Pricing Moving-Average Reset Warrants
3.1 Standard Monte Carlo simulation………………………………………………6
3.2 Moving-Average Reset Call Warrants………………………………………….8
3.3 Moving-Average Reset Put Warrants……………………………………………9
3.4 Least Square Monte-Carlo simulation…………………………………….…11
4. Numerical analysis
4.1 Different reset period and reset ratio……………………………………13
4.2 Stock price volatilities and moving-average…………………………….14
4.3 Reset frequencies effect………………………………………………………15
4.4 Risk characteristic…………………………………………………………….15
5.Liquidity Cost and Optimal Reset Ratio
5.1 The Data……………………………………………………………………………16
5.2 The Results……………………………………………………………………….17
6.Conclusion…………………………………………………………………………..18
Appendix A………………………………………………………………………………20
References………………………………………………………...………………...23

Amihud,Y. (2002), “Illiquidity and Stock Returns: Cross-Section and Time-Series Effects,” Journal of Financial Markets 5 (2002) 31-56.

Brenner, M., R. Eldor and S. Hauser (2001), “The Price of Option Illiquidity,” The Journal of Financial Vol. LVI, NO. 2, April 2001.

Boyle, P. (1977), ”Options: A Monte Carlo Approach,” Journal of Financial Economics, May, pp.323-338.

Barraquand, J. and D. Martineau, ”Numerical Valuation of High Dimensional Multivariate American Securities,” Journal of Financial and Quantitative Analysis, 30 (1995), pp.383-405.

Broadie, M. and P. Glasserman, (1997), ”Pricing American-style securities using simulation,” Journal of Economic Dynamics and Control, Vol. 21, pp.1323-1352.

Etling, C. and Miller, T.W., Jr. (2000), “The Relationship Between Index Option Monetness and Relative Liquidity,” The Journal of Futures Markets, Vol. 20, No. 10, 971-987 (2000).

Elyasiani, E., S. Hauser and B. Lauterbach. (2000), “Market Response to Liquidity Improvements: Evidence from Exchange Listings,” The Financial Review 41 (2000) 1-14.

Longstaff, F. A. and E. S. Schwartz (2001), ”Valuing American Options by Simulation: A Simple Least-Square Approach,” The Review of Financial Studies, Vol.14, No.1, 113-147.

Mayhew, S., A. Sarin and K. Shastri (1999), “What Drives Option Liquidity,” Working paper, University of Pittsburgh.

Tilley, J.A.,(1993),”Valuing American Options in a Path Simulation Model,” Trans. Society of Actuaries, pp.83-104.