×

A generalization of option pricing to price-limit markets. (English) Zbl 1451.91197

Summary: This paper proposes an analytic solution for pricing options in markets with daily price limits. The Black-Scholes model is a nested case in which the daily price limit approaches infinity. Compared to the Black-Scholes model, our solution may solve the mispricing problem and could yield consistent results with existing numerical methods. Practitioners trading options in price-limit markets may resort to the finite difference method or Monte Carlo simulations. However, applying these numerical methods is often time consuming, thereby further illustrating the importance of an analytic solution.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ban, J.; Choi, HI; Ku, H., Valuation of European options in the market with daily price limit, Applied Mathematical Finance, 7, 61-74 (2000) · Zbl 1021.91024 · doi:10.1080/135048600450293
[2] Bhattacharya, RN; Waymire, EC, Stochastic processes with applications (1990), New York: Wiley, New York · Zbl 0744.60032
[3] Black, F.; Scholes, M., The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637-659 (1973) · Zbl 1092.91524 · doi:10.1086/260062
[4] Brady, NF; Cotting, JC; Kirby, RG; Opel, JR; Stein, HM; Glauber, RR, Report of the presidential task force on market mechanisms (1988), Washington, DC: Government Printing Office, Washington, DC
[5] Brennan, MJ, A theory of price limits in futures markets, Journal of Financial Economics, 16, 213-233 (1986) · doi:10.1016/0304-405X(86)90061-9
[6] Brunnermeier, KM; Pedersen, HL, Predatory trading, Journal of Finance, 60, 1825-1863 (2005) · doi:10.1111/j.1540-6261.2005.00781.x
[7] Carr, P.; Madan, DB, Option valuation using the fast Fourier transform, Journal of Computational Finance, 2, 61-73 (1999) · doi:10.21314/JCF.1999.043
[8] Chang, CC; Chung, H.; Wang, TI, Pricing options with price limits and market illiquidity, Research in Finance, 22, 187-214 (2005) · doi:10.1016/S0196-3821(05)22007-5
[9] Chou, PH; Lin, MC; Yu, MT, The effectiveness of coordinating price limits across futures and spot markets, Journal of Futures Markets, 23, 577-602 (2003) · doi:10.1002/fut.10076
[10] Duffie, D.; Pan, J.; Singleton, K., Transform analysis and asset pricing for affine jump-diffusions, Econometrica, 68, 1343-1376 (2000) · Zbl 1055.91524 · doi:10.1111/1468-0262.00164
[11] George, TJ; Hwang, CY, Transitory price changes and price-limit rules: Evidence from the Tokyo Stock Exchange, Journal of Financial and Quantitative Analysis, 30, 313-327 (1995) · doi:10.2307/2331123
[12] Guo, JH; Chang, LF; Hung, MW, Limit hits and informationally-related stocks, Journal of Financial Markets, 34, 31-47 (2017) · doi:10.1016/j.finmar.2017.02.002
[13] Harris, JH; Swartz, LM; Kolb, RW; Overdahl, JA, Equity derivatives, Financial derivatives: Pricing and risk management, 103-113 (2009), New York: Wiley, New York
[14] Henke, H.; Voronkova, S., Price limits on a call auction market: Evidence from the Warsaw Stock Exchange, International Review of Economics and Finance, 14, 439-453 (2005) · doi:10.1016/j.iref.2004.02.001
[15] Hsieh, PH; Kim, YH; Yang, JJ, The magnet effect of price limits: A logit approach, Journal of Empirical Finance, 16, 830-837 (2009) · doi:10.1016/j.jempfin.2009.06.002
[16] Kim, KA; Limpaphayom, P., Characteristics of stocks that frequently hit price limits: Empirical evidence from Taiwan and Thailand, Journal of Financial Markets, 3, 315-332 (2000) · doi:10.1016/S1386-4181(00)00009-4
[17] Kim, KA; Liu, H.; Yang, JJ, Reconsidering price limit effectiveness, The Journal of Financial Research, 36, 4, 493-517 (2013) · doi:10.1111/jfir.12021
[18] Kim, KA; Rhee, SG, Price limit performance: Evidence from the Tokyo Stock Exchange, Journal of Finance, 52, 885-901 (1997) · doi:10.1111/j.1540-6261.1997.tb04827.x
[19] Kim, YH; Yagüe, J.; Yang, JJ, Relative performance of trading halts and price limits: Evidence from the Spanish Stock Exchange, International Review of Economics and Finance, 17, 197-215 (2008) · doi:10.1016/j.iref.2007.06.003
[20] Kim, YH; Yang, JJ, What makes circuit breakers attractive to financial markets? A survey, Financial Markets, Institutions and Instruments, 13, 109-146 (2004) · doi:10.1111/j.0963-8008.2004.00074.x
[21] Kim, YH; Yang, JJ, Effect of price limits: Initial public offerings versus seasoned equities, International Review of Finance, 9, 3, 295-318 (2009) · doi:10.1111/j.1468-2443.2009.01092.x
[22] Kou, SG; Wang, Hui, Option pricing under a double exponential jump diffusion model, Management Science, 50, 9, 1178-1192 (2004) · doi:10.1287/mnsc.1030.0163
[23] Leland, HE, Option pricing and replication with transactions costs, Journal of Finance, 40, 1283-1301 (1985) · doi:10.1111/j.1540-6261.1985.tb02383.x
[24] Li, H.; Zheng, D.; Chen, J., Effectiveness, cause and impact of price limit-Evidence from China’s cross-listed stocks, Journal of International Financial Markets, Institutions & Money, 29, 217-241 (2014) · doi:10.1016/j.intfin.2013.12.007
[25] Phylaktis, K.; Kavussanos, M.; Manalis, G., Price limits and stock market volatility in the Athens Stock Exchange, European Financial Management, 5, 69-84 (1999) · doi:10.1111/1468-036X.00080
[26] Shanker, L.; Balakrishnan, N., Optimal clearing margin, capital and price limits for futures clearinghouses, Journal of Banking & Finance, 29, 1611-1630 (2005) · doi:10.1016/j.jbankfin.2004.06.037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.