ISSN: 2056-3736 (Online Version) | 2056-3728 (Print Version)

Option Pricing: Channels, Target Zones and Sideways Markets

Zura Kakushadze

Correspondence: Zura Kakushadze,

Quantigic Solutions LLC, USA

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After a market downturn, especially in an uncertain economic environment such as the current state, there can be a relatively long period with a sideways market, where indexes, stocks, etc., move in channels with support and resistance levels. We discuss option pricing in such scenarios, in both cases of unattainable as well as attainable boundaries, and obtain closed-form option pricing formulas. Our results also apply to FX rates in target zones without interest rate pegging (USD/HKD, digital currencies, etc.).


  Option pricing, channel, reflecting boundaries, Brownian motion, volatility, drift, barriers, mean-reversion, mean-repelling, FX, digital currencies, target zone, sideways market, interest rate, attainable boundaries, unattainable boundaries, arbitrage, stock, put, call, binary, knockout, rebate.


Baxter, M. and Rennie, A. (1996) Financial Calculus: An Introduction to Derivative Pricing. Cambridge, UK: Cambridge University Press.Beaglehole, D. (1992) Down and Out, Up and In Options. Working Paper. Iowa City, IA: The University of Iowa.Bhagavatula, R. and P. Carr (1995) Valuing Double Barrier Options with Time-dependent Parameters. Working Paper. Ithaca, NY: Cornell University.Broadie, M. and Detemple, J. (1995) American Capped Call Options on Dividend-Paying Assets. Review of Financial Studies 8(1): 161-191.Carr, P. (1995) Two extensions to barrier option valuation. Applied Mathematical Finance 2(3): 173-209.Carr, P. (2017) Bounded Brownian Motion. Risks 5(4): 61.Carr, P. and Kakushadze, Z. (2017) FX Options in Target Zones. Quantitative Finance 17(10): 1477-1486. Available online:, H. and Yor, M. (1996) Pricing and Hedging Double-Barrier Options: A Probabilistic Approach. Mathematical Finance 6(4): 365-378.Harrison, J.M. and Pliska, S.R. (1981) Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications 11(3): 215-260.Haug, E.G. (2007) The Complete Guide to Option Pricing Formulas. (2nd ed.) New York, NY: McGraw-Hill.Hui, C.C. (1996) One-touch double barrier binary option values. Applied Financial Economic 6(4): 343-346.Hull, J.C. (2012) Options, Futures and Other Derivatives. Upper Saddle River, NJ: Prentice Hall.Kakushadze, Z. (2015) Phynance. Universal Journal of Physics and Application 9(2): 64-133. Available online:, Z. (2019) Healthy… Distress… Default. Journal of Risk & Control 6(1): 113-119. Available online:, Z. and Yu, W. (2019) iCurrency? World Economics 20(4): 151-175. Available online:, N. and Ikeda, M. (1992) Pricing Options with Curved Boundaries. Mathematical Finance 2(4): 275-298.Madan, D.B. (2017) Pricing options on mean reverting underliers. Quantitative Finance 17(4): 497-513.