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No-Arbitrage Bounds On Two One-Touch Options

Author

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  • YUKIHIRO TSUZUKI

    (Graduate School of Economics, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan)

Abstract

This paper investigates no arbitrage relationships between the prices of two one-touch options with the same maturity but with different barrier levels. We find the no-arbitrage range of prices for a no-touch option, given the price of a second no-touch option and the prices of co-maturing vanilla call options. The upper and lower bounds are the cost of a super-replicating portfolio and a sub-replicating portfolio respectively. These consist of call options, put options, digital options and a one-touch option. We assume that the underlying process is a continuous martingale but do not postulate a model.

Suggested Citation

  • Yukihiro Tsuzuki, 2015. "No-Arbitrage Bounds On Two One-Touch Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-22.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:03:n:s0219024915500211
    DOI: 10.1142/S0219024915500211
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