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Proportional Transaction Costs: An Introduction

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Stochastic Dominance Option Pricing

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Abstract

This chapter reviews the limited literature on option pricing in the presence of transaction costs outside the stochastic dominance (SD) approach. It starts by pointing out the importance of the topic, given the indeterminacy in defining the “true” price of a traded option because of the wide bid-ask spreads observed in the option markets. It then summarizes the studies that demonstrate the failure of the no arbitrage approach even when the underlying market is complete and there are transaction costs in trading the underlying asset. Last, it presents the generic investor’s dynamic asset allocation problem between a risky and a riskless asset given proportional transaction costs on the risky asset and derives the no transaction zone when the dynamics of the risky asset tend to diffusion or jump diffusion. These are inputs for the application of the SD approach to option pricing under transaction costs.

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Notes

  1. 1.

    Mark Rubinstein (1985, p. 465).

  2. 2.

    See Perrakis (2017), as well as Chap. 6 of this book, for the impact of such large option bid-ask spreads on existing empirical option studies that assume frictionless markets.

  3. 3.

    Even for cash-settled options it can be shown that optimal hedging corresponds to replication beyond a certain number of steps in the backward recursion.

  4. 4.

    This assumption can be easily relaxed when dealing with American options, as analyzed in detail in the next chapter. For the empirically important cases where the dividends accrue to the bond account and for normal parameter values it can be shown that including the dividends in the risky asset yields a very close approximation to the optimal policies; see Czerwonko and Perrakis (2016b).

  5. 5.

    The results extend routinely to the case that consumption occurs at each trading date and utility is defined over consumption at each of the trading dates and over the net worth at the terminal date.

  6. 6.

    If utility is defined only for non-negative net worth, then the decision variable is constrained to be a member of a convex set that ensures the non-negativity of the net worth.

  7. 7.

    This subsection is based on Constantinides (1986), who applied the discrete time results to the derivation of the NT zone in diffusion asset dynamics that also illustrates the small number of restructurings in most realistic cases.

  8. 8.

    For the convergence problems, see Czerwonko and Perrakis (2016a). The extension to jump diffusion in the continuous time case is in Liu and Loewenstein (2007, 2013).

  9. 9.

    For this reason, the empirical applications of this approach by Constantinides, Jackwerth and Perrakis (2007, 2009) did not extend beyond two periods.

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Authors and Affiliations

  1. Financial Derivatives, John Molson School of Business, Concordia University, Montreal, QC, Canada

    Stylianos Perrakis

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Perrakis, S. (2019). Proportional Transaction Costs: An Introduction. In: Stochastic Dominance Option Pricing. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-11590-6_3

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  • DOI: https://doi.org/10.1007/978-3-030-11590-6_3

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  • Print ISBN: 978-3-030-11589-0

  • Online ISBN: 978-3-030-11590-6

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