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Pricing American call options under a hard-to-borrow stock model

Published online by Cambridge University Press:  22 September 2017

GUIYUAN MA  and
SONG-PING ZHU
GUIYUAN MA
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong NSW 2522, Australia emails: [email protected], [email protected]
SONG-PING ZHU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong NSW 2522, Australia emails: [email protected], [email protected]
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Abstract

While a classic result by Merton (1973, Bell J. Econ. Manage. Sci., 141–183) is that one should never exercise an American call option just before expiration if the underlying stock pays no dividends, the conclusion of a very recent empirical study conducted by Jensen and Pedersen (2016, J. Financ. Econ.121(2), 278–299) suggests that one should ‘never say never’. This paper complements Jensen and Pedersen's empirical study by presenting a theoretical study on how to price American call options under a hard-to-borrow stock model proposed by Avellaneda and Lipkin (2009, Risk22(6), 92–97). Our study confirms that it is the lending fee that results in the early exercise of American call options and we shall also demonstrate to what extent lending fees have affected the early exercise decision.

Keywords

Hard-to-borrow stockEarly exerciseLending feesOption pricing
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 3 , June 2018 , pp. 494 - 514
Copyright
Copyright © Cambridge University Press 2017 

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References

Avellaneda, M. & Lipkin, M. (2009) A dynamic model for hard-to-borrow stocks. Risk 22 (6), 92–97.Google Scholar
Black, F. & Scholes, M. (1973) The pricing of options and corporate liabilities. J. Polit. Econ. 81 (3), 637–654.Google Scholar
Bollerslev, T., Gibson, M. & Zhou, H. (2011) Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities. J. Econ. 160 (1), 235–245.Google Scholar
Clarke, N. & Parrott, K. (1999) Multigrid for american option pricing with stochastic volatility. Appl. Math. Financ. 6 (3), 177–195.Google Scholar
Diamond, D. W. & Verrecchia, R. E. (1987) Constraints on short-selling and asset price adjustment to private information. J. Financ. Econ. 18 (2), 277–311.Google Scholar
Duffie, D., Garleanu, N. & Pedersen, L. H. (2002) Securities lending, shorting, and pricing. J. Financ. Econ. 66 (2), 307–339.Google Scholar
Evans, R. B., Geczy, C. C., Musto, D. K. & Reed, A. V. (2009) Failure is an option: Impediments to short selling and options prices. Rev. Financ. Stud. 22 (5), 1955–1980.Google Scholar
Fouque, J.-P., Papanicolaou, G. & Sircar, K. R. (2000) Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, Cambridge, UK.Google Scholar
Heston, S. L. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6 (2), 327–343.Google Scholar
Hintermüller, M., Ito, K. & Kunisch, K. (2002) The primal-dual active set strategy as a semismooth newton method. SIAM J. Optim. 13 (3), 865–888.Google Scholar
Ikonen, S. & Toivanen, J. (2007) Componentwise splitting methods for pricing american options under stochastic volatility. Int. J. Theor. Finance 10 (02), 331–361.Google Scholar
Ikonen, S. & Toivanen, J. (2008) Efficient numerical methods for pricing american options under stochastic volatility. Numer. Methods Partial Differ. Equ. 24 (1), 104–126.Google Scholar
Ito, K. & Kunisch, K. (2006) Parabolic variational inequalities: The lagrange multiplier approach. J. Math. Appl. 85 (3), 415–449.Google Scholar
Ito, K. & Toivanen, J. (2009) Lagrange multiplier approach with optimized finite difference stencils for pricing american options under stochastic volatility. SIAM J. Sci. Comput. 31 (4), 2646–2664.Google Scholar
Jensen, M. V. & Pedersen, L. H. (2016) Early option exercise: Never say never. J. Financ. Econ. 121 (2), 278–299.Google Scholar
Jones, C. M. & Lamont, O. A. (2002) Short-sale constraints and stock returns. J. Financ. Econ. 66 (2), 207–239.Google Scholar
Ma, G., Zhu, S.-P. & Chen, W.-T. (2017) Pricing european call options under a hard-to-borrow stock model. Submitted for publication. Available at SSRN: https://ssrn.com/abstract=2975887.Google Scholar
Merton, R. C. (1973) Theory of rational option pricing. Bell J. Econ. Manage. Sci., 4, 141–183.Google Scholar
Merton, R. C., Brennan, M. J. & Schwartz, E. S. (1977) The valuation of american put options. J. Finance 32 (2), 449–462.Google Scholar
Nielsen, L. T. (1989) Asset market equilibrium with short-selling. Rev. Econ. Stud. 56 (3), 467–473.Google Scholar
Rouah, F. D. (2013) The Heston Model and Its Extensions in Matlab and C, John Wiley & Sons, New Jersey, US.Google Scholar
Tankov, P. (2003) Financial Modelling with Jump Processes, Vol. 2, CRC Press, Florida, US.Google Scholar
Wilmott, P. (2013) Paul Wilmott on Quantitative Finance, John Wiley & Sons, New Jersey, US.Google Scholar
Wilmott, P., Howison, S. & Dewynne, J. (1995) The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press, Cambridge, UK.Google Scholar
Zhu, S.-P. & Chen, W.-T. (2011) A predictor–corrector scheme based on the adi method for pricing american puts with stochastic volatility. Comput. Math. Appl. 62 (1), 1–26.Google Scholar
Zvan, R., Forsyth, P. & Vetzal, K. (1998) Penalty methods for american options with stochastic volatility. J. Comput. Appl. Math. 91 (2), 199–218.Google Scholar