Abstract
There is no method of predicting the price of an option other than hedging strategies such as the binomial hedging strategy, the Black–Scholes hedging strategy and others. We will study these two basic hedging strategies in terms of their feasibility, and we will see that the Black–Scholes hedging strategy is not feasible because this strategy demands instantaneously rebuilding the replicating portfolio. Consequently, the real world prices of the options are not relevant at all with the Black–Scholes hedging strategy! We will suitably redefine the binomial hedging strategy so that it will be practically useful and present other feasible and generally more effective hedging strategies with some of them practically useful for options with no tradable underlying assets. Finally, we will mention some open questions related to the above.
References
[1] L. Bachelier, Théorie de la spéculation, Ann. Sc. Éc. Norm. Supér. (3) 17 (1900), 21–86. 10.24033/asens.476Search in Google Scholar
[2] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), no. 3, 637–654. 10.1086/260062Search in Google Scholar
[3] J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, J. Financ. Econ. 7 (1979), no. 3, 229–263. 10.1016/0304-405X(79)90015-1Search in Google Scholar
[4] J. C. Cox and M. Rubinstein, Options Markets, Prentice-Hall, Englewood Cliffs, 1985. Search in Google Scholar
[5] N. Halidias, On the practical point of view of option pricing, Monte Carlo Methods Appl. 28 (2022), no. 4, 307–318. 10.1515/mcma-2022-2122Search in Google Scholar
[6] J. Hull, Options, Futures and other Derivatives, Pearson Education, London, 2022. Search in Google Scholar
[7] W. Margrabe, The value of an option to exchange one asset for another, J. Finance 33 (1978), 177–186. 10.1111/j.1540-6261.1978.tb03397.xSearch in Google Scholar
[8] M. Musiela and M. Rutkowski, Martingale Methods in Financial Modelling, 2nd ed., Stoch. Model. Appl. Probab. 36, Springer, Berlin, 2005. 10.1007/b137866Search in Google Scholar
[9] Y. Tian, A flexible binomial option pricing model, J. Futures Markets 19 (1999), no. 7, 817–843. 10.1002/(SICI)1096-9934(199910)19:7<817::AID-FUT5>3.0.CO;2-DSearch in Google Scholar
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