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Option Pricing: Examples and Open Problems
Version 1
: Received: 9 November 2022 / Approved: 11 November 2022 / Online: 11 November 2022 (02:40:18 CET)
Version 2 : Received: 7 December 2022 / Approved: 8 December 2022 / Online: 8 December 2022 (07:41:16 CET)
Version 3 : Received: 28 April 2023 / Approved: 28 April 2023 / Online: 28 April 2023 (08:50:06 CEST)
Version 4 : Received: 20 June 2023 / Approved: 21 June 2023 / Online: 21 June 2023 (08:56:07 CEST)
Version 2 : Received: 7 December 2022 / Approved: 8 December 2022 / Online: 8 December 2022 (07:41:16 CET)
Version 3 : Received: 28 April 2023 / Approved: 28 April 2023 / Online: 28 April 2023 (08:50:06 CEST)
Version 4 : Received: 20 June 2023 / Approved: 21 June 2023 / Online: 21 June 2023 (08:56:07 CEST)
A peer-reviewed article of this Preprint also exists.
Halidias, N. Option Pricing: Examples and Open Problems. Monte Carlo Methods and Applications 2023, 30, 1–17, doi:10.1515/mcma-2023-2014. Halidias, N. Option Pricing: Examples and Open Problems. Monte Carlo Methods and Applications 2023, 30, 1–17, doi:10.1515/mcma-2023-2014.
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. The price of an option is defined to be equal to the amount the seller needs to implement a hedging strategy. 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 are practically useful for options with no tradable underlying assets. Finally, we will mention some open questions related to the above.
Keywords
option pricing; realistic binomial model, hedging strategies
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Nikos Halidias
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