Preprint Short Note Version 3 Preserved in Portico This version is not peer-reviewed

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)

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

The option pricing problem is equivalent with the hedging problem of the option, i.e. what the writer should do in order to hedge the risk that she undertakes selling a contract and moreover what is the probability of profit selling at a specific price. In other words, the writer first designs a way to hedge the risk and then prices the contract according to the amount needed to hedge that risk. The probability of profit is also a useful information for the buyer. The hedging strategy should be practically possible for the writer otherwise has no meaning. In this note we will discuss the option pricing problem and in particular the effect of the volatility on the binomial model which is a way to hedge practically a specific option in contrast to every pricing model that assumes rebuilding of the replicating portfolio continuously in time. In order to use the binomial model we have to modified it accordingly as we have seen in a previous paper. We also point out four open problems regarding the hedging problem.

Keywords

option pricing; realistic binomial model

Subject

Computer Science and Mathematics, Applied Mathematics

Comments (1)

Comment 1
Received: 28 April 2023
Commenter: Nikos Halidias
Commenter's Conflict of Interests: Author
Comment: I have added two more theorems.
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