Version 1
: Received: 15 August 2022 / Approved: 16 August 2022 / Online: 16 August 2022 (09:48:35 CEST)
Version 2
: Received: 8 September 2022 / Approved: 8 September 2022 / Online: 8 September 2022 (09:18:40 CEST)
Halidias, N. On the Practical Point of View of Option Pricing. Monte Carlo Methods and Applications 2022, 28, 307–318, doi:10.1515/mcma-2022-2122.
Halidias, N. On the Practical Point of View of Option Pricing. Monte Carlo Methods and Applications 2022, 28, 307–318, doi:10.1515/mcma-2022-2122.
Halidias, N. On the Practical Point of View of Option Pricing. Monte Carlo Methods and Applications 2022, 28, 307–318, doi:10.1515/mcma-2022-2122.
Halidias, N. On the Practical Point of View of Option Pricing. Monte Carlo Methods and Applications 2022, 28, 307–318, doi:10.1515/mcma-2022-2122.
Abstract
In this note we describe a new approach to the option pricing problem by introducing the notion of the safe (and acceptable) for the writer price of an option, in contrast to the fair price used in the Black-Scholes model. Our starting point is that the option pricing problem is closely related with the hedging problem by practical techniques. Recalling that the Black - Scholes model does not give us the price of the option but the initial value of a replicating portfolio we observe easily that has a serious disadvantage because assumes the building of this replicating portfolio continuously in time and this is a disadvantage of any model that assumes such a construction. Here we study the problem from the practical point of view concerning mainly the over the counter market. This approach is not affected by the number of the underlying assets and is particularly useful for incomplete markets. In the usual Black-Scholes or binomial or some other approaches one assumes that one can invest or borrow at the same risk free rate $r>0$ which is not true in general. Even if this is the case one can immediately observes that this risk free rate is not a universal constant but is different among different people or institutions. So, the fair price of an option is not so much fair! Moreover, the two sides are not, in general, equivalent against the risk therefore the notion of a fair price has no meaning at all. We also define a variant of the usual binomial model, by estimating safe upward and downward rates $u,d$, trying to give a cheaper safe or acceptable price for the option.
Keywords
Safe price; multi asset options; Bermudan options; incomplete markets
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.
Commenter: Nikos Halidias
Commenter's Conflict of Interests: Author