On Market Completions Approach to Option Pricing
https://doi.org/10.26794/2308-944X-2021-9-3-77-93
Abstract
Option pricing is one of the most important problems of contemporary quantitative finance. It can be solved in complete markets with non-arbitrage option price being uniquely determined via averaging with respect to a unique risk-neutral measure. In incomplete markets, an adequate option pricing is achieved by determining an interval of non-arbitrage option prices as a region of negotiation between seller and buyer of the option. End points of this interval characterise the minimum and maximum average of discounted pay-off function over the set of equivalent risk-neutral measures. By estimating these end points, one constructs super hedging strategies providing a risk-management in such contracts. The current paper analyses an interesting approach to this pricing problem, which consists of introducing the necessary amount of auxiliary assets such that the market becomes complete with option price uniquely determined. One can estimate the interval of non-arbitrage prices by taking minimal and maximal price values from various numbers calculated with the help of different completions. It is a dual characterisation of option prices in incomplete markets, and it is described here in detail for the multivariate diffusion market model. Besides that, the paper discusses how this method can be exploited in optimal investment and partial hedging problems.
Keywords
option pricing,
complete markets,
incomplete markets,
non-arbitrage prices,
hedging strategies,
risk-management
Supporting agencies: The research was supported by the NSERC Discovery Grant RES 0043487.
About the Authors
I. Vasilev
University of Alberta
Canada
Canada
Ilia Vasilev — PhD Candidate, MSc Moscow Institute of Physics and Technology (State University), BSc Moscow Institute of Physics and Technology (State University). Edmonton, AB. WoS ResearcherID AAR‑3773-2021
A. Melnikov
University of Alberta
Canada
Canada
Alexander Melnikov — Professor, DSc from Steklov Mathematical Institute, Russia, PhD from Steklov Mathematical Institute, Russia, MSc from Moscow State University, Russia. Edmonton, AB. Web of Science ResearcherID P‑4620-2017
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Review
For citations:
Vasilev I., Melnikov A. On Market Completions Approach to Option Pricing. Review of Business and Economics Studies. 2021;9(3):77-93. https://doi.org/10.26794/2308-944X-2021-9-3-77-93
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