A stochastic control approach to bid-ask price modelling
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Date
2022
Authors
Dela Vega, E.J.C.
Elliott, R.J.
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Journal article
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International Journal of Theoretical & Applied Finance, 2022; 25(4-5, article no. 2250021):1-30
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Abstract
This paper develops a model for the bid and ask prices of a European-type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain. A Girsanov theorem for Markov chains is implemented for the change of coefficients, including the diffusion coefficient which cannot be changed by the usual Girsanov theorem for Brownian motion. The price of a European-type asset is then determined using an Esscher transform and a system of partial differential equations. A dynamic programming principle and a maximum/minimum principle associated with the stochastic control problem are then derived to model bid and ask prices. These prices are not quotes of traders or market makers but represent estimates in our model on which reasonable quantities could be traded.
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Link to a related website: https://unpaywall.org/10.1142/S0219024922500212, Open Access via Unpaywall
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Copyright 2022 World Scientific Publishing Company
Access Condition Notes: Accepted manuscript available after 1 October 2023