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Utility‐based pricing and hedging of contingent claims in Almgren‐Chriss model with temporary price impact
Author(s) -
Ekren Ibrahim,
Nadtochiy Sergey
Publication year - 2022
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12330
Subject(s) - bellman equation , economics , order (exchange) , value (mathematics) , representation (politics) , function (biology) , quadratic equation , mathematical economics , econometrics , probabilistic logic , construct (python library) , valuation of options , mathematical optimization , mathematics , computer science , finance , geometry , evolutionary biology , politics , political science , law , biology , programming language , statistics
In this paper, we construct the utility‐based optimal hedging strategy for a European‐type option in the Almgren‐Chriss model with temporary price impact. The main mathematical challenge of this work stems from the degeneracy of the second order terms and the quadratic growth of the first‐order terms in the associated Hamilton‐Jacobi‐Bellman equation, which makes it difficult to establish sufficient regularity of the value function needed to construct the optimal strategy in a feedback form. By combining the analytic and probabilistic tools for describing the value function and the optimal strategy, we establish the feedback representation of the latter. We use this representation to derive an explicit asymptotic expansion of the utility indifference price of the option, which allows us to quantify the price impact in options' market via the price impact coefficient in the underlying market.