2019/10/03 by Ibrahim Ekren, Ekren, Ibrahim, Sergey Nadtochiy +1 · 2 citations
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Stochastic processes and financial applications #Atmospheric and Environmental Gas Dynamics #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.1910.01778
In this paper, we construct the utility-based optimal hedging strategy for a\nEuropean-type option in the Almgren-Chriss model with temporary price impact.\nThe main mathematical challenge of this work stems from the degeneracy of the\nsecond order terms and the quadratic growth of the first order terms in the\nassociated HJB equation, which makes it difficult to establish sufficient\nregularity of the value function needed to construct the optimal strategy in a\nfeedback form. By combining the analytic and probabilistic tools for describing\nthe value function and the optimal strategy, we establish the feedback\nrepresentation of the latter. We use this representation to derive an explicit\nasymptotic expansion of the utility indifference price of the option, which\nallows us to quantify the price impact in options' market via the price impact\ncoefficient in the underlying market.\n