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Abstract 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.
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A simple microstructural explanation of the concavity of price impact
Abstract This article provides a simple explanation of the asymptotic concavity of the price impact of a meta‐order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship between the order flow and the fundamental price (i.e., the local price impact) is linear, with a constant slope, which makes the model dynamically consistent. Nevertheless, the expected impact on midprice from a large sequence of co‐directional trades is nonlinear and asymptotically concave. The main practical conclusion of the proposed explanation is that, throughout a meta‐order, the volumes at the best bid and ask prices change (on average) in favor of the executor. This conclusion, in turn, relies on two more concrete predictions, one of which can be tested, at least for large‐tick stocks, using publicly available market data.
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- Award ID(s):
- 1855309
- PAR ID:
- 10361860
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Mathematical Finance
- Volume:
- 32
- Issue:
- 1
- ISSN:
- 0960-1627
- Page Range / eLocation ID:
- p. 78-113
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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