Nonlinear price impact and portfolio choice

Guasoni, Paolo; Weber, Marko

doi:10.1111/mafi.12234

Cited by 20 publications

(2 citation statements)

References 58 publications

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“…Finite trading speed-that is, the absolute continuity of the number of shares of the risky asset-occurs in market impact models, cf. Guasoni and Weber (2020) and the references therein. See also Bruhn et al (2016).…”

Section: Conflicts Of Interestmentioning

confidence: 99%

Asymptotic Methods for Transaction Costs

Mayerhofer

2024

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We propose a general approximation method for the determination of optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems, from optimally tracking benchmarks and hedging the log contract to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between the trading frequency and trade size to ensure satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.

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Section: Conflicts Of Interestmentioning

confidence: 99%

Asymptotic Methods for Transaction Costs

Mayerhofer

2024

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“…2 More generally, the term market frictions encompasses, for example, price impact, short-selling constraints, and margin requirements (see Guasoni and Muhle-Karbe (2013), Guasoni and Weber (2020) and and the references therein).…”

Section: Notesmentioning

confidence: 99%

Almost Perfect Shadow Prices

Mayerhofer

2024

JRFM

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Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that is, for small bid–ask spreads, asymptotically optimal at the third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at the fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices.

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High-frequency trading with fractional Brownian motion

2020

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In the high-frequency limit, conditionally expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon and making dynamic optimisation problems tractable. We find an explicit formula for locally mean–variance optimal strategies and their performance for an asset price that follows fractional Brownian motion. Without trading costs, risk-adjusted profits are linear in the trading horizon and rise asymmetrically as the Hurst exponent departs from Brownian motion, remaining finite as the exponent reaches zero while diverging as it approaches one. Trading costs penalise numerous portfolio updates from short-lived signals, leading to a finite trading frequency, which can be chosen so that the effect of trading costs is arbitrarily small, depending on the required speed of convergence to the high-frequency limit.

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Nonlinear price impact and portfolio choice

Cited by 20 publications

References 58 publications

Asymptotic Methods for Transaction Costs

Asymptotic Methods for Transaction Costs

Almost Perfect Shadow Prices

High-frequency trading with fractional Brownian motion

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