Monte Carlo Optimization for Multi-Asset Portfolio Execution

Summary

The document frames large-order execution as a trade-off between liquidity costs and price risk. Trading quickly can increase market impact when liquidity is limited, while trading slowly leaves the order exposed to adverse price moves during the execution horizon. It describes a mean-variance approach to this problem and notes that an earlier single-asset model with stochastic liquidity and volatility leads to a nonlinear partial differential equation that must be solved numerically.

The proposed alternative uses quasi-Monte Carlo methods to optimize executions across any number of assets. The authors also describe it as suitable for real-time use, with stochastic-process parameters adjustable during execution. The supplied summary states the approach and its claimed flexibility, but gives no numerical results, validation details, or implementation specifics, so its comparative performance and practical limitations cannot be assessed from this text alone.

Key ideas

• Large orders create a trade-off between market impact and exposure to price movements.
• The described objective balances liquidity costs against price risk in a mean-variance framework.
• A prior single-asset stochastic model requires numerical solution of a nonlinear partial differential equation.
• The proposed quasi-Monte Carlo method is intended to support execution across multiple assets and real-time parameter changes.

Tags

# A Monte Carlo method for optimal portfolio executions


# A Monte Carlo method for optimal portfolio executions









Traders are often faced with large block orders in markets with limited liquidity and varying volatility. Executing the entire order at once usually incurs a large trading cost because of this limited liquidity. In order to minimize this cost traders split up large orders over time. Varying volatility however implies that they now take on price risk, as the underlying assets' prices can move against the traders over the execution period. This execution problem therefore requires a careful balancing between trading slow to reduce liquidity cost and trading fast to reduce the volatility cost. R. Almgren solved this problem for a market with one asset and stochastic liquidity and volatility parameters, using a mean-variance framework. This leads to a nonlinear PDE that needs to be solved numerically. We propose a different approach using (quasi-)Monte Carlo which can handle any number of assets. Furthermore, our method can be run in real-time and allows the trader to change the parameters of the underlying stochastic processes on-the-fly.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.