Authors: Emilio Barucci, Yuheng Lan, Daniele Marazzina.
This paper investigates the optimal execution and pricing of financial contracts commonly used in merger and acquisition (M&A) transactions, focusing on agreements between a broker and a counterparty. In particular, we analyze three classes of contracts: linear instruments such as Total Return Swaps (TRS), nonlinear structures such as collar contracts, and path-dependent contracts based on Time-Weighted Average Price (TWAP).
In M&A operations, acquiring firms often rely on derivatives rather than direct stock purchases to build positions in a target company while mitigating market impact and complying with regulatory constraints. Through such contracts, the broker intermediates the acquisition process by gradually executing trades in the underlying asset and managing inventory. These arrangements provide flexibility but also introduce significant challenges in pricing, hedging, and execution due to market illiquidity and price impact.
We develop a framework in which the broker determines both the optimal trading strategy and the contract fee using an indifference utility approach. The model incorporates both temporary and permanent linear market impact, capturing the feedback effect of trading activity on asset prices. Within this setting, the broker simultaneously hedges the derivative exposure and manages inventory over the contract’s lifetime, under either cash settlement or physical delivery.
Our analysis extends existing literature on illiquid derivative pricing by considering a broader class of payoff structures, including linear, nonlinear, and path-dependent contracts. We show that the nature of settlement plays a crucial role. Cash-settled contracts are systematically more expensive than physically delivered ones. The intuition is that, under cash settlement, the broker must unwind the hedging position at maturity, incurring additional market impact costs, whereas physical delivery aligns the hedging activity with the final obligation.
A central contribution of the paper is the analysis of market manipulation and statistical arbitrage opportunities arising from these contracts. We demonstrate that linear cash-settled contracts are particularly vulnerable to manipulation. The broker’s trading incentives are time-inconsistent: early in the contract, trading is driven by hedging needs, while near maturity, inventory liquidation dominates. This shift can induce trading patterns that exploit price impact, leading to profitable round-trip strategies (statistical arbitrage). In contrast, physically delivered contracts significantly reduce these opportunities, as the broker’s trading remains aligned with the need to accumulate shares for delivery.
We further show that nonlinear contracts, such as collars, introduce additional complexity, as optimal trading strategies become state-dependent and react dynamically to price movements. Similarly, TWAP-based contracts, due to their path dependence, can also generate manipulation incentives and statistical arbitrage opportunities, as the broker may influence the average price through strategic execution.
Overall, the paper delivers two key findings. First, cash settlement increases the cost of contracts relative to physical delivery due to the necessity of position unwinding under market impact. Second, cash-settled and path-dependent contracts are more prone to manipulation and statistical arbitrage, while physical delivery provides a more robust structure by aligning incentives between hedging and execution.
These results contribute to the literature on derivative pricing under illiquidity and to the growing body of work on market manipulation in price impact models, offering practical insights for the design and regulation of M&A-related financial contracts
