Optimal Timing to Trade Along a Randomized Brownian Bridge

TL;DR

This paper develops an optimal trading framework using a randomized Brownian bridge model to incorporate market views and noise, providing strategies for various prior distributions and revealing complex trading region structures.

Contribution

It introduces a novel modeling approach with randomized Brownian bridges for optimal trading, analyzing strategies under different prior beliefs and noise conditions.

Findings

Optimal strategies are derived numerically for various priors.

Disconnected continuation/exercise regions occur with specific distributions.

The model captures the impact of market views and noise on trading timing.

Abstract

This paper studies an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by an exponential randomized Brownian bridge (rBb) and consider various prior distributions for the random endpoint. We solve for the optimal strategies to sell a stock, call, or put, and analyze the associated delayed liquidation premia. We solve for the optimal trading strategies numerically and compare them across different prior beliefs. Among our results, we find that disconnected continuation/exercise regions arise when the trader prescribe a two-point discrete distribution and double exponential distribution.