"On optimal execution strategy of a portfolio of options under market impact" by Saad Mouti (UCSB)

Event Date: 

Monday, November 22, 2021 - 3:30pm to 4:30pm

Abstract: We consider the optimal execution of a book of options when market impact drives the option price. First, we develop a framework that transfers the underlying market impact onto the option price and justify the choice of our impact function. This model is inspired from Leland’s option replication with transaction costs and leads to the option execution price being expressed through a Black-Scholes PDE with modified volatility that depends on the size of the trade. We then minimize the mean-variance criterion for the impact function. We set up a stochastic control problem that minimizes the utility function and solve a Hamilton-Jacobi-Bellman problem. The simple expectation only cost suggests that the strategy is characterized by a convex increasing trading speed, in contrast to the equity case where the optimal strategy results in a constant trading speed. However, in this framework, the underlying price does not seem to affect the agent’s decision. By taking the agent risk aversion into account through the variance, the strategy seems to be more sensitive to the underlying price evolution, urging the agent to trade faster at the beginning of the strategy.