Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Trading with market frictions, asymptotics and options

Tuesday, March 06, 2012 at 11:00am - 12:00pm

Speaker: Jonathan Goodman, New York University

I discuss dynamic trading strategies in the presence of small market frictions -- transaction costs or market impact. The idealized dynamic trading strategies of Merton (for investment) and Black and Scholes (for hedging) assume that there are no market frictions. Starting with Whaley and Wilmott, optimal strategies for markets with small frictions have been approximated using matched multi-scale asymptotic expansions and the idealized strategies. I give a simple heuristic explanation for the scalings found by Whaley and Wilmott as a tradeoff between losses to market frictions and opportunity loss from missing the optimal allocation. I explain a generalization to multi-asset problems and general utility functions. Finally, I explain how to modify the expansions to accommodate a single exchange traded option. Strategies that include an option have less cost (in the sense of asymptotics) than strategies with just a geometric Brownian motion (stock) and risk free asset (cash). The strategies that achieve this improved performance resemble Delta and Gamma hedging. This is joint work with Daniel Ostrov and Lin Li.

Speaker: Jonathan Goodman, New York University

Location   Hill 705