Join us for the Brooklyn Quant Experience (BQE) Lecture Series on Thursday, October 21st at 6 pm ET on Zoom. Only the NYU Community is allowed to attend in person until further notice. All other guests can attend synchronously via Zoom.
“Arbitrage-Based Derivative Pricing without Stochastic Calculus”
David Shimko
Industry Full Professor
NYU Tandon FRE
*Please note a meeting password is required for this event.
Meeting ID: 973 0109 4125
Password: BQEDS1021
Abstract
In the famous Black-Scholes-Merton model, continuous arbitrage in a frictionless environment leads to a well-known arbitrage-based pricing relationship between a single European call option and an underlying stock. In our discrete-time model, we use static arbitrage relationships across all options to find the same result. Our analysis also lays bare the impact of the powerful self-financing (SF) condition. While BSM requires the SF condition, we do not, leading to a stronger result. Additionally, we find that derivatives can be valued in the static CAPM provided a no-static-arbitrage constraint is included in the assumption set, resolving a 40-year-old dilemma. Finally, we show that option pricing could have been rigorously developed before the CAPM was created, using high school mathematics.