---
abstract: |
    Black-Scholes (BS) is the standard mathematical model for European option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes, however, in practice it varies. How do traders come to learn these parameters?

    We introduce natural models of learning agents, in which they update their beliefs about the true implied volatility based on the opinions of other traders. We prove exponentially fast convergence of these opinion dynamics using techniques from control theory and leader-follower models, thus providing a resolution between theory and market practices. We allow for two different models, one with feedback and one with an unknown leader.
author:
- |
    Tushar Vaidya\
    SUTD\
    tushar\thompsonregina@example.com
- |
    Carlos Murguia\
    SUTD\
    murguia\thompsonregina@example.com
- |
    Georgios Piliouras\
    SUTD\
    thompsonregina@example.com
bibliography:
- 'nips17.bib'
title: 'Learning Agents in Black-Scholes Financial Markets'
---

Acknowledgements {#acknowledgements .unnumbered}
================

The authors would like to thank Elchanan Mossel, Ioannis Panageas, Ionel Popescu and JM Schumacher for fruitful discussions. Tushar Vaidya would like to acknowledge a SUTD Presidential fellowship. Carlos Murguia would like to acknowledge the National Research Foundation (NRF), Prime Minister's Office, Singapore, under its National Cybersecurity R&D Programme (Award No. NRF2014NCR-NCR001-40) and administered by the National Cybersecurity R&D Directorate. Georgios Piliouras would like to acknowledge SUTD grant SRG ESD 2015 097 and MOE AcRF Tier 2 Grant 2016-T2-1-170.

{'source': 'arXiv_out/1704'}