Article

 

A SHORT NOTE ON ALGORITHMIC APPROACHES TO IMPLIED VOLATILITY OF AN OPTION (p.53-59)

by

REZA HABIBI, IRAN BANKING INSTITUTE

Keywords : Arbitrage opportunity, Implied volatility, NR approximation, Optimal control, SA method

JEL classification : G12

Abstract

This paper is concerned with the implied volatilities of financial derivatives, specially options. While analyzing the option including its price, or implied volatility, some algorithms are needed which a unified version of algorithm is proposed. First, some recursive implied volatilities are derived using the Monte Carlo-based Newton-Raphson (NR) and the stochastic approximation (SA) method. Then, to extend the work of Liao (2003) in call option derivatives to almost all financial derivatives, a Bayes filter is fitted to implied volatility. Then, the existence of arbitrage opportunity in an option market is surveyed using optimal. Finally, a conclusion section is also given.