Volatility smile at the Russian option market

Abstract

The main derivative exchange in Russia is FORTS (Futures and Options in RTS) which is a division of Russian Trade System (RTS). The underlying assets of option contracts are futures on Russian companies’ shares: OJSC “EES"¹, OJPC “Lukoil"² and OJSC “Gazprom"³. A basic model for estimation of fair option price is Black‐Scholes model, developed in the beginning of 70‐s’ years of the last century. This model defines the option premium as a cost of its hedging by underlying asset. It uses a number of assumptions: prices of underlying assets follow log‐normal distribution; hedging is accomplished continuously; an underlying asset is infinitely divisible; a volatility is constant on all period of option life. However, according to practice, prices of shares and futures do not follow normal or log‐normal distribution, a volatility can change during a life of option, and hedging is a discrete process. Thus, Black‐Scholes model can yield inexact results in real markets, especially it concerns deeply “in the money” or deeply “out of the money” options. The basic purpose of the paper is to investigate opportunities to apply Black‐Scholes model for an estimation of option premiums in the Russian market.

First published online: 14 Oct 2010