Variance swaps: Pricing and replication; Focused on volatility skew in Indian markets

Abstract

This report is focused on study of Variance Swaps and Volatility Skew of relatively liquid Indian stocks. Variance Swaps and other volatility based financial instruments are aimed at giving the investor direct exposure to volatility of stock. Since normal stock options delta-hedging strategies only provide pure volatility exposure as long as stock prices don’t change, they are not efficient. As soon as stock price changes, variance exposure of all the options of all available strikes changes. Thus we need a financial instrument which can give pure exposure to volatility and zero exposure to direction of stock movements. Variance Swaps and Volatility fulfill this need of consumer. We have looked at sample terms of Variance Swap contracts, its convexity payoff curve, who can invest in Variance Swaps, and its general applications for various trading strategies. Variance Swaps are mainly over-the-counter trading instruments. In Indian context, they are almost non existent except being used as inter-desk instrument between two traders within a company. Next, we try to replicate them using a portfolio of call and put options with same time to maturity as Variance Swap. This replicated portfolio can be used for deciding the fair price (delivery price) for Variance Swap. In real markets not all strike prices are available, so we use a valuation formula meant for discrete strike prices and value a 3 month variance swap contract for Infosys. For Infosys’s variance swap valuation we use a portfolio of call and put options which will mature in 90 days. Next, we verify underlying assumptions of Valuation Model. After that we move on study of Volatility Skew model on Indian stocks. Volatility Skew is a map between various strike prices and their volatility. It is normally skewed downward for equities. While testing Volatility Skew model on Indian stocks, we found that though Volatility Skew exists, there is a difference in the implied volatility of Call and Put options. Either it is due to temporary high risk free rates or due to violation of Put Call parity. In both cases, it presents a unique arbitrage opportunity. Next to verify, if this arbitrage opportunity is temporary or if it exists in all Indian equities and over time, we look at volatility skews of Infosys for years 2008 and 2009 with different times to maturity (30 Days, 20 Days, and 10 days). After Infosys, we look at companies in other sectors like Tata Steel and Reliance. Finally to find out if it is specific to a company or it is available for all companies in these sectors we look at TCS in IT sector, ONGC in Oil & Gas, and SAIL in steel industry. Finally we interpret results in terms of, based on interactions with traders from Edelweiss & MS: 1) Liquidity scenario. 2) Put vs. Call Implied volatilities. 3) Roll of Mutual Funds & inflation of NAVs. 4) How institutional investors trade in options market at lower prices. 5) Difference in steepness of volatility skew curve across industries.