Volatility and variance swaps : A comparison of quantitative models to calculate the fair volatility and variance strike

Volatility is a common risk measure in the field of finance that describes the magnitude of an asset’s up and down movement. From only being a risk measure, volatility has become an asset class of its own and volatility derivatives enable traders to get an isolated exposure to an asset’s volatility. Two kinds of volatility derivatives are volatility swaps and variance swaps. The problem with volatility swaps and variance swaps is that they require estimations of the future variance and volatility, which are used as the strike price for a contract. This thesis will manage that difficulty and estimate strike prices with several different models. I will de- scribe how the variance strike for a variance swap can be estimated with a theoretical replicating scheme and how the result can be manipulated to obtain the volatility strike, which is a tech- nique that require Laplace transformations. The famous Black-Scholes model is described and how it can be used to estimate a volatility strike for volatility swaps. A new model that uses the Greeks vanna and vomma is described and put to the test. The thesis will also cover a couple of stochastic volatility models, Exponentially Weighted Moving Average (EWMA) and Gener- alized Autoregressive Conditional Heteroskedasticity (GARCH). The models’ estimations are compared to the realized volatility. A comparison of the mod- els’ performance over 2015 is made as well as a more extensive backtesting for Black-Scholes, EWMA and GARCH. The GARCH model performs the best in the comparison and the model that uses vanna and vomma gives a good result. However, because of limited data, one can not fully conclude that the model that uses vanna and vomma can be used when calculating the fair volatility strike for a volatility swap.