Abstract:
In this dissertation, the price of variance swaps under stochastic volatility
models based on the work done by Barndorff-Nielsen and Shepard (2001) and
Heston (1993) is discussed. The choice of these models is as a result of properties
they possess which position them as an improvement to the traditional
Black-Scholes (1973) model. Furthermore, the popularity of these models in
literature makes them particularly attractive. A lot of work has been done
in the area of pricing variance swaps since their inception in the late 1990’s.
The growth in the number of variance contracts written came as a result of
investors’ increasing need to be hedged against exposure to future variance
fluctuations. The task at the core of this dissertation is to derive closed or
semi-closed form expressions of the fair price of variance swaps under the two
stochastic models. Although various researchers have shown that stochastic
models produce close to market results, it is more desirable to obtain the fair
price of variance derivatives using models under which no assumptions about
the dynamics of the underlying asset are made. This is the work of a useful
analytical formula derived by Demeterfi, Derman, Kamal and Zou (1999)
in which the price of variance swaps is hedged through a finite portfolio of
European call and put options of different strike prices. This scheme is practically
explored in an example. Lastly, conclusions on pricing using each of the
methodologies are given.
