Volatility derivatives

Specialeforsvar: Rasmus Dall-Hansen

Titel: Volatility derivatives

Resume: Valuation of variance swaps is a question about
calculating expected future realized variance. One way forecasting future
realized variance is to use implied volatilities, since they indicate what the
market expects about uncertainty in the future. The methods implemented are a
Black-Scholes setup with volatility as a deterministic function of time, a
method using the Heston model and finally a practical method which transfers
the result from the Black-Scholes part to formulas which can be calculated using
traded products - a bundle consisting of a portfolio of European put- and call
options together with a necessary delta-hedging. Especially implementing the
Heston model is a large computational burden, but the simplicity of the formula
in the Heston model after the calibration is attractive. In order to boost the
performance of the Heston model a method which ”observes” two of the parameters
in the market and calibrate the rest is as well implemented. The empirical
results shows that in general all three methods provide good results and catch
the same ”maturity-strike”-relation but the Heston parameters seems to vary
significantly over

Vejleder: Rolf Poulsen
Censor: David Skovmand