Abstracts

The literature on pricing dividend derivatives is sparse. Dividend derivatives constitute a recent market that has generated increasingly great interest on European derivatives markets. There are futures with a December calendar maturity roll up to ten years and also European call and put options with a wide range of strike prices, for the same maturities. The underlying is the Dow Jones Euro STOXX 50 dividend index and we used dividend derivatives data between December 2008 and February 2012. From the equity derivatives pricing literature it seems conclusive that dividends are stochastic in nature. Hence, it is important to find models that can be easily implemented but that also preserve the stochastic character of dividends.
The first model proposed for pricing dividend derivatives is a jump-diffusion model with beta distributed jump sizes, proposed for the equity dividend index. The jumps are only downwards and the dividend payments are determined also by the evolution of the equity index itself. A Monte Carlo approach is described for pricing vanilla dividend derivatives. It was illustrated that this model can fit the smile of the European call and put dividend index options.
The main result of the paper is related to the stochastic logistic diffusion model, that would be useful to calculate analytically the conditional moments of the cum-dividend underlying variable. The two models developed here for pricing dividend derivative are very different, the first one modeling the dividend payment series while the latter follows the cum-dividend series. Both models rely on the Monte Carlo approach for implementation but there are immediate advantages in doing so since other path dependent derivatives would be priced directly based on the same set of simulations. Both models are specified under the physical measure. The parameters are estimated from the historical time-series.
The term structure of market price of risk is used to fix the martingale pricing measure and it is determined from the dividend futures curves. Then, under this measure, the call and put options are priced consistently for each maturity and across the strike range, fitting the smile (smirk) really well.