Abstracts

Within equity models discrete dividends are often assumed to be proportional to spot or deterministic. In order to better capture dividend dynamics practitioners also represent dividends as affine functions of spot, where near dividends are deterministic and far dividends are proportional, see Overhaus et al. [1]. The resulting model has inhomogeneous spot dynamics. This paper presents a homogenous equity model with realistic dividend dynamics. Firstly, a family of equity models is introduced allowing for dynamics such as local or stochastic volatility. This family is defined as dividend discount models where all dividends are driven by a single factor. It is shown that the family includes as special cases important discrete dividend models such as deterministic, proportional and affine dividends as well as the Korn-Rogers model [2]. Secondly, the proposed model is introduced as special case within this family. In contrast to other models the impact of the factor on a given dividend decreases with time such that, with respect to a future time, near dividends are less volatile than far dividends. Analytic approximations for Vanilla and forward starting options in a setting with deterministic volatility are given. Numerical approaches for model calibration with local and stochastic volatility are also presented. These rely on Monte Carlo simulation and fixed-point method. Finally, it is shown that the model remedies some of the shortcomings of other dividend models, in particular non-homogeneity of dividend treatment.

[1] M. Overhaus et al.: Equity Hybrid Derivatives. Wiley, 2007.
[2] R. Korn and L. C. G. Rogers: Stocks paying discrete dividends: modelling and option pricing. The Journal of Derivatives 13, 44-48, 2005.