Dynamic portfolio strategies under a fully correlated jump-diffusion process

This paper presents the first continuous-time model to feature a flexible dependence structure among jump intensity, stock variance, and stock returns. In particular, it addresses a gap in the financial portfolio optimization literature concerning the non-trivial correlation between stock return variance and the intensity of price jumps. The model permits closed-form representations for the optimal strategy and value functions in an expected utility theory setting. It also produces analytical expressions for the value function associated with relevant suboptimal strategies. Such an analytical setting allows for the first wealth-equivalent utility loss (WEL) analysis of the pitfalls of ignoring the aforementioned dependence. The model and results can be easily extended to the pair intensity-covariance in multi-assets. The WEL analysis is carried out for three different suboptimal classes: tailor-made incomplete markets, misspecifications in the parameters of the model, and time-independent (myopic) strategies. For the numerical section, we focus on the correlation between jump intensity and stock variance, which is assumed to be either zero or one in the existing literature. We demonstrate that simplistic assumptions like perfect dependence or independence could lead to wealth-equivalent losses of up to 61%. Similarly, a failure to hedge these variances and intensity drivers could cause losses of up to 95% (in particular, up to 60% due to the factors driving the dependence).