Optimal annuitisation in a deterministic financial environment

Decisions in Economics and Finance - The global reforms to public pension schemes over the last thirty years have progressively reduced individuals’ post-retirement social security income. In...     

Minimizing the Risk of a Financial Product Using a Put Option

In this article, we elaborate a method for determining the optimal strike price for a put option, used to hedge a position in a financial product such as a basket of shares and a bond. This strike price is optimal in the sense that it minimizes, for a given budget, a class of risk measures satisfying certain properties. Formulas are derived for one single underlying as well as for a weighted sum of underlyings. For the latter we will consider two cases depending on the dependence structure of the components in this weighted sum. Applications and numerical results are presented.     

A self-exciting switching jump diffusion: properties,calibration and hitting time

A way to model the clustering of jumps in asset prices consists in combining a diffusion process with a jump Hawkes process in the dynamics of the asset prices. This article proposes a new alternative model based on regime switching processes, referred to as a self-exciting switching jump diffusion (SESJD) model. In this model, jumps in the asset prices are synchronized with changes of states of a hidden Markov chain. The matrix of transition probabilities of this chain is designed in order to approximate the dynamics of a Hawkes process. This model presents several advantages compared to other jump clustering models. Firstly, the SESJD model is easy to fit to time series since estimation can be performed with an enhanced Hamilton filter. Secondly, the model explains various forms of option volatility smiles. Thirdly, several properties about the hitting times of the SESJD model can be inferred by using a fluid embedding technique, which leads to closed form expressions for some financial derivatives, like perpetual binary options.