Modelling rain risk: a multi‐order Markov chain model approach

Purpose - The purpose of this paper is to investigate the best frequency description of a chain dependent Markov process for the daily simulation of precipitation. The influence of the order of the Markov chain model to simulate daily precipitation occurrence is evaluated. A mixed‐order model is constructed and compared to a simple first‐order model to evaluate the importance of the model order for the pricing of a rainfall index put option. Design/methodology/approach - For the first time a mixed‐order Markov chain model is presented where the monthly varying order was chosen based on a Bayesian information criteria analysis of rainfall data for one weather station in the US. The outcome of this model is compared to simpler Markov models and to burn analysis results. Findings - The comparison indicate that there is only a slightly better representation of the rain statistics in the theoretically best mixed‐order Markov chain model compared to a more simple first‐order model. Clear differences between the daily simulation and the burn method are found when pricing a put option on a rainfall index. All daily simulation models underestimate the volatility of the monthly rainfall amount especially in the summer months. Research limitations/implications - To assess the robustness and any geographical dependence of the bias in the volatility a systematic analysis could be applied to more weather stations across the US in further studies. Practical implications - The bias in the volatility has significant influence on the price of the put option considered here and limits the use of such a model for risk analyses, e.g. for an extreme event cover. Originality/value - For the first time a multi‐order Markov chain model is applied to price a precipitation derivative. While the focus of previous studies was the appropriate choice for the intensity process, the importance of the frequency process is investigated in this paper.