Dividend based risk measures: A Markov chain approach

Computations of risk measures in the context of the dividend valuation model is a crucial aspect to deal with when investors decide to buy a share of common stock. This is achieved by using a Markov chain model of growth-dividend evolution, imposing an assumption that controls the growth of the dividend process and in turn allows for the computation of the moments of the price process and the fulfillment of a set of transversality conditions which allows avoiding the presence of speculative bubbles in the market. The probability distribution of the fundamental value of the stock is recovered by solving a moment problem, based on the solution of a maximum-entropy approach from which it is possible to compute classical risk measures based on these fundamental variables. The methodology is applied to real dividend data from the S&P 500 index. Results show that our model provides complete information about the fundamental price not limited to its expectation.