A directional movement trading strategy using jump-diffusion price dynamics

The purpose of this paper is to forecast stock prices using Merton's jump-diffusion model and develop a directional movement (DM) trading strategy based on the price forecasts. The formula for the probability density function of Merton's daily logarithmic stock return has been simplified. Stock price dynamics of ten companies listed in Bombay Stock Exchange are studied. Both the Black-Scholes and Merton models are compared to fit the historical stock data as well as forecasting stock prices and it is found that the Merton model gives superior in-sample and out-of-sample performances. The adaptive barrier algorithm of Lange is used to find the maximum likelihood estimates of the Merton parameters. Finally, two trading strategies - the buy-and-hold (BH) strategy and the DM strategy are compared. The DM strategy outperforms the BH strategy for most of these ten stocks as well as when traded with a Markowitz minimum variance portfolio of these stocks.