Pricing equity warrants with a promised lowest price in Merton’s jump–diffusion model

Motivated by the empirical evidence of jumps in the dynamics of firm behavior, this paper considers the problem of pricing equity warrants in the presence of a promised lowest price when the price of the underlying asset follows the Merton’s jump–diffusion process. Using the Martingale approach, we propose a valuation model of equity warrants based on the firm value, its volatility, and parameters of the jump component, which are not directly observable. To implement our pricing model empirically, this paper also provides a promising estimation method for obtaining these desired variables based on observable data, such as stock prices and the book value of total liability. We conduct an empirical study to ascertain the performance of our proposed model using the data of Changdian warrant collected from 25 May 2006 (the listing date) to 29 January 2007 (the expiration date). Furthermore, the comparison of traditional models (such as the Black–Scholes model, the Noreen–Wolfson model, the Lauterbach–Schultz model, and the Ukhov model) with our model is presented. From the empirical study, we can see that the mean absolute error of our pricing model is 16.75%. By contrast, the Black–Scholes model, the Noreen–Wolfson model, the Lauterbach–Schultz model, and the Ukhov model applied to the same warrant produce mean absolute errors of 92.24%, 45.38%, 87.34%, 76.12%, respectively. Thus both the dilution effect and the jump feature cannot be ignored in determining the valuation of equity warrants.