Pricing equity warrants in Merton jump–diffusion model with credit risk

To take the jump effect into the dynamics of the firm’s value and to consider the debt of the levered firms, this paper considers the problem of pricing equity warrants in a firm with debt when the price of the underlying asset follows the Merton’s jump–diffusion process. Using the martingale approach, based on the firm value, its volatility, and parameters of the jump component, we propose a valuation framework for pricing equity warrants with different maturity of the debt. To implement our pricing model empirically, this paper also provides two promising estimation methods for obtaining these desired variables based on observed data, such as stock prices and the book value of liability. Furthermore, we provide numerical examples to study implementation of our model and to compare our model with some existing ones, including the Black–Scholes model, the Ukhov model and the Abínzano-Navas model.