Abstract: In order to reflect the long memory property of the financial asset, the sub-fractional Brownian motion is introduced to capture the underlying asset of covered warrants. The pricing model of covered warrants is proposed by using the theory of stochastic integration and the method of partial differential equations. Moreover, the problem of parameter estimation is also discussed in this paper. Finally, an empirical study based on China's warrant market is presented. The pricing results of different models illustrate that the long memory property and the transaction costs have a significant impact on pricing results.

Key words: sub-fractional Brownian motion, transaction costs, covered warrants, partial differential equation, quadratic variation