Monte Carlo simulation

The valuation of knock-out power calls under Black–Scholes framework

Knock-out power calls are options that incorporate barriers to the valuation of power calls.  Introducing barriers to power calls reduces the costs to hold power calls which are known to have higher leverage than the standard vanillas.  In this paper, we model the valuation of knock-out power calls using Crank–Nicolson and Monte Carlo simulation under Black–Scholes environment.  Results show that Crank–Nicolson is more accurate and more efficient than Monte Carlo simulation for pricing knock-out power calls.