Monte Carlo simulation

Incorporating long memory into the modeling of gold prices

Inflation causes many people to move to gold as an option for savings because gold may be used as a hedging tool against currency devaluation and purchasing power erosion.  This has contributed to the increased interest in forecasting the prices at the gold market, just like predicting the prices at the stock market, which exhibits uncertain movement, which can be described mathematically with Geometric Brownian Motion (GBM) and Geometric Fractional Brownian Motion (GFBM).  This study aims to model Malaysian gold prices using both GBM and GFBM processes and compare the

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.