Options Pricing Monte Carlo vs Option Calculation

The Options Pricing Monte Carlo app prices power options: max(S^i -K,0) or max(K-S^i,0). It also shows the % of paths with positive payoffs. The normal inverse is calculated with Beasley-Springer-Moro method. The Heston tab is used to price options under stochastic volatility using Monte Carlo. It also prices European options using Black-Scholes and can also calculate Implied Vol. Normal is calculated by direct integration using Simpson method with a low tolerance. So 4 calculators in one: - Monte Carlo simulator for regular European and Power options. - Monte Carlo simulator for European options with stochastic vol (Heston model). - Black Scholes calculator for price and greeks and implied vol. - Simulation tab lets you visualize Brownian Motion with drift. (2D or vs time).

This is an effective and practical app for calculation of European-style option! Based on BSM Model: • support to calculate option price, implied volatility, put-call parity. • When you calculate option price/implied volatility, the greeks are calculated and show simultaneously. • Support to show option price/delta/gamma for 2D/3D interactively! • Overlay contracts' curve with different days/implied volatility in same graph. For example, to calculate option price: input underlying price, strike price, days to expire, riskless rate, implied volatility, tap the blue button in the bottom, the option price will be calculated and show immediately! Then tap the button in the top right, show function line of delta/gamma and underlying price in theory. Slide to change the underling price, see how price/delta/gamma changes.