Implied volatility estimation for Asian options via monte carlo methods

Abstract

First of all, we discuss about the major issue of computing the implied volatility for multiple kinds of options, such as European options, digital options, but most of all are the over-the-counter (OTC) traded Asian options, via Monte Carlo (MC) methods. The other method we combine with is the Newton-Raphson (Newton) which helps to solve the non-linear equations to get the implied volatility. The optimized results of the methods depend on the accuracy, fast and efficient computation of the corresponding options’ Vegas. To get those expected results, we utilize the method of logarithmic derivatives instead of the common classical approach method to archive the best results. With our simulation justifications, our document shows that the new method results are much more better than the classical one. Finally, we indicate the localization and variance reducing can significantly improve the numerical results of the method. Keyword: Asian Options, Implied volatility, Exotic options, Monte Carlo Simulation, Logarithmic derivative, Newton method.