Author : Szymon Borak
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (13 download)
Book Synopsis FFT Based Option Pricing by : Szymon Borak
Download or read book FFT Based Option Pricing written by Szymon Borak and published by . This book was released on 2017 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Black-Scholes formula, one of the major breakthroughs of modern finance, allows for an easy and fast computation of option prices. But some of its assumptions, like constant volatility or log-normal distribution of asset prices, do not find justification in the markets. More complex models, which take into account the empirical facts, often lead to more computations and this time burden can become a severe problem when computation of many option prices is required, e.g. in calibration of the implied volatility surface. To overcome this problem Carr and Madan (1999) developed a fast method to compute option prices for a whole range of strikes. This method and its application are the theme of this chapter. In Section 1.3, we briefly discuss the Merton, Heston and Bates models concentrating on aspects relevant for the option pricing method. In the following section, we present the method of Carr and Madan which is based on the fast Fourier transform (FFT) and can be applied to a variety of models. We also consider brie∞y some further developments and give a short introduction to the FFT algorithm. In the last section, we apply the method to the three analyzed models, check the results by Monte Carlo simulations and comment on some numerical issues.