Pricing Correlation Options: from the P. Carr and D. Madan Approach to the New Method Based on the Fourier Transform

Abstract

Pricing of options plays an important role in the financial industry. Investors knowing how to price derivative contracts quickly and accurately can beat the market. On the other hand market participants constructing their investment strategies with the use of options based on techniques that do not assure the highest computational speed and efficiency are doomed to failure. The aim of the article is to extend the existing methodology of pricing correlation options based on the Fourier transform. The article starts with a presentation of Carr and Madan's concept (Carr & Madan, 1999). Then other methods of pricing options with the use of the Fourier transform are summarized. Finally, a new approach to pricing derivative contracts is derived and then applied to the correlation options.

Pricing European Options in the Heston and the Double Heston models

“…There are many approaches to determining characteristic function of and calculating its inverse Fourier transform [Carr & Madan 1999, Attari 2004, Bates 2006and Orzechowski 2018. As some of the approaches has already been presented [Orzechowski 2020] in the later part of the article only formulas concerning the double Heston model are of interest.…”

Pricing European Options in the Variance Gamma Model

“…Assuming is the natural logarithm the exercise price , 0 is the price of the underlying asset at time = 0 and is the risk-free rate of return, the formulas for the price of the European call in the methods of P. Carr and D. Madan [Carr, Madan 1999], G. Bakshi and D. Madan [Bakshi, Madan 2000], M. Attari [Attari 2004], and A. Orzechowski [Orzechowski 2018] are the following: 1. P. Carr and D. Madan [1999] for = 1 (the method is referred to as VG-CM): (10) 2.…”

Is There Still Room for Increasing Speed in Algorithmic and High-Frequency Trading? The Case of European Options Priced in the Heston Model

“…In consequence, there are many ways of determining value of the European options in the Heston model. In the article special attention in this matter will be directed to the formulas developed by P. Carr and D. Madan [Carr, Madan 1999], G. Bakshi and D. Madan [Bakshi, Madan 2000], M. Attari [Attari 2004], and A. Orzechowski [Orzechowski 2018], i.e. : 1.…”