On highly efficient methods for pricing options with and without early exercise
C. Oosterlee (Netherlands and Delft University of Technology, Netherlands)
In this presentation we will present two different methods for pricing options and compare their performance. The first method is fast and accurate for pricing early exercise and certain exotic options in computational finance.
It is the so-called CONV method, which is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by recognising that it is a convolution. The resulting convolution is dealt with numerically by using the Fast Fourier Transform (FFT).
The second, more recent, pricing method is based on the Fourier-cosine expansion of the risk-neutral valuation formula. It is applicable to options with and without early exercise features, to a wide variety of payoffs and only requires the knowledge of the characteristic function of the model.
As such the method is applicable within many regular affine models, among which the class of exponential L'evy models. We will show that this method is also highly efficient for pricing options under the Heston model and is thus a suitable candidate for calibration.
We will compare the two pricing methods presented for some extreme test cases.