SWIFT valuation of discretely monitored arithmetic Asian options

Abstract

In this work, we propose an efficient and robust valuation of discretely monitored arithmetic Asian options based on Shannon wavelets. We employ the so-called SWIFT method, a Fourier inversion numerical technique with several important advantages with respect to the existing related methods. Particularly interesting is that SWIFT provides mechanisms to determine all the free-parameters in the method, based on a prescribed precision in the density approximation. The method is applied to two general classes of dynamics: exponential Lévy models and squareroot diffusions. Through the numerical experiments, we show that SWIFT outperforms state-ofthe-art methods in terms of accuracy and robustness, and shows an impressive speed in execution time.

SWIFT Calibration of the Heston Model

“…The calibration speed has been tested for three different sets of strike prices and maturities, which are available in Appendix B. In order to be sure that the calibration problem was properly converging, we chose θ (2) as the objective value for the Heston parameters. When testing each set, we perform the following actions,…”

“…Regarding the pricing, we use the SWIFT method presented in [1] for European options. This belongs to the class of Fourier inversion methods and has already been used for pricing Bermudan, barrier and Asian options (see [2,3]). The power of the SWIFT method partly relies on the knowledge of the characteristic function (ChF) in analytical form.…”

“…The last three sets of parameters are representative of long-term FX, interest rate, and equity options, respectively [32]. (1) is obtained from [5] and θ (2) is a plausible set of parameters proposed by us. It may not be representative of any real-world market, but it is only used as our objective value in our speed tests.…”

“…It may not be representative of any real-world market, but it is only used as our objective value in our speed tests. In Section 5.2, we will use an initial guess of θ (2) 0 = (1.5768, 0.0398, 0.5751, −0.5711, 0.0175) T .…”

“…Generate option price values for each strike-expiry pair using θ (2) as input. For this step, we used the SWIFT method (we also generated them using the CP method and checked that the difference between both results stayed under 10 −7 );…”