The recently concluded SIAM Conference on Financial Mathematics and Engineering (FM23) witnessed a presentation by a PhD student of our group, Michael Samet, on Quasi-Monte Carlo for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models. The Conference held at Philadelphia, Pennsylvania, U.S., between June 6-9, 2023.
Abstract:
High-dimensional option pricing using Fourier-based approaches is still active area of intensive research. When the expression of characteristic function is available, carefully designed Fourier pricing methods are prominent because they profit from high regularity of the integrand in the frequency space. In this work, we propose the use of Randomized Quasi-Monte Carlo (RQMC) method to efficiently evaluate multi-asset European options expressed via Fourier valuation formula. RQMC takes advantage of the smoothness of the integrand to achieve fast convergence, and allows for cheap computation of error estimates. However, the use of RQMC requires a change of variable mapping the unbounded integration domain to the hypercube, which may result in singularities at the corners of the hypercube. Moreover, a naive transformation of the integration domain may deteriorate the rate of convergence of the RQMC. To overcome this difficulty, we design a domain transformation strategy based on boundary growth conditions on the transformed integrand, which allows us to preserve the regularity of the integrand and consequently retain near-optimal convergence rates of RQMC. We showcase the effectiveness of combining the proposed domain transformation procedure with RQMC to compute the option price in the Fourier space for various multivariate pricing models and payoff functions.
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