Dr Chittaranjan Mishra to discuss “Fast pricing of multi-asset American options under jump-diffusion models”

In the next chapter of Departmental Seminars Series, Department of Mathematics, SRM University-AP, Andhra Pradesh welcomes Dr Chittaranjan Mishra, Department of Mathematics, Indian Institute of Technology Ropar, to deliver a lecture on “Fast pricing of multi-asset American options under jump-diffusion models” on March 24, 2021, at 3 pm.

Multi-asset American options are interesting in many ways, e.g., they give the holder the flexibility to exercise at any time up to maturity, allow for risk diversification and for us, these contracts are mathematically challenging to price due to the non-availability of a closed-form formula. When jumps are introduced to model underlying assets, one will be required to solve a partial integro-differential complementary problem (PIDCP) for pricing these contracts. In these cases, we find that computing sufficiently accurate option prices in real-time is extremely difficult. That is because the in hand PIDCP involves a multi-dimensional partial integro-differential equation with a non-local double integral term. Solving these multi-dimensional PIDCP by advanced numerical techniques, such as a customized finite difference method, is very time-consuming, as the corresponding discretization matrices are huge in size. More importantly, the integral approximation matrix is also dense, posing a serious challenge to handle storage memory. Many efficient techniques are proposed primarily to handle the double integral term. However, the required solving time is still not practicable for practitioners.

In our research, we exploit the amazing parallel architecture of modern graphics processing units (GPUs) to solve computationally expensive scientific problems. Nevertheless, resolving the problem at hand by employing a GPU is not straightforward. It requires one to overcome many bottlenecks, such as in. In this work, we have investigated these issues in order to achieve substantial speed-ups compared to a sequential FD implementation.

Mathematics enthusiasts are requested to avail this opportunity to listen to our distinguished speaker on March 24th, at 3 pm.