Econometrics models form the backbone of data driven financial organisations. They allow economic phenomena to be modelled with statistical methods, leading to better-informed decision making.
Man Group, an active investment management firm headquartered in London, relies on option pricing models such as Cox-Ross-Rubinstein to value millions of options every day. Man Group’s quantitative researchers are continuously working to improve the performance of these models to gain a competitive edge, a search which has recently seen them evaluate IPUs, with impressive results.
“Option pricing is a critical workload for Man Group, and one that is computationally demanding. The Cox-Ross-Rubinstein method is still a good benchmark for testing this on IPUs. Recent research with Graphcore has demonstrated the massively parallel nature of the IPU, which can price options up to 21x faster than our CPUs,” said Balazs Domonkos, Senior Engineer in Alpha Technology, Man Group.
CPUs are still frequently chosen over GPUs as the hardware of choice in many financial institutions, due to their flexibility to handle econometrics workloads that cannot be easily vectorised. IPUs provide a good alternative to CPUs, as they can speed up these workloads by providing the same MIMD flexibility as the CPU, while offering much higher flop-rates and processing speed. Three types of hard-to-vectorise workloads that fit into this category are detailed below.
Conditional termination workloads. These workloads contain loops that continue until a condition is met, or a certain number of iterations have completed which is determined by the inputs. If using batch processing, all samples will have to complete before the batch can be considered complete. Examples include autocallable option pricing models, which can terminate if the autocall event has been triggered.
Sequential workloads. These can include iterative, loop-based and recursive workloads. In the case of a sequential workload which doesn't need to be run many times, it's not possible to vectorise because the output of the current operation is required as an input to the next. Examples include Hamiltonian Monte Carlo, which iteratively simulates Hamiltonian dynamics.
Input-dependent routing workloads. These are tree-based models and other forms of models that make use of conditional statements (if-statements). These workloads can be hard to vectorise if the operations performed on each element of the batch diverge. Decision trees with variable depths are a strong example.
In this blog post, we’ll look at an algorithm known as the Cox-Ross-Rubinstein (CRR) model. CRR is a popular algorithm for options pricing because its flexibility allows it to handle a wide range of conditions, such as the right of an holder to exercise the option at any time. We’ll talk through the workings of the CRR model, some of the intricacies that can come with vectorisation, and how you can implement it at scale in production on the IPU.
Pricing options with the CRR model
The Cox-Ross-Rubinstein (CRR) model prices an option by considering how the price of the asset could vary over a discrete number of simulated timesteps (n) between the valuation date and the expiration date. The higher the number of simulated timesteps, the more accurate the pricing.
There are two phases to the model. In phase 1, known as the forward pass, a tree of prices is generated by assuming the price of the underlying asset will either increase or decrease by a specific factor at each simulated timestep, from the current spot price S0. The factor by which the asset could increase or decrease is calculated as a function of the vo
