Abstract

Purpose – The primary objective of this research is to develop new algorithms in the framework of deep neural networks for the valuation of options under dynamics driven by stochastic volatility models. We aim to use the Heston model for equity options to demonstrate the accuracy of our approach.

Design/methodology/approach – Physics-informed neural networks (PINNs) are trained to minimize a loss function that includes terms from the partial differential equation residuals, initial condition and boundary conditions evaluated at selected points in the space-time domain. Speed and accuracy comparisons are carried out against single hidden-layer neural networks, called physics-informed extreme learning machines (PIELMs). American options are formulated as linear complementarity problems, and PINNs are applied in conjunction with penalty methods for the computation of the option prices.

Findings – For American options under the Heston model, PINNs yield accurate prices. Computed Greeks sensitivities are in close agreement with those reported for mesh-based methods. In contrast to mesh-based penalty methods for American options, PINNs work with smaller values of the penalty term. For the real estate index American option problem, numerical prices obtained using PINNs have comparable accuracies as those obtained by a high-order radial basis functions finite difference scheme.

Practical implications – There is a lack of reliable pricing models for pricing property derivatives. This work contributes to developing accurate neural network algorithms.

Kyoto, Japan -- Superconductors are materials that can conduct electricity with zero resistance, usually only at very low temperatures. Most superconductors behave according to well-established rules, but strontium ruthenate, Sr₂RuO₄, has defied clear understanding since its superconducting properties were discovered in 1994. It is considered one of the cleanest and best-studied unconventional superconductors, yet scientists still debate the precise structure and symmetry of the electron pairing that gives rise to its remarkable properties.

One powerful way to identify the underlying superconducting state is to measure how the superconducting transition temperature, or T_c, changes under strain, since different superconducting states respond differently when a crystal is stretched, compressed, or twisted. Many earlier experiments, especially ultrasound studies, suggested that Sr₂RuO₄ might host a two-component superconducting state, a more complex form of superconductivity that can support exotic behaviors such as internal magnetic fields or multiple coexisting superconducting domains. But a genuine two-component state is expected to respond strongly to shear strain.

This inspired a team of researchers from Kyoto University to use strain to understand the true nature of the superconducting state of Sr₂RuO₄. The researchers developed a technique that allowed them to apply three distinct kinds of shear strain to extremely thin Sr₂RuO₄ crystals. Shear strain is a type of distortion that shifts part of the crystal sideways, similar to sliding the top of a deck of cards relative to the bottom. The strain levels were carefully measured using high-resolution optical imaging down to 30 degrees K (−243 degrees C). The key discovery: the superconducting temperature hardly changed at all. Any shift in T_c was smaller than 10 millikelvin per percent strain, effectively below the detection limit.

Every day, liquefied natural gas terminals around the world warm ultra cold LNG back into gas so it can be delivered to homes, power plants, and industry. In the process, an enormous amount of cold energy is released and largely wasted. A new study shows that this overlooked resource could be used to recover valuable hydrocarbons such as ethane and liquefied petroleum gas, creating both economic and environmental benefits.

Scientists have discovered wintertime seismic activity in the ocean around Antarctica controls summer growth of phytoplankton, tiny organisms that fuel the marine food web and sequester huge amounts of carbon from Earth’s atmosphere.

More than a decade ago, data from the Cassini Mission to Saturn suggested that the planet's largest moon, Titan, had a vast ocean of liquid water below its frozen surface. In a new study, UW researchers teamed up with NASA scientists to show that the interior is likely composed of slushy layers instead.

A team from the Institute of Industrial Science, The University of Tokyo has developed MatAgent, an AI system powered by a large language model. By reasoning in natural language, using memory, and learning from feedback, MatAgent explores new inorganic materials with a human-like process while explaining each step it takes.