Richard Liu — Page 2

arXiv2020

A Scalable and Cloud-Native Hyperparameter Tuning System

In this paper, we introduce Katib: a scalable, cloud-native, and production-ready hyperparameter tuning system that is agnostic of the underlying machine learning framework. Though there are multiple hyperparameter tuning systems available, this is the first one that caters to the needs of both users and administrators of the system. We present the motivation and design of the system and contrast it with existing hyperparameter tuning systems, especially in terms of multi-tenancy, scalability, fault-tolerance, and extensibility. It can be deployed on local machines, or hosted as a service in on-premise data centers, or in private/public clouds. We demonstrate the advantage of our system using experimental results as well as real-world, production use cases. Katib has active contributors from multiple companies and is open-sourced at \emph{https://github.com/kubeflow/katib} under the Apache 2.0 license.

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arXiv2018

Deep Learning-Based BSDE Solver for Libor Market Model with Application to Bermudan Swaption Pricing and Hedging

The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives with Libor market models is mainly carried out with Monte Carlo simulation. The PDE grid approach is not particularly feasible due to Curse of Dimensionality. The standard Monte Carlo method for American/Bermudan swaption pricing more or less uses regression to estimate expected value as a linear combination of basis functions (Longstaff and Schwartz). However, Monte Carlo method only provides the lower bound for American option price. Another complexity is the computation of the sensitivities of the option, the so-called Greeks, which are fundamental for a trader's hedging activity. Recently, an alternative numerical method based on deep learning and backward stochastic differential equations appeared in quite a few researches. For European style options the feedforward deep neural networks (DNN) show not only feasibility but also efficiency to obtain both prices and numerical Greeks. In this paper, a new backward DNN solver is proposed for Bermudan swaptions. Our approach is representing financial pricing problems in the form of high dimensional stochastic optimal control problems, FBSDEs, or equivalent PDEs. We demonstrate that using backward DNN the high-dimension Bermudan swaption pricing and hedging can be solved effectively and efficiently. A comparison between Monte Carlo simulation and the new method for pricing vanilla interest rate options manifests the superior performance of the new method. We then use this method to calculate prices and Greeks of Bermudan swaptions as a prelude for other Libor callable derivatives.

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