An Importance Sampling Approach for Exploring Likelihoods of Stochastic Differential Equations

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Grant Schneider*+
• Companies: OSU
• Keywords: Stochastic Differential Equations ; Importance Sampler

Abstract

Stochastic Differential Equations (SDEs) are used to model processes from many different disciplines, including finance, biology, and engineering. While these processes are continuously defined, inference is based on data observed at only a finite number of locations. This typically leads to intractable likelihoods, which causes difficulty in statistical inference, as it is impossible to observe a complete path in practice. Two competing methods have been proposed to overcome the problem of intractable likelihoods. The first method develops approximate likelihoods, whereas the second builds a likelihood based on a "skeleton", a sample of plausible missing paths compatible with the observed data. Both methods have practical difficulties. To overcome these issues we propose a novel importance sampler that combines the best of both methods. Using data simulated from various models in both discrete and continuous time settings, we demonstrate the performance of our method. We motivate this research with an application from finance.