Efficient computation of the likelihood expansions for diffusion models

Chenxu Li, Yu An, Dachuan Chen, Qi Lin and Nian Si

IISE Transactions, 2016, vol. 48, issue 12, 1156-1171

Abstract: Closed-form likelihood expansion is an important method for econometric assessment of continuous-time models driven by stochastic differential equations based on discretely sampled data. However, practical applications for sophisticated models usually involve significant computational efforts in calculating high-order expansion terms in order to obtain the desirable level of accuracy. We provide new and efficient algorithms for symbolically implementing the closed-form expansion of the transition density. First, combinatorial analysis leads to an alternative expression of the closed-form formula for assembling expansion terms from that currently available in the literature. Second, as the most challenging task and central building block for constructing the expansions, a novel analytical formula for calculating the conditional expectation of iterated Stratonovich integrals is proposed and a new algorithm for converting the conditional expectation of the multiplication of iterated Stratonovich integrals to a linear combination of conditional expectation of iterated Stratonovich integrals is developed. In addition to a procedure for creating expansions for a nonaffine exponential Ornstein–Uhlenbeck stochastic volatility model, we illustrate the computational performance of our method.

Date: 2016
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DOI: 10.1080/0740817X.2016.1200201

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