We present a stochastic model of the within-host population dynamics of lymphatic filariasis, and use a simulated goodness-of-fit (GOF) method to estimate immunological parameters and their confidence intervals from experimental data. A variety of deterministic moment closure approximations to the stochastic system are explored and compared with simulation results. For the maximum GOF parameter estimates, none of the methods of closure accurately reproduce the behaviour of the stochastic model. However, direct analysis of the stochastic model demonstrates that the high levels of variation observed in the data can be reproduced without requiring parameters to vary between hosts. This indicates that the observed aggregation of parasite load may be dynamically generated by random variation in the development of an effective immune response against parasite larvae.