The aim of this dissertation is to analyze price changes from the aspects of market microstructure, study the optimal portfolio selection of an individual with the target level of wealth, and estimate multi-factor term structure models.
These studies, which are important both in academic and industrial financial engineering, provide the following contributions.
In the first study, I use the TAQ data of KOSPI 200 index futures market to test the effect of orders at the best quotes on price changes with the model proposed in Cont et al. (2014).
The test results suggest that additional assumptions are necessary when the model is considered.
The model performance varying with observation timescale is also discussed.
The second study deals with the problem of determining optimal strategies of an individual who has a target level of wealth at a specific time.
In this case, the individual's utility function of terminal wealth is not differentiable.
I use a simulation-based approach using Malliavin calculus, and obtain the optimal policies for achieving the goal.
This is an extension of the method proposed in Detemple et al. (2003) in the sense that a non-smooth utility function is considered.
In the third study, I estimate and compare multi-factor term structure models using the efficient method of moments estimation.
The affine and quadratic term structure models are considered.
The difference between the existing literature and this study is that the positivity constraint is not imposed, which reflects the recently observed negative interest rates.
Relaxing the constraint results in improvement in the goodness-of-fit test.
This implies that it has to be reconsidered to impose the positivity constraint of interest rates on term structure models.