Simulation estimation of continuous-time models with applications to finance

摘要: Over recent years, we have witnessed a rapid development in the body of economic theory with applications to finance. It has had great success finding theoretical explanations phenomena. Typically, theories are employed that defined by mathematical models. Finance particular drawn upon and developed stochastic differential equations. These produce elegant tractable frameworks which help us better understand world. To directly apply such theories, models must be assessed their parameters estimated. Implementation requires estimation model's elements using statistical techniques. fit model observed data. Unfortunately, existing methods do not work satisfactorily when applied many financial methods, complex often yield inaccurate results. Consequently, simpler analytical preferred, but these typically unrealistic representations underlying process, given stylised facts reported literature. In practical applications, data is at discrete intervals discretisation used approximate continuous-time model. This can lead biased estimates, since true assumed continuous. thesis develops new estimate types models, objective obtaining more accurate estimates present. The applicable general As solution continuous process rarely known for rely on building an Euler-Maruyama simulation techniques obtain distribution unknown quantities interest. We propose simulate missing paths between points reduce bias from Alternatively, one could use sophisticated scheme discretise process. implementation require density evaluate any point. until now only been possible scheme. One contribution show existence closed form higher order Milstein likelihood based method implemented within Bayesian paradigm, as context analytically easier. Concerning methodology, emphasis placed efficiency; design affects accuracy stability conjunction estimation, it important provide inference diagnostic procedures. Meaningful information results extracted summarised. necessitates developing plausibility hence dataset. An aspect evaluation concerns ability compare across range alternatives. advantage framework allows comparison non-nested aim thus efficient conduct meaningful inference, performance being through tools.