Stochastic Process for Shocks in Financial Markets: An Application of Damped Harmonic Oscillation

• Main Authors: Tun-Hao Han, 韓敦皓
• Other Authors: Yao-Wen Hsu
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/8n7edz

碩士 === 國立臺灣大學 === 統計碩士學位學程 === 104 === In financial economics, the efficient-market hypothesis is well known for stating market behavior. Under this hypothesis, asset prices fully reflect all historical information, which implies that only new relevant information affects market prices. Investors’ reactions to the information is random and in a normally distributed pattern so that the change on the market price is also normally distributed. This is a strong argument for the use of geometric Brownian motion (GBM) on modeling stock prices. However, GBM is not a completely realistic model, in particular it fails to describe some properties of stock prices. One is that GBM is a continuous path through time, but in real life, stock price often show jumps. The other is the mean-reverting property. When stock price is far from its equilibrium due to some shocks, it will have a high chance to be adjusted to its equilibrium nearby, but GBM will still follow the trend even in an unreasonable price level. There have been several models conducted to modify GBM, some examples like Ornstein-Uhlenbeck model for mean-reverting property, jump-diffusion model for discontinuity, and affine jump-diffusion model for both. Recently, more and more economists believes the inefficiency of the market. Investors predictably overreact to new information, creating a large effect on the stock price, making the price oscillate. This kind of oscillation has not been described by those classical models. My thesis is to discuss the dynamic of the oscillation, and introducing a process in the framework of damped harmonic oscillation.