考慮保證金約束下的套利限制

Abstract

本論文主要研究在隨機波動度下，當套利者面對套利機會時，套利者會如何決定自身的最適動態投資決策，本文得到套利者會隨著套利機會的大小而調整投資套利資產的比重；同時，若考慮財富限制下，套利者可能會採取部份投資行為，並主要去討論套利者的資本不足所產生的「財富效果｣現象。 而在數學模型部份，我們假設隨著波動度增加，在套利過程中會產生擴大現象，因此在數值分析中，分別考慮固定波動度、隨機波動度、固定風險溢酬係數與動態風險溢酬係數的情況下，我們可以找出套利價值與波動度之間的變動關係，得到套利價值在波動度的敏感程度較大時，可能很容易產生套利價值僵固性的現象。

The main purpose of the thesis is that in the stochastic volatility state when arbitrageurs face the arbitrage opportunities , they will decide their optimal dynamic portfolio strategy . We obtain the conclusion that arbitrageurs would adjust the weight with the value of arbitrage portfolio , and they find it optimal to underinvest in the arbitrage by taking a smaller position than collateral constraints allow . Furthermore, we discuss the existence of the Wealth effect , the main cause of the Wealth effect is that arbitrageurs are short of their capital . In the theoretical model , we assume that as the volatility increases , we find that there is an amplification phenomenon in the arbitrage . In the numerical analysis , under different conditions, such as constant volatility , stochastic volatility , constant risk premium and dynamic risk premium , we also find the relation between the value of arbitrage portfolio and the volatility .When the sensitivity of the volatileity is large enough , there may exist the rigidity of the value of arbitrage portfolio .