Information and option pricings
将股票波动与基于信息的人类活动联系起来，提出一个不完整市场模型，结合Black-Scholes模型和隐马尔可夫过程，给出欧式看涨期权的无套利定价公式，并用IBM股票模拟验证信息影响市场。
How can one relate stock fluctuations and information-based human activities? We present a model of an incomplete market by adjoining the Black-Scholes exponential Brownian motion model for stock fluctuations with a hidden Markov process, which represents the state of information in the investors' community. The drift and volatility parameters take different values depending on the state of this hidden Markov process. Standard option pricing procedure under this model becomes problematic. Yet, with an additional economic assumption, we provide an explicit closed-form formula for the arbitrage-free price of the European call option. Our model can be discretized via a Skorohod embedding technique. We conclude with an example of a simulation of IBM stock, which shows that, not surprisingly, information does affect the market.