By means of Malliavin Calculus we see that the classical Hull and White formula for option pricing can be extended to the case where the noise driving the volatility process is correlated with the noise driving the stock prices. This extension will allow us to construct option pricing approximation formulas. Numerical examples are presented.

This paper provides a novel method to estimate β thoroughly based on option prices. Through combining the market model and the multivariate risk-neutral valuation relationship in Stapleton and Subrahmanyam (1984) and Câmara (2003), we develop a pricing model for individual stock options involving the volatility of the market index level and the levels of the β and the idiosyncratic risk of the ...

I propose a new measure of common, time-varying tail risk for large cross sections of stock returns. Stock return tails are described by a power law in which the power law exponent is allowed to transition smoothly through time as a function of recent data. It is motivated by asset pricing theory and is estimable via quasi-maximum likelihood. Estimates indicate substantial time variation in sto...

Uncertain differential equation with jumps is a type of differential equation driven by two classes of uncertain processes, namely canonical process and renewal process. Based on uncertain differential equation with jumps, this paper proposes a stock model with jumps for uncertain financial markets. Furthermore, the European call and put option pricing formulas for the stock model are formulate...

The stock market is a popular topic in Twitter. The number of tweets concerning a stock varies over days, and sometimes exhibits a significant spike. In this paper, we investigate the relationship between Twitter volume spikes and stock options pricing. We start with the underlying assumption of the Black–Scholes model, the most widely used model for stock options pricing, and investigate when ...

In recent years, graphics processing units have made parallel processing affordable with the price of personal desktop computers. This report investigates the computational aspects of calculating simple moving average and exponential moving average operations, two of the most popular financial indicators. In this report, we also investigate the usage of GPU to run artificial neural network as a...

Using a new dataset which contains monthly data on 1,015 stocks traded on the London Stock Exchange between 1825 and 1870, we investigate the cross section of stock returns in this early capital market. Unique features of this market allow us to evaluate the veracity of several popular explanations of asset pricing behavior. Using portfolio analysis and Fama-MacBeth regressions, we find that st...