Predicting stock price movement is generally accepted to be challenging such that until today it is continuously being attempted. This paper attempts to address the problem of stock price movement using continuous time models. Specifically, the paper provides comparative analysis of continuous time models-General Brownian Motion (GBM) and Variance Gamma (VG) in predicting the direction and accurate stock price levels using Monte Carlo methods-Quasi Monte Carlo (QMC) and Least Squares Monte Carlo (LSMC). The hit ratio and mean-absolute percentage error (MAPE) were used to evaluate the models. The empirical tests suggest that either the GBM model or VG model in any Monte Carlo method can be used to predict the direction of stock price movement. In terms of predicting the stock price values, the empirical findings suggest that the GBM model performs well in the QMC method and the VG model performs well in the LSMC method.
The paper looks at the quantification of risks of trading strategies in incomplete markets. We realized that the no-arbitrage price intervals are unacceptably large. From a risk management point of view, we are concerned with finding prices that are acceptable to the market. The acceptability of the prices is assessed by risk measures. Plausible risk measures give price bounds that are suitable for use as bid-ask prices. Furthermore, the risk measures should be able to compensate for the unhedgeable risk to an extent. Conic finance provides plausible bid-ask prices that are determined by the probability distribution of the cash flows only. We apply the theory to obtain bid-ask prices in the assessment of the risks of trading strategies. We analyze two popular trading strategies-bull call the spread strategy and bear call spread strategy. Comparison of risk profiles for the strategies is done between the Variance Gamma Scalable Self Decomposable model and the Black-Scholes model. The findings indicate that using bid-ask prices compensates for the unhedgeable risk and reduces the spread between bid-ask prices.
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