When simulating discrete-time approximations of solutions of stochastic differential equations (SDEs), in particular martingales, numerical stability is clearly more important than some higher order of convergence. Discrete-time approximations of solutions of SDEs with multiplicative noise, similar to the Black-Scholes model, are widely used in simulation in finance. The stability criterion presented in this paper is designed to handle both scenario simulation and Monte Carlo simulation, i.e. both strong and weak approximations. Methods are identified that have the potential to overcome some of the numerical instabilities experienced when using the explicit Euler scheme. This is of particular importance in finance, where martingale dynamics arise frequently and the diffusion coefficients are often multiplicative. Stability regions for a range of schemes are visualized and analysed to provide a methodology for a better understanding of the numerical stability issues that arise from time to time in practice. The result being that schemes that have implicitness in the approximations of both the drift and the diffusion terms exhibit the largest stability regions. Most importantly, it is shown that by refining the time step size one can leave a stability region and may face numerical instabilities, which is not what one is used to experiencing in deterministic numerical analysis.

This paper introduces a behavioral sentiment model to explore the stylized facts in limit order markets. Simulation results show that both the noise and sentiment trading can generate the absence of autocorrelation in returns, long memory in the absolute returns and bid-ask spread, and the hump shaped mean depth profile of the order book. However, sentiment trading plays a unique role in explaining the fat tails in the return distribution, long memory in the trading volume, an increasing and non-linear relationship between trade imbalance and mid-price returns, and also the diagonal effect or event clustering in order submission types, all of which cannot be explained by noise trading. Therefore, behavioral sentiment is an important driving force behind some of the well-documented stylized facts in limit order markets.

This paper studies the Chinese warrant market that has been developed since August 2005. Empirical evidence shows that the market prices of warrants are much higher systematically than the Black-Scholes prices with historical volatility. The prices of a warrant and its underlying asset do not support the monotonicity, perfect correlation and option redundancy properties. The cumulated delta-hedged gains for almost all expired warrants are negative. The negative gains are mainly driven by the volatility risk, and the trading values of the warrants for puts and the market risk for calls. The investors are trading some other risks in addition to the underlying risk.

, and the guest editor, Qiaoqiao Zhu, and two anonymous referees for their helpful comments and suggestions. We acknowledge Chao Xu, Haichuan Xu, and Hongli Che for their assistance, and thank the CFFEX research center for data support. This paper is extracted from the final research report of the joint project submitted to CFFEX in February 2012; on May 31, 2012, CFFEX announced an increase in the position limit of the CSI 300 index futures to 300, in accordance with the policy suggestion in this paper. The views expressed here are those of the authors and do not necessarily reflect the view of CFFEX. The contents of this paper are the sole responsibility of the authors.

This paper studies the Chinese warrant market that has been developing since August 2005. Empirical evidence shows that the market prices of warrants are much higher systematically than the Black-Scholes prices with historical volatility. The prices of a warrant and its underlying asset do not support the monotonicity, perfect correlation and option redundancy properties. The cumulated delta-hedged gains for almost all expired warrants are negative. The negative gains are mainly driven by the volatility risk, and the trading values of the warrants for puts and the market risk for calls. The investors are trading some other risks in addition to the underlying risks.