A Research On Interest Rate Regulation, Index Tracking, Options Hedging Based On Stochastic Model Predictive Control

Uncertainties need to be carefully considered when making decision in money market, stock market and options market.Uncertainties represent risks that need considered when making decision. Application of advanced control methods to solve economic and financial problems has an important reference value. In recent years, research of stochastic model predictive control has made some progress. This paper study the monetary policy, index tracking, and dynamic hedging options based on stochastic model predictive control, making the following work:(1) TVP-VAR model is built based on output gap, CPI, short-term interest rate data of China form 2000-2015. Model parameters are estimated by the Markov Chain Monte Carlo. Coefficient of TVP-VAR model vary with time fitting well with the fact that China macroeconomic model’s evolution. Subsequently, stochastic model predictive control and linear quadratic optimal control were compared in simulation, the results show that stochastic model predictive control’s advantage in dealing with constraints. Stochastic model predictive control is forward-looking, avoiding the short-sighted of "discretion", on the other hand can consider constraint conditions, more flexibility compared to the "optimal commitment".(2)By modeling the asset dynamics as a linear system subject to state and control multiplicative noise,considering transaction costs, short selling restrictions, the proportion of total assets investing on stock limit, index tracking can be tackled by stochastic model predictive control. Simulation and empirical results based on the actual data of Chinese stock market also demonstrate the effectiveness of the stochastic model predictive control.(3) The classical BSM model and BCC model, containing stochastic volatility,stochastic interest rate, jumping risk,are used to describe stock price dynamics. By employing existing option pricing engines for estimating future option prices, dynamic option hedging can be solved by stochastic model predictive control based on scenario simulation. Monte Carlo simulation and actual data on Shanghai 50 ETF options verify the validity and flexibility of stochastic model predictive control.The result is better than delta hedging.Stochastic model predictive control’s flexibility, explicit processing capacity constraints provides a new way to solve the problem. This paper improved the studies of the regulation of interest rates, stock tracking and dynamic hedging options, and has a certain reference value forthe related decision problem in actual.