Calibration in the “real world” of a partially specified stochastic volatility model
研究了部分指定随机波动率模型的真实世界校准方法，不依赖期权价格，仅使用资产对数收益率和投资者先验信息，通过随机最优控制求解，并用S&P500数据验证了预测效果。
Abstract We study the “real world” calibration of a partially specified stochastic volatility model, where the analytic expressions of the asset price drift rate and of the stochastic variance drift are not specified. The model is calibrated matching the observed asset log returns and the priors assigned by the investor. No option price data are used in the calibration. The priors chosen for the asset price drift rate and for the stochastic variance drift are those suggested by the Heston model. For this reason, the model presented can be considered as an “enhanced” Heston model. The calibration problem is formulated as a stochastic optimal control problem and solved using the dynamic programming principle. The model presented and the Heston model are calibrated using synthetic and Standard & Poor 500 (S&P500) data. The calibrated models are used to produce 6, 12, and 24 months in the future synthetic and S&P500 forecasts.