Modeling and evaluation of the option book hedging problem using stochastic programming
针对存在交易成本的不完全市场，开发了一个随机规划模型来对冲期权组合，该模型使用非参数方法估计无套利的波动率曲面，并在瑞典OMXS30指数期权上测试，证明其比动态delta和delta-vega对冲策略具有更低的风险和成本。
Hedging of an option book in an incomplete market with transaction costs is an important problem in finance that many banks have to solve on a daily basis. In this paper, we develop a stochastic programming (SP) model for the hedging problem in a realistic setting, where all transactions take place at observed bid and ask prices. The SP model relies on a realistic modeling of the important risk factors for the application, the price of the underlying security and the volatility surface. The volatility surface is unobservable and must be estimated from a cross section of observed option quotes that contain noise and possibly arbitrage. In order to produce arbitrage-free volatility surfaces of high quality as input to the SP model, a novel non-parametric estimation method is used. The dimension of the volatility surface is infinite and in order to be able solve the problem numerically, we use discretization and principal component analysis to reduce the dimensions of the problem. Testing the model out-of-sample for options on the Swedish OMXS30 index, we show that the SP model is able to produce a hedge that has both a lower realized risk and cost compared with dynamic delta and delta-vega hedging strategies.