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- 2016
基于随机模型预测控制的欧式期权动态对冲
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Abstract:
本文应用随机模型预测控制的方法研究欧式期权的动态对冲问题。使用股票价格变动的BCC模型作为预测模型，模拟可能会出现的股票价格和期权价格的情景。在不考虑交易费用的情况下建立以跟踪误差的方差最小化为控制目标的优化控制模型。在考虑交易费用的情况下建立以跟踪误差的CVaR最小化为控制目标的优化控制模型。最后，通过蒙特卡洛仿真对基于随机模型预测控制的对冲方法和delta对冲方法的效果进行了对比分析，并且对华夏上证50ETF期权合约进行了实证分析，检验结果表明了基于随机模型预测控制的对冲方法的有效性。
| [1] | Merton R C.A Rational Theory of Option Pricing”[J].Bell Journal of Economics & Management Science, 1973, 4(1):141-183 |
| [2] | PP Boyle, T Vorst.Option Replication in Discrete Time with Transaction Costs[J].Journal of Finance, 1992, 47(1):271-293 |
| [3] | Scholes M S, Black F S.The Pricing of Options and Other Corporate Liabilities[J].Journal of Political Economy, 1973, 81(3):637-54 |
| [4] | Nguyen T H, Pergamenshchikov S.Approximate hedging problem with transaction costs in stochastic volatility markets[J]. Mathematical Finance, 2015, published online: 30 JUN 2015, DOI: 10.1111/mafi.12094. |
| [5] | Bemporad A, Puglia L, Gabbriellini T.A stochastic model predictive control approach to dynamic option hedging with transaction costs[C]// Proceedings of the American Control Conference. 2011:3862-3867. |
| [6] | HAYNE E.LELAND ?Option Pricing and Replication with Transactions Costs[J].Research Program in Finance Working Papers, 1985, 40(5):1283-1301 |
| [7] | Gondzio J, Kouwenberg R, Vorst T.Hedging options under transaction costs and stochastic volatility ☆[J].Journal of Economic Dynamics & Control, 2003, 27(6):1045-1068 |
| [8] | Zhao Y, Ziemba W T.A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation[J].Mathematical Programming, 2000, 89(2):293-309 |
| [9] | Merton R C.Option Prices When Underlying Stock Returns Are Discontinuous[J].Journal of Financial Economics, 1976, 3(1-2):125-144 |
| [10] | Heston S L.A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options[J].Review of Financial Studies, 1993, 6(2):327-343 |
| [11] | Primbs J A.LQR and receding horizon approaches to multi-dimensional option hedging under transaction costs[C]//American Control Conference (ACC), 2010. IEEE, 2010: 6891-6896. |
| [12] | Bemporad A, Gabbriellini T, Puglia L, et al.Scenario-based stochastic model predictive control for dynamic option hedging[C]// Decision and Control (CDC), 2010 49th IEEE Conference on. IEEE, 2010:6089-6094. |
| [13] | 尹力博, 韩立岩.人民币外汇期权套保策略:基于随机规划模型[J].管理科学学报, 2012, 15(11):31-44 |
| [14] | Bates D S.Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in thePHLX Deutschemark Options[J].Review of Financial Studies, 1996, 9(1):69-107 |
| [15] | Carr P, Stanley M, Madan D B.Option Valuation Using the Fast Fourier Transform[J]. Journal of Computational Finance, 2010, 2:61--73. |
| [16] | Lewis A L.A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes[J]. Ssrn Electronic Journal, 2010.1-24 |
| [17] | A Theory of the Term Structure of Interest Rates.A Theory of the Term Structure of Interest Rates[J].Econometrica, 1985, 53(2):385-407 |
| [18] | Bakshi G, Cao C, Chen Z.Empirical Performance of Alternative Option Pricing Models[J].Journal of Finance, 1997, 52(5):2003-2049 |
| [19] | James A.PrimbsDynamic hedging of basket options under proportional transaction costs using receding horizon control[J].International Journal of Control, 2009, 82(10):1841-1855 |
| [20] | Rockafellar R T, Uryasev S.Optimization of Conditional Value-At-Risk[J].Journal of Risk, 1999, 29(1):1071-1074 |
