汇率期权套期保值模型及其应用
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摘要
针对出口企业汇率风险管理问题,考虑购买期权预算约束,建立汇率期权套期保值模型。借助Copula函数推导出套期保值组合的分布函数,建立最小化CVaR的期权套期保值模型。利用等价转换法对模型进一步转化,并给出了模型的算法步骤。最后,以中国铂金出口企业汇率期权套期保值问题进行实证分析。实证结果表明:企业利用汇率期权套期保值可以降低CVaR风险;最优敲定价格不受出口企业风险规避度的影响;企业风险规避度越大,利用汇率期权套期保值其CVaR风险越小。期权最优敲定价格随着预算的增加而增加,但在预算一定的条件下,企业不能盲目购买敲定价格高的看跌期权,建议购买敲定价格略小于汇率当前值的期权进行套期保值。
In view of the exchange rate risk management issues in export enterprises, and considering the budget constraint on purchasing options, a hedging model of exchange rate options was proposed. First, the Copula function was used to derive the distribution function of the hedged portfolio. Then, the hedging model of options with the objective of minimizing CVaR(conditional value-at-risk) was established. Besides, the model was further transformed by using the equivalence transformation method, and the algorithm steps of the model were presented. Finally, an empirical analysis was conducted by taking a Chinese platinum export enterprise as an example. The results show that the CVaR can be decreased by hedging of exchange rate options. The subjective risk aversion of the enterprise does not play any role with respect to the optimal option strike price, and as the risk aversion increases, the CVaR decreases. The optimal strike price increases with the budget enhancing. However, the export enterprise should not arbitrarily buy put options with higher strike prices. Given a budget, the optimal strike price is suggested to be slightly less than the current value of the exchange rate.
In view of the exchange rate risk management issues in export enterprises, and considering the budget constraint on purchasing options, a hedging model of exchange rate options was proposed. First, the Copula function was used to derive the distribution function of the hedged portfolio. Then, the hedging model of options with the objective of minimizing CVaR(conditional value-at-risk) was established. Besides, the model was further transformed by using the equivalence transformation method, and the algorithm steps of the model were presented. Finally, an empirical analysis was conducted by taking a Chinese platinum export enterprise as an example. The results show that the CVaR can be decreased by hedging of exchange rate options. The subjective risk aversion of the enterprise does not play any role with respect to the optimal option strike price, and as the risk aversion increases, the CVaR decreases. The optimal strike price increases with the budget enhancing. However, the export enterprise should not arbitrarily buy put options with higher strike prices. Given a budget, the optimal strike price is suggested to be slightly less than the current value of the exchange rate.
引文
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[28]张高勋,田益祥,李秋敏.多元非线性期权定价模型及实证分析[J].系统管理学报,2014,23(2):200-207.
[29]Patton A J.Copula-based models for financial time series[M].Berlin:Springer,2009.
[30]Werner H.Conditional value-at-risk bounds for compound Poisson risk and a normal approximation[J].Journal of Applied Mathematics,2003,3(3):141-153.
[31]Bajo E,Barbi M,Romagnobi S.A generalized approach to optimal hedging with option contracts[J].The European Journal of Finance,2015,21(9):713-733.
[2]Bodnar G M,Wong M H F.Estimating exchange rate exposures:Issues in model structure[J].Financial Management,2003,32(1):35-67.
[3]Ito T,Koibuchi S,Sato K,et al.Exchange rate exposure and risk management:The case of Japanese exporting firms[J].Journal of The Japanese and International Economies,2016,41(9):17-29.
[4]Allayannis G,Ofek E.Exchange rate exposure,hedging,and the use of foreign currency derivatives[J].Journal of International Money and Finance,2001,20(2):273-296.
[5]Aabo T,Ploeen R.The german humpback:Internationalization and foreign exchange hedging[J].Journal of Multinational Financial Management,2014,27(2):114-129.
[6]斯文.银行衍生品的信贷扩张效应研究[J].金融论坛,2013,211(7):54-61.
[7]斯文.我国外汇衍生品市场发展对出口影响的实证分析[J].世界经济研究,2013,228(2):35-41.
[8]Bodnar G M,Gebhardt G.Derivatives usage by USnon-financial firms:A comparative survey[J].Journal of International Financial Management and Accounting,1999,10(3):153-187.
[9]尹力博,韩立岩.国际投资汇率风险的综合套保策略研究[J].中国管理科学,2014,22(2):1-6.
[10]Adam-Muller A F A.Export and hedging decisions under revenue and exchange rate risk:A note[J].European Economic Review,1997,41(7):1421-1426.
[11]Wong K P.International trade and hedging under joint price and exchange rate uncertainty[J].International Review of Economics and Finance,2013,27(2):160-170.
[12]马超群,王宝兵.基于Copula-GARCH模型的外汇期货套期保值比率研究[J].统计与决策,2011,8(12):124-128.
[13]余湄,谢海滨,高茜.国际投资中的汇率风险对冲问题研究[J].系统工程理论与实践,2014,34(S):67-74.
[14]Benet B A,Luft C F.Hedging performance of SPXindex options and S&P 500futures[J].Journal of Futures Markets,1995,156:691-717.
[15]Lien D,Tse Y K.Hedging downside risk:Futures versus options[J].International Review of Economics and Finance,2001,102:1059-1069.
[16]Wong K P.Export flexibility and currency hedging[J].International Economic Review,2003,44(4):1295-1312.
[17]Wong K P.Production and futures hedging with statedependent background risk[J].International Review of Economics&Finance,2012,24(3):177-184.
[18]廖萍康,张卫国,傅俊辉.考虑机会成本的最优期货备用保证金需求[J].系统管理学报,2013,22(1):91-98.
[19]Sklar A.Fonction de repartition an dirnensionset lears marges[J].Pubucations de lInstitut de Statistique de LUniversite de Paris,1959,8:229-231.
[20]韦艳华,张世英.Copula理论及其在金融分析上的应用[M].北京:清华大学出版社,2008.
[21]Chen Y H,Tu A H.Estimating hedged portfolio value-at-risk using the conditional copula:An illustration of model risk[J].International Review of Economics&Finance,2013,27(6):514-528.
[22]Rivieccio G,Luca G D.Copula function approaches for the analysis of serial and cross dependence in stock returns[J].Finance Research Letters,2016,17(5):55-61.
[23]Domino K,Blachowicz T.The use of copula functions for modeling the risk of investment in shares traded on the Warsaw stock exchange[J].Physica AStatistical Mechanics&Its Application,2015,424(11):142-151.
[24]Ahn D H,Boudoukh J,Richardson M,et al.Optimal risk management using options[J].Journal of Finance,1999,54(1):359-375.
[25]Melnikov A,Smirnov I.Dynamic hedging of conditional value-at-risk[J].Insurance Mathematics&Economics,2012,51(1):182-190.
[26]Capinsk M J.Hedging conditional value at risk with options[J].European Journal of Operational Research,2015,242(2):688-691.
[27]Bajo E,Barbi M,Romagnoli S.Optimal corporate hedging using options with basis and production risk[J].North American Journal of Economics and Finance,2014,30(11):56-71.
[28]张高勋,田益祥,李秋敏.多元非线性期权定价模型及实证分析[J].系统管理学报,2014,23(2):200-207.
[29]Patton A J.Copula-based models for financial time series[M].Berlin:Springer,2009.
[30]Werner H.Conditional value-at-risk bounds for compound Poisson risk and a normal approximation[J].Journal of Applied Mathematics,2003,3(3):141-153.
[31]Bajo E,Barbi M,Romagnobi S.A generalized approach to optimal hedging with option contracts[J].The European Journal of Finance,2015,21(9):713-733.