随机利率下的PPP项目实物期权评价研究
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摘要
PPP项目通常实施周期长,风险突出。传统的实物期权评价方法考虑了未来的不确定性和管理者柔性的价值,但是一般假设无风险利率是固定的,不符合利率长期内波动的特点,会造成投资者决策失误。本文考虑了未来无风险利率波动条件下,PPP项目中实物期权的价值。首先分析了PPP项目中通常存在的期权形式,其次研究了无风险利率三角逆变函数以及在此基础上得出模拟实物期权模型,并用案例对比分析固定利率和随机利率下的期权价值。结果显示,随机利率比固定利率下的期权价值更高,研究结论可以为PPP项目的投资者进行决策提供重要依据。
Due to the long concession period of PPP projects,there are many risks.The traditional real option evaluation takes into account the value of future uncertainty and flexibility of managers,where it is generally assumed that the risk-free rate is fixed.However,it fluctuates in a long term,and the ignorance of the fluctuation will lead to policy mistakes made by investors.The value of real option in PPP projects is evaluated considering the volatility of risk-free rate in future.This paper analyzes the options in PPP projects first.Then risk-free rate delta inverter function is studied,on this basis of which we get the model of real option through simulation.Using case analysis the research compares the differences of real option value at fixed interest rate and stochastic interest rate.The results illustrate that the value of the options under stochastic interest rate is greater than that of the options under the fixed interest rate.The contribution of this research is to provide scientific basis for investors of PPP projects to make decisions.
Due to the long concession period of PPP projects,there are many risks.The traditional real option evaluation takes into account the value of future uncertainty and flexibility of managers,where it is generally assumed that the risk-free rate is fixed.However,it fluctuates in a long term,and the ignorance of the fluctuation will lead to policy mistakes made by investors.The value of real option in PPP projects is evaluated considering the volatility of risk-free rate in future.This paper analyzes the options in PPP projects first.Then risk-free rate delta inverter function is studied,on this basis of which we get the model of real option through simulation.Using case analysis the research compares the differences of real option value at fixed interest rate and stochastic interest rate.The results illustrate that the value of the options under stochastic interest rate is greater than that of the options under the fixed interest rate.The contribution of this research is to provide scientific basis for investors of PPP projects to make decisions.
引文
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[3]Ni J Z,Melnyk S A,Ritchie,W J.,Flynn,B F.Why be first if it doesn't pay?The case of early adopters of CTPAT supply chain security certification[J].International Journal of Operations&Production Management,2016,36(10):1161-1181.DOI:10.1108/IJOPM-01-2015-0041.
[4]Liu J,Gao R,Cheah C Y J,Luo J.Evolutionary game of investors'opportunistic behaviour during the operational period in PPP projects[J].Construction Management and Economics,2017,35(3):137-153.DOI:10.1080/01446193.2016.1237033.
[5]侯峻.PPP模式在城市公共产品投资中的应用研究[J].现代城市研究,2008,6:21.
[6]叶晓甦,石世英,刘李红.PPP项目伙伴主体,合作环境与公共产品供给的关系研究——基于结构方程模型的分析[J].北京交通大学学报:社会科学版,2017,16(1):45-54.DOI:10.16797/j.cnki.11-5224/c.20170105.005.
[7]Zhang X.Win–win concession period determination methodology[J].Journal of Construction Engineering and Management,2009,135(6):550-558.DOI:10.1061/(ASCE)CO.1943-7862.0000012.
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[11]Myers S C.Determinants of corporate borrowing[J].Journal of Financial Economics,1977,5(2):147-175.DOI:10.1016/0304-405X(77)90015-0.
[12]Cheah C Y J,Liu J.Real option evaluation of complex infrastructure projects:The case of Dabhol Power[J].Journal of Financial Management of Property and Construction,2005,10(1):55-68.DOI:10.1108/13664380580001064.
[13]Cheah C Y J,Liu J.Valuing governmental support in infrastructure projects as real options using Monte Carlo simulation[J].Construction Management and Economics,2006,24(5):545-554.DOI:10.1080/01446190500435572.
[14]Paddock J,Siegel D,Smith J.Option valuation of claims on physical assets:the case of off shore petroleum lease[J].Quarterly Journal Economics,1988,103(3):479-508.
[15]李岱.企业技术创新战略投资最优时机的实物期权分析[J].系统工程,2014,32(1):82-86.
[16]Merton R C.Theory of rational option pricing[J].Bell Journal of Economics and Management Science,1973,4(1):141-183.
[17]曹国华,陈冀.基于随机利率和时间偏好不一致的实物期权定价[J].统计与决策,2008(10):36-38.
[18]曹国华,章文芳,陈艳丽.随机利率下投资项目价值研究[J].技术经济,2011,30(4):73-76.
[19]袁国军,肖庆宪.基于近似对冲跳跃风险的期权定价[J].系统工程,2013,31(3):15-19.Yuan G.Xiao Q.The pricing options based on approximating hedge jump risk[J].Systems Engineering,2013,31(3):15-19.
[20]朱秀丽,邱菀华.基于实物期权的铁路地下化项目PPP模式投资决策分析[J].系统工程,2011,29(3):117-120.
[21]李明顺,陈涛,滕敏.交通基础设施PPP项目实物期权定价及敏感性分析[J].系统工程,2011,29(3):67-73.
[22]唐文彬,张飞涟,马超群.基于模糊实物期权的城市轨道交通项目投资价值[J].系统工程,2011,29(12):110-115.
[23]Galera A L L,Soli1 A S.A real options approach for the valuation of highway concessions[J].Transportation Science,2010,44(3):416-427.
[24]Brouthers K D,Brouthers L E,Werner S.Real options,international entry mode choice and performance[J].Journal of Management Studies,2008,45(5):936-960.
[25]Brouthers K D,Dikova D.Acquisitions and real options:The greenfield alternative[J].Journal of Management Studies,2010,47(6):1048-1071.
[26]Ho S H,Liao S H.A fuzzy real option approach for investment project valuation[J].Expert Systems with Applications,2011,38(12):15296-15302.
[27]Martins J,Marques R C,Cruz C O.Real options in infrastructure:Revisiting the literature[J].Journal of Infrastructure Systems,2013,21(1):04014026.
[28]Dixit R K,Pindyck R S.Investment under uncertainty[M].Princeton University Press,2012.
[29]Liu J,Yu X,Cheah C Y J.Evaluation of restrictive competition in PPP projects using real option approach[J].International Journal of Project Management,2014,32(3):473-481.
[30]Xu Y,Chan A P C,Yeung J F Y.Developing a fuzzy risk allocation model for PPP projects in China[J].Journal of Construction Engineering and Management,2010,136(8):894-903.DOI:10.1061/(ASCE)CO.1943-7862.0000189.
[31]柯永建,王守清,陈炳泉.基础设施PPP项目的风险分担[J].建筑经济,2008,4:31-35.DOI:10.14181/j.cnki.1002-851x.2008.04.007.
[32]苏伯尼,黄弘,张楠.基于情景模拟的城市内涝动态风险评估方法[J].清华大学学报(自然科学版),2015,55(6):684-690.DOI:10.16511/j.cnki.qhdxxb.2015.06.014.
[33]杨春鹏,吴冲锋,吴国富.实物期权中放弃期权与增长期权的相互影响研究[J].系统工程理论与实践,2005,25(1):26-31.
[34]刘继才,宋金龙.基于实物期权的PPP项目投资评价研究[J].世界科技研究与发展,2012,34(3):514-518.DOI:10.16507/j.issn.1006-6055.2012.03.044.
[35]Black F,Scholes M.The pricing of options and corporate liabilities[J].Journal of Political Economy,1973:637-654.DOI:10.1086/260062.
[36]刘继才,唐丝丝,刘永胜.项目融资风险分析与污水处理项目特许期决策[M].北京:科学出版社,2014:88-100.
[2]Mota J,Moreira A C.The importance of non-financial determinants on public–private partnerships in Europe[J].International Journal of Project Management,2015,33(7):1563-1575.DOI:10.1016/j.ijproman.2015.04.005.
[3]Ni J Z,Melnyk S A,Ritchie,W J.,Flynn,B F.Why be first if it doesn't pay?The case of early adopters of CTPAT supply chain security certification[J].International Journal of Operations&Production Management,2016,36(10):1161-1181.DOI:10.1108/IJOPM-01-2015-0041.
[4]Liu J,Gao R,Cheah C Y J,Luo J.Evolutionary game of investors'opportunistic behaviour during the operational period in PPP projects[J].Construction Management and Economics,2017,35(3):137-153.DOI:10.1080/01446193.2016.1237033.
[5]侯峻.PPP模式在城市公共产品投资中的应用研究[J].现代城市研究,2008,6:21.
[6]叶晓甦,石世英,刘李红.PPP项目伙伴主体,合作环境与公共产品供给的关系研究——基于结构方程模型的分析[J].北京交通大学学报:社会科学版,2017,16(1):45-54.DOI:10.16797/j.cnki.11-5224/c.20170105.005.
[7]Zhang X.Win–win concession period determination methodology[J].Journal of Construction Engineering and Management,2009,135(6):550-558.DOI:10.1061/(ASCE)CO.1943-7862.0000012.
[8]Hayes R H,Garvin D A.Managing as if tomorrow mattered[J].Harvard Business Review,1982,60(3):70-79.
[9]Ross S A.Uses,abuses,and alternatives to the net-present-value rule[J].Financial Management,1995:96-102.
[10]傅涛松,母小曼.投资决策中实物期权法与净现值法的比较[J].经营与管理,2011(8):101-103.DOI:10.16517/j.cnki.cn12-1034/f.2011.08.021.
[11]Myers S C.Determinants of corporate borrowing[J].Journal of Financial Economics,1977,5(2):147-175.DOI:10.1016/0304-405X(77)90015-0.
[12]Cheah C Y J,Liu J.Real option evaluation of complex infrastructure projects:The case of Dabhol Power[J].Journal of Financial Management of Property and Construction,2005,10(1):55-68.DOI:10.1108/13664380580001064.
[13]Cheah C Y J,Liu J.Valuing governmental support in infrastructure projects as real options using Monte Carlo simulation[J].Construction Management and Economics,2006,24(5):545-554.DOI:10.1080/01446190500435572.
[14]Paddock J,Siegel D,Smith J.Option valuation of claims on physical assets:the case of off shore petroleum lease[J].Quarterly Journal Economics,1988,103(3):479-508.
[15]李岱.企业技术创新战略投资最优时机的实物期权分析[J].系统工程,2014,32(1):82-86.
[16]Merton R C.Theory of rational option pricing[J].Bell Journal of Economics and Management Science,1973,4(1):141-183.
[17]曹国华,陈冀.基于随机利率和时间偏好不一致的实物期权定价[J].统计与决策,2008(10):36-38.
[18]曹国华,章文芳,陈艳丽.随机利率下投资项目价值研究[J].技术经济,2011,30(4):73-76.
[19]袁国军,肖庆宪.基于近似对冲跳跃风险的期权定价[J].系统工程,2013,31(3):15-19.Yuan G.Xiao Q.The pricing options based on approximating hedge jump risk[J].Systems Engineering,2013,31(3):15-19.
[20]朱秀丽,邱菀华.基于实物期权的铁路地下化项目PPP模式投资决策分析[J].系统工程,2011,29(3):117-120.
[21]李明顺,陈涛,滕敏.交通基础设施PPP项目实物期权定价及敏感性分析[J].系统工程,2011,29(3):67-73.
[22]唐文彬,张飞涟,马超群.基于模糊实物期权的城市轨道交通项目投资价值[J].系统工程,2011,29(12):110-115.
[23]Galera A L L,Soli1 A S.A real options approach for the valuation of highway concessions[J].Transportation Science,2010,44(3):416-427.
[24]Brouthers K D,Brouthers L E,Werner S.Real options,international entry mode choice and performance[J].Journal of Management Studies,2008,45(5):936-960.
[25]Brouthers K D,Dikova D.Acquisitions and real options:The greenfield alternative[J].Journal of Management Studies,2010,47(6):1048-1071.
[26]Ho S H,Liao S H.A fuzzy real option approach for investment project valuation[J].Expert Systems with Applications,2011,38(12):15296-15302.
[27]Martins J,Marques R C,Cruz C O.Real options in infrastructure:Revisiting the literature[J].Journal of Infrastructure Systems,2013,21(1):04014026.
[28]Dixit R K,Pindyck R S.Investment under uncertainty[M].Princeton University Press,2012.
[29]Liu J,Yu X,Cheah C Y J.Evaluation of restrictive competition in PPP projects using real option approach[J].International Journal of Project Management,2014,32(3):473-481.
[30]Xu Y,Chan A P C,Yeung J F Y.Developing a fuzzy risk allocation model for PPP projects in China[J].Journal of Construction Engineering and Management,2010,136(8):894-903.DOI:10.1061/(ASCE)CO.1943-7862.0000189.
[31]柯永建,王守清,陈炳泉.基础设施PPP项目的风险分担[J].建筑经济,2008,4:31-35.DOI:10.14181/j.cnki.1002-851x.2008.04.007.
[32]苏伯尼,黄弘,张楠.基于情景模拟的城市内涝动态风险评估方法[J].清华大学学报(自然科学版),2015,55(6):684-690.DOI:10.16511/j.cnki.qhdxxb.2015.06.014.
[33]杨春鹏,吴冲锋,吴国富.实物期权中放弃期权与增长期权的相互影响研究[J].系统工程理论与实践,2005,25(1):26-31.
[34]刘继才,宋金龙.基于实物期权的PPP项目投资评价研究[J].世界科技研究与发展,2012,34(3):514-518.DOI:10.16507/j.issn.1006-6055.2012.03.044.
[35]Black F,Scholes M.The pricing of options and corporate liabilities[J].Journal of Political Economy,1973:637-654.DOI:10.1086/260062.
[36]刘继才,唐丝丝,刘永胜.项目融资风险分析与污水处理项目特许期决策[M].北京:科学出版社,2014:88-100.