模糊实物期权框架下初创企业估值
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摘要
为量化描述初创企业估值不确定性,该文赋予关键参数区间变化,推导出基于模糊理论的现金流折现模型和复合实物期权定价模型。研究表明:模糊实物期权是对现金流折现模型的改进,通过获得企业价值变化范围,使得估值结果更加合理;对模糊参数的敏感性分析表明,初创企业价值不确定性与模糊性负相关,最小取值与左宽度正相关,最大取值与右宽度正相关;分析不同情形下初创企业价值状态,可提高投资决策的准确性。通过案例分析,进一步验证了模糊实物期权在初创企业多阶段价值评估中的有效性。
Key parameter interval changes are used to quantify start-ups uncertainty and to deduce the discounted cash flow(DCF)and a compound real options model based on fuzzy theory.This research shows that the fuzzy real option method improves the DCF by giving the range of values with a fuzzy uncertainty to make more reasonable valuations. The fuzzy parameter sensitivity analysis shows that the start-ups uncertainty negatively correlates with the probability,the minimum value positively correlates with the left width,and the maximum value positively correlates with the right width.Analyses of the start-ups values for different situations can improve the investment decision accuracy.A case study further verifies the effectiveness of the fuzzy real options method in multi-stage investments for start-ups.
Key parameter interval changes are used to quantify start-ups uncertainty and to deduce the discounted cash flow(DCF)and a compound real options model based on fuzzy theory.This research shows that the fuzzy real option method improves the DCF by giving the range of values with a fuzzy uncertainty to make more reasonable valuations. The fuzzy parameter sensitivity analysis shows that the start-ups uncertainty negatively correlates with the probability,the minimum value positively correlates with the left width,and the maximum value positively correlates with the right width.Analyses of the start-ups values for different situations can improve the investment decision accuracy.A case study further verifies the effectiveness of the fuzzy real options method in multi-stage investments for start-ups.
引文
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[2] MYERS S C.Determinants of corporate borrowing[J].Journal of Financial Economics,1977,5(2):147-175.
[3]郑征,朱武祥.运用复合实物期权方法研究初创企业的估值[J].投资研究,2017,36(4):118-135.ZHENG Z,ZHU W X.Application of compound real options method in the start-ups valuation[J].Review of Investment Studies,2017,36(4):118-135.(in Chinese)
[4] ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[5] BUCKLEY J J.The fuzzy mathematics of finance[J].Fuzzy Sets and Systems,1987,21(3):257-273.
[6] CARLSSON C,FULLR R.A fuzzy approach to real option valuation[J]. FuzzySetsandSystems, 2003,139(2):297-312.
[7] YOSHIDA Y.A discrete-time model of American put option in an uncertain environment[J]. European Journal of Operational Research,2003,151(1):153-166.
[8] WU H C.Pricing European options based on the fuzzy pattern of Black-Scholes formula[J]. Computers&Operations Research,2004,31(7):1069-1081.
[9] WU H C.Using fuzzy sets theory and Black-Scholes formula to generate pricing boundaries of European options[J].Applied Mathematics and Computation,2007,185(1):136-146.
[10]XU W J,PENG X L,XIAO W L.The fuzzy jump-diffusion model to pricing European vulnerable options[J].International Journal of Fuzzy Systems,2013,15(3):317-325.
[11]WANG X D,HE J M,LI S W.Compound option pricing underfuzzyenvironment[J]. JournalofApplied Mathematics,2014:875319.
[12]TAVAKKOLNIA A.A binomial tree valuation approach for compound real options with fuzzy phase-specific volatility[C]//Proceedings of the 12th International Conference on Industrial Engineering.Tehran,Iran,2016:73-78.
[13]BI X, WANG X F.The application of fuzzy-real option theory in BOT project investment decision-making[C]//Proceedings of the 16th International Conference on Industrial Engineering and Engineering Management.Beijing,China,2009:289-293.
[14]PUSHKAR S,MISHRA A.IT project selection model using real option optimization with fuzzy set approach[M]//ARIWA E, EL-QAWASMEH. Digital enterprise and information systems.Berlin, Germany:Springer,2011,194:116-128.
[15]WANG Q,KILGOUR D M,HIPEL K W.Facilitating risky project negotiation:An integrated approach using fuzzy real options,multicriteria analysis,and conflict analysis[J].Information Sciences,2015,295:544-557.
[16]BIANCARDI M,VILLANI G.Robust Monte Carlo method for R&D real options valuation[J]. Computational Economics,2017,49(3):481-498.
[17]DE ANDRS-SNCHEZ J.An empirical assestment of fuzzy Black and Scholes pricing option model in Spanish stock option market[J].Journal of Intelligent&Fuzzy Systems,2017,33(4):2509-2521.
[18]ZMEKALZ. Applicationofthefuzzy-stochastic methodology to appraising the firm value as a European call option[J].European Journal of Operational Research,2001,135(2):303-310.
[19]YAO J S,CHEN M S,LIN H W.Valuation by using a fuzzy discounted cash flow model[J]. Expert Systems with Applications,2005,28(2):209-222.
[20]WANG J,HWANG W L.A fuzzy set approach for R&D portfolio selection using a real options valuation model[J].Omega,2007,35(3):247-257.
[21]SEMERCIOGLU N, TOLGA A. A multi-stage new product development using fuzzy type-2sets in a real option valuation[C]//Proceedings of 2015 IEEE International Conference on Fuzzy Systems.Istanbul,Turkey,2015:1-7.
[22]赵振武,唐万生.模糊实物期权理论在风险投资项目价值评价中的应用[J].北京理工大学学报(社会科学版),2006,8(1):49-51.ZHAO Z W,TANG W S.The application of fuzzy real option theory in the venture investment value evaluation[J].Journal of Beijing Institute of Technology(Social Sciences Edition),2006,8(1):49-51.(in Chinese)
[23]张维功,何建敏,吕宏生.基于B-S公式的模糊实物期权研究[J].统计与决策,2009(3):143-145.ZHANG W G,HE J M,LH S.Research on fuzzy real option based on B-S formula[J].Statistics and Decision,2009(3):143-145.(in Chinese)
[24]张茂军,秦学志,南江霞.基于三角直觉模糊数的欧式期权二叉树定价模型[J].系统工程理论与实践,2013,33(1):34-40.ZHANG M J,QIN X Z,NAN J X.Binomial tree model of the European option pricing based on the triangular intuitionistic fuzzy numbers[J]. Systems Engineering:Theory&Practice,2013,33(1):34-40.(in Chinese)
[25]李双兵,冀巨海.高新技术企业风险投资价值评估:基于模糊实物期权视角[J].财会通讯,2016(5):8-10.LI S B,JI J H.Value evaluation of venture capital in hi-tech enterprises:Based on fuzzy real option perspective[J].Communication of Finance and Accounting,2016(5):8-10.(in Chinese)
[26]赵昕,薛岳梅,丁黎黎.灰色模糊环境下基于跳扩散过程的脆弱期权定价模型[J].系统工程,2017,35(12):35-42.ZHAO X,XUE Y M,DING L L.Vulnerable option pricing model based on jump-diffusion process for grey ambiguity condition[J].Systems Engineering,2017,35(12):35-42.(in Chinese)
[2] MYERS S C.Determinants of corporate borrowing[J].Journal of Financial Economics,1977,5(2):147-175.
[3]郑征,朱武祥.运用复合实物期权方法研究初创企业的估值[J].投资研究,2017,36(4):118-135.ZHENG Z,ZHU W X.Application of compound real options method in the start-ups valuation[J].Review of Investment Studies,2017,36(4):118-135.(in Chinese)
[4] ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[5] BUCKLEY J J.The fuzzy mathematics of finance[J].Fuzzy Sets and Systems,1987,21(3):257-273.
[6] CARLSSON C,FULLR R.A fuzzy approach to real option valuation[J]. FuzzySetsandSystems, 2003,139(2):297-312.
[7] YOSHIDA Y.A discrete-time model of American put option in an uncertain environment[J]. European Journal of Operational Research,2003,151(1):153-166.
[8] WU H C.Pricing European options based on the fuzzy pattern of Black-Scholes formula[J]. Computers&Operations Research,2004,31(7):1069-1081.
[9] WU H C.Using fuzzy sets theory and Black-Scholes formula to generate pricing boundaries of European options[J].Applied Mathematics and Computation,2007,185(1):136-146.
[10]XU W J,PENG X L,XIAO W L.The fuzzy jump-diffusion model to pricing European vulnerable options[J].International Journal of Fuzzy Systems,2013,15(3):317-325.
[11]WANG X D,HE J M,LI S W.Compound option pricing underfuzzyenvironment[J]. JournalofApplied Mathematics,2014:875319.
[12]TAVAKKOLNIA A.A binomial tree valuation approach for compound real options with fuzzy phase-specific volatility[C]//Proceedings of the 12th International Conference on Industrial Engineering.Tehran,Iran,2016:73-78.
[13]BI X, WANG X F.The application of fuzzy-real option theory in BOT project investment decision-making[C]//Proceedings of the 16th International Conference on Industrial Engineering and Engineering Management.Beijing,China,2009:289-293.
[14]PUSHKAR S,MISHRA A.IT project selection model using real option optimization with fuzzy set approach[M]//ARIWA E, EL-QAWASMEH. Digital enterprise and information systems.Berlin, Germany:Springer,2011,194:116-128.
[15]WANG Q,KILGOUR D M,HIPEL K W.Facilitating risky project negotiation:An integrated approach using fuzzy real options,multicriteria analysis,and conflict analysis[J].Information Sciences,2015,295:544-557.
[16]BIANCARDI M,VILLANI G.Robust Monte Carlo method for R&D real options valuation[J]. Computational Economics,2017,49(3):481-498.
[17]DE ANDRS-SNCHEZ J.An empirical assestment of fuzzy Black and Scholes pricing option model in Spanish stock option market[J].Journal of Intelligent&Fuzzy Systems,2017,33(4):2509-2521.
[18]ZMEKALZ. Applicationofthefuzzy-stochastic methodology to appraising the firm value as a European call option[J].European Journal of Operational Research,2001,135(2):303-310.
[19]YAO J S,CHEN M S,LIN H W.Valuation by using a fuzzy discounted cash flow model[J]. Expert Systems with Applications,2005,28(2):209-222.
[20]WANG J,HWANG W L.A fuzzy set approach for R&D portfolio selection using a real options valuation model[J].Omega,2007,35(3):247-257.
[21]SEMERCIOGLU N, TOLGA A. A multi-stage new product development using fuzzy type-2sets in a real option valuation[C]//Proceedings of 2015 IEEE International Conference on Fuzzy Systems.Istanbul,Turkey,2015:1-7.
[22]赵振武,唐万生.模糊实物期权理论在风险投资项目价值评价中的应用[J].北京理工大学学报(社会科学版),2006,8(1):49-51.ZHAO Z W,TANG W S.The application of fuzzy real option theory in the venture investment value evaluation[J].Journal of Beijing Institute of Technology(Social Sciences Edition),2006,8(1):49-51.(in Chinese)
[23]张维功,何建敏,吕宏生.基于B-S公式的模糊实物期权研究[J].统计与决策,2009(3):143-145.ZHANG W G,HE J M,LH S.Research on fuzzy real option based on B-S formula[J].Statistics and Decision,2009(3):143-145.(in Chinese)
[24]张茂军,秦学志,南江霞.基于三角直觉模糊数的欧式期权二叉树定价模型[J].系统工程理论与实践,2013,33(1):34-40.ZHANG M J,QIN X Z,NAN J X.Binomial tree model of the European option pricing based on the triangular intuitionistic fuzzy numbers[J]. Systems Engineering:Theory&Practice,2013,33(1):34-40.(in Chinese)
[25]李双兵,冀巨海.高新技术企业风险投资价值评估:基于模糊实物期权视角[J].财会通讯,2016(5):8-10.LI S B,JI J H.Value evaluation of venture capital in hi-tech enterprises:Based on fuzzy real option perspective[J].Communication of Finance and Accounting,2016(5):8-10.(in Chinese)
[26]赵昕,薛岳梅,丁黎黎.灰色模糊环境下基于跳扩散过程的脆弱期权定价模型[J].系统工程,2017,35(12):35-42.ZHAO X,XUE Y M,DING L L.Vulnerable option pricing model based on jump-diffusion process for grey ambiguity condition[J].Systems Engineering,2017,35(12):35-42.(in Chinese)