Abstract

This paper examines the pricing disparity between green and conventional bonds (the greenium), drawing on empirical research findings that have yielded mixed re- sults. We introduce a mathematical model to elucidate the conditions under which green bonds may be priced differently from their conventional counterparts. Un- like previous studies primarily focused on firm-level characteristics, our model incor- porates investors’ prosocial attitudes, income levels, and risk preferences to derive market prices for green bonds. By considering both supply and demand dynamics, we pioneer an equilibrium-based approach to pricing, departing from the assump- tions of traditional models like CAPM and Black-Scholes. Additionally, we integrate regulatory risk into our analysis, introducing the concept of ”green default” along- side pecuniary default. Our findings underscore the influence of investors’ prosocial preferences, issuer environmental commitments, and issuance costs on the greenium. Moreover, stringent environmental policies and advancements in green technology mitigate the likelihood of green default, thereby bolstering market demand for green bonds. While climate risk exerts downward pressure on bond prices overall, its im- pact on the greenium varies based on the relative reduction in the equilibrium price of green bonds compared to conventional bonds.

Keywords

  • Investment
  • green bond
  • conventional bond utility
  • optimization
  • risk aversion
  • environmental regulation
  • green default

References

  1. Abdellaoui, M., & Wakker, P. P. (2005). The likelihood method for decision under uncertainty. Theory and Decision, 58 . doi: 10.1007/s11238-005-8320-4
  2. Aimin, H. (2010). Uncertainty, risk aversion and risk management in agriculture.
  3. Agriculture and Agricultural Science Procedia, 1 . doi: 10.1016/j.aaspro.2010
  4. .09.018
  5. Akter, S., Krupnik, T. J., & Khanam, F. (2017). Climate change skepticism and index versus standard crop insurance demand in coastal bangladesh. Regional Environmental Change, 17 . doi: 10.1007/s10113-017-1174-9
  6. Allais, M. (1953). Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’ecole americaine. Econometrica, 21 . doi: 10.2307/ 1907921
  7. Aref, S., & Wander, M. M. (1997). Long-term trends of corn yield and soil organic matter in different crop sequences and soil fertility treatments on the morrow plots. Advances in Agronomy, 62 . doi: 10.1016/S0065-2113(08)60568-4
  8. Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9 . doi: 10.1111/1467-9965.00068
  9. Babcock, B. A. (2015). Using cumulative prospect theory to explain anomalous crop insurance coverage choice (Vol. 97). doi: 10.1093/ajae/aav032
  10. Baillon, A., Bleichrodt, H., Keskin, U., & ... (2013). Learning under ambiguity: An experiment using initial public offerings on a stock market.
  11. Baillon, A., Liu, N., & van Dolder, D. (2017). Comparing uncertainty aversion towards different sources. Theory and Decision, 83 . doi: 10.1007/s11238-016-9584-6
  12. Barberis, N. C. (2013). Thirty years of prospect theory in economics: A review and assessment (Vol. 27). doi: 10.1257/jep.27.1.173
  13. Bard, S. K., & Barry, P. J. (2001). Assessing farmers’ attitudes toward risk using the ”closing-in” method. Journal of Agricultural and Resource Economics, 26 .
  14. Batchelor, W. D., Basso, B., & Paz, J. O. (2002). Examples of strategies to analyze spatial and temporal yield variability using crop models. In (Vol. 18). doi: 10.1016/S1161-0301(02)00101-6
  15. Ben-Tal, A., & Hochman, E. (1985). Approximation of expected returns and op- timal decisions under uncertainty using mean and mean absolute deviation. Zeitschrift fu¨r Operations Research, 29 . doi: 10.1007/BF01918761
  16. Ben-Tal, A., & Teboulle, M. (1986). Expected utility, penalty functions, and duality in stochastic nonlinear programming. Management Science, 32 . doi: 10.1287/ mnsc.32.11.1445
  17. Bert, F. E., Laciana, C. E., Podest´a, G. P., Satorre, E. H., & Men´endez, A. N. (2007). Sensitivity of ceres-maize simulated yields to uncertainty in soil properties and daily solar radiation. Agricultural Systems, 94 . doi: 10.1016/j.agsy.2006.08
  18. .003
  19. Boyer, C. N., Larson, J. A., Roberts, R. K., McClure, A. T., Tyler, D. D., & Zhou,
  20. V. (2013). Stochastic corn yield response functions to nitrogen for corn after corn, corn after cotton, and corn after soybeans. Journal of Agricultural and Applied Economics, 45 . doi: 10.1017/s1074070800005198
  21. Bullock, D. G., & Bullock, D. S. (1994). Quadratic and quadratic-plus-plateau models for predicting optimal nitrogen rate of corn: A comparison. Agronomy Journal,
  22. 86 . doi: 10.2134/agronj1994.00021962008600010033x
  23. Cabas, J. H., Leiva, A. J., & Weersink, A. (2008). Modeling exit and entry of farmers in a crop insurance program. In (Vol. 37). doi: 10.1017/S1068280500002173
  24. Cameron, T. A., & Quiggin, J. (1994). Estimation using contingent valuation data from a dichotomous choice with follow-up questionnaire. Journal of Environ- mental Economics and Management, 27 . doi: 10.1006/jeem.1994.1035
  25. Cao, R., Carpentier, A., & Gohin, A. (2011). Measuring farmers’ risk aversion: the unknown properties of the value function. 2011 International Congress, . . . .
  26. Cerrato, M. E., & Blackmer, A. M. (1990). Comparison of models for describing; corn yield response to nitrogen fertilizer. Agronomy Journal, 82 . doi: 10.2134/ agronj1990.00021962008200010030x
  27. Chambers, R. G., Chung, Y., & Fa¨re, R. (1996). Benefit and distance functions.
  28. Journal of Economic Theory, 70 . doi: 10.1006/jeth.1996.0096
  29. Chung, Y. H., F¨are, R., & Grosskopf, S. (1997). Productivity and undesirable outputs: A directional distance function approach. Journal of Environmental Management, 51 . doi: 10.1006/jema.1997.0146
  30. Coble, K. H., Knight, T. O., Patrick, G. F., & Baquet, A. E. (2002). Understanding the economic factors influencing farm policy preferences. Review of Agricultural Economics, 24 . doi: 10.1111/1467-9353.00021
  31. Dalhaus, T., Barnett, B. J., & Finger, R. (2020). Behavioral weather insurance: Applying cumulative prospect theory to agricultural insurance design under narrow framing. PLoS ONE , 15 . doi: 10.1371/journal.pone.0232267
  32. Dinar, A., & Yaron, D. (1992). Adoption and abandonment of irrigation technologies.
  33. Agricultural Economics, 6 . doi: 10.1016/0169-5150(92)90008-M
  34. Dogan, E., Copur, O., Kahraman, A., Kirnak, H., & Guldur, M. E. (2011). Sup- plemental irrigation effect on canola yield components under semiarid climatic conditions. Agricultural Water Management, 98 . doi: 10.1016/j.agwat.2011.04
  35. .006
  36. Dowling, J. A., Rinaldi, K. Z., Ruggles, T. H., Davis, S. J., Yuan, M., Tong, F., . . . Caldeira, K. (2020). Role of long-duration energy storage in variable renewable electricity systems. Joule, 4 . doi: 10.1016/j.joule.2020.07.007
  37. Ellsberg, D. (1961). Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics, 75 . doi: 10.2307/1884324
  38. Eurosif. (2018, 6). Eurosif 2018 sri study. Retrieved from https://
  39. www.eurosif.org/wp-content/uploads/2022/06/Eurosif-Report-June
  40. -22-SFDR-Policy-Recommendations.pdf
  41. Feder, G., Just, R. E., & Zilberman, D. (1985). Adoption of agricultural innovations in developing countries: a survey. Economic Development Cultural Change,
  42. 33 . doi: 10.1086/451461
  43. Fern´andez, C., Koop, G., & Steel, M. F. (2002). Multiple-output production with undesirable outputs: An application to nitrogen surplus in agriculture. Journal of the American Statistical Association, 97 . doi: 10.1198/016214502760046989
  44. Fersund, F. R. (2009). Good modelling of bad outputs: Pollution and multiple-output production. International Review of Environmental and Resource Economics,
  45. 3 . doi: 10.1561/101.00000021
  46. Flaten, O., Lien, G., Koesling, M., Valle, P. S., & Ebbesvik, M. (2005). Compar- ing risk perceptions and risk management in organic and conventional dairy farming: Empirical results from norway. Livestock Production Science, 95 . doi: 10.1016/j.livprodsci.2004.10.014
  47. Foster, A. D., & Rosenzweig, M. R. (1995). Learning by doing and learning from others: human capital and technical change in agriculture. Journal of Political Economy, 103 . doi: 10.1086/601447
  48. Foster, A. D., & Rosenzweig, M. R. (2010). Microeconomics of technology adop- tion. Annual Review of Economics, 2 . doi: 10.1146/annurev.economics.102308
  49. .124433
  50. Foudi, S., & Erdlenbruch, K. (2012). The role of irrigation in farmers’ risk manage- ment strategies in france (Vol. 39). doi: 10.1093/erae/jbr024
  51. Friedman, M., & Savage, L. J. (1948). The utility analysis of choices involving risk.
  52. Journal of Political Economy, 56 . doi: 10.1086/256692
  53. Frittelli, M., & Gianin, E. R. (2002). Putting order in risk measures. Journal of Banking and Finance, 26 . doi: 10.1016/S0378-4266(02)00270-4
  54. Fuentes-Arderiu, X., & Dot-Bach, D. (2009). Measurement uncertainty in manual differential leukocyte counting. Clinical Chemistry and Laboratory Medicine,
  55. 47 . doi: 10.1515/CCLM.2009.014
  56. Fa¨re, R., Grosskopf, S., Noh, D. W., & Weber, W. (2005). Characteristics of a polluting technology: Theory and practice. Journal of Econometrics, 126 . doi: 10.1016/j.jeconom.2004.05.010
  57. Fa¨re, R., Grosskopf, S., & Weber, W. L. (2006). Shadow prices and pollution costs in
  58. u.s. agriculture. Ecological Economics, 56 . doi: 10.1016/j.ecolecon.2004.12.022 Fo¨llmer, H., & Schied, A. (2002). Convex measures of risk and trading constraints.
  59. Finance and Stochastics, 6 . doi: 10.1007/s007800200072
  60. Goodwin, B. K. (1993). An empirical analysis of the demand for multiple peril crop insurance. American Journal of Agricultural Economics, 75 . doi: 10.2307/ 1242927
  61. Han, X., Zhang, G., Xie, Y., Yin, J., Zhou, H., Yang, Y., . . . Bai, W. (2019).
  62. Weather index insurance for wind energy. Global Energy Interconnection, 2 . doi: 10.1016/j.gloei.2020.01.008
  63. Hasenkamp, G. (1976). A study of multiple-output production functions. klein’s rail- road study revisited. Journal of Econometrics, 4 . doi: 10.1016/0304-4076(76) 90036-1
  64. Hayhoe, K., Wuebbles, D., Easterling, D., Fahey, D., Doherty, S., Kossin, J., . . . Wehner, M. (2018). Our changing climate. in impacts, risks, and adaptation in the united states: Fourth national climate assessment, volume ii. Impacts, Risks, and Adaptation in the United States: Fourth National Climate Assess- ment, Volume II , II .
  65. Heath, C., & Tversky, A. (1991). Preference and belief: Ambiguity and competence in choice under uncertainty. Journal of Risk and Uncertainty, 4 . doi: 10.1007/ BF00057884
  66. Hertwig, R., Barron, G., Weber, E. U., & Erev, I. (2004). Decisions from experience and the effect of rare events in risky choice. Psychological Science, 15 . doi: 10.1111/j.0956-7976.2004.00715.x
  67. Huettel, S. A., Stowe, C. J., Gordon, E. M., Warner, B. T., & Platt, M. L. (2006). Neural signatures of economic preferences for risk and ambiguity. Neuron, 49 . doi: 10.1016/j.neuron.2006.01.024
  68. Ipcc. (2013). Working group i contribution to the ipcc fifth assessment report, climate change 2013: The physical science basis. Ipcc, AR5 .
  69. Ipcc. (2022). Ar6 synthesis report outline: Climate change 2022. Re-
  70. trieved from https://www.ipcc.ch/site/assets/uploads/2021/12/IPCC
  71. -52 decisions-adopted-by-the-Panel.pdf
  72. Iyer, P., Bozzola, M., Hirsch, S., Meraner, M., & Finger, R. (2020). Measuring farmer risk preferences in europe: A systematic review. Journal of Agricultural Economics, 71 . doi: 10.1111/1477-9552.12325
  73. Kahn, B. E., & Sarin, R. K. (1988). Modeling ambiguity in decisions under uncer- tainty. Journal of Consumer Research, 15 . doi: 10.1086/209163
  74. Kahneman, D., & Tversky, A. (1979). Kahneman tversky (1979) - prospect theory - an analysis of decision under risk.pdf (Vol. 47).
  75. Kessler, R. (2021, 3). Texas wind farms face billion-dollar losses from blackouts in ’illegal wealth transfer’. Retrieved from https://www.windaction.org/posts/ 52234
  76. Kilka, M., & Weber, M. (2001). What determines the shape of the probability weighting function under uncertainty? Management Science, 47 . doi: 10.1287/ mnsc.47.12.1712.10239
  77. Knight, F. H. (1921). Risk uncertainty and profit knight (Vol. 36).
  78. Kooperman, Chen, Hoffman, Koven, Lindsay, Pritchard, . . . Randerson (2018). Forest response to rising co2 drives zonally asymmetric rainfall change over tropical land. Nature Climate Change. doi: https://doi.org/10.1038/s41558-018-0144-7
  79. Koundouri, P., Nauges, C., & Tzouvelekas, V. (2006). Technology adoption under pro- duction uncertainty: Theory and application to irrigation technology. American Journal of Agricultural Economics, 88 . doi: 10.1111/j.1467-8276.2006.00886.x
  80. Kumbhakar, S. C. (2002). Specification and estimation of production risk, risk pref- erences and technical efficiency. American Journal of Agricultural Economics,
  81. 84 . doi: 10.1111/1467-8276.00239
  82. Kumbhakar, S. C., & Lovell, C. A. K. (2000). Stochastic frontier analysis. doi: 10.1017/cbo9781139174411
  83. Kweilin Ellingrud, B. Q., Alex Kimura, & Ralph, J. (2022). Five steps to improve in- novation in the insurance industry. McKinsey & Co. Retrieved from https:// www.mckinsey.com/industries/financial-services/our-insights/
  84. five-steps-to-improve-innovation-in-the-insurance-industry
  85. Laeven, R. J., & Stadje, M. (2014). Robust portfolio choice and indifference valuation.
  86. Mathematics of Operations Research, 39 . doi: 10.1287/moor.2014.0646
  87. Lee, D. (2005). Agricultural sustainability and technology adoption: Issues and policies for developing countries. American Journal of Agricultural Economics,
  88. 87 . doi: 10.1111/j.1467-8276.2005.00826.x
  89. Lempert, R., Popper, S., & Bankes, S. (2019). Shaping the next one hundred years: New methods for quantitative, long-term policy analysis. doi: 10.7249/mr1626
  90. Levy, I., Snell, J., Nelson, A. J., Rustichini, A., & Glimcher, P. W. (2010). Neu- ral representation of subjective value under risk and ambiguity. Journal of Neurophysiology, 103 . doi: 10.1152/jn.00853.2009
  91. Link, J., Graeff, S., Batchelor, W. D., & Claupein, W. (2006). Evaluating the economic and environmental impact of environmental compensation payment policy under uniform and variable-rate nitrogen management. Agricultural Sys- tems, 91 . doi: 10.1016/j.agsy.2006.02.003
  92. Llewelyn, R. V., & Featherstone, A. M. (1997). A comparison of crop production functions using simulated data for irrigated corn in western kansas. Agricultural Systems, 54 . doi: 10.1016/S0308-521X(96)00080-7
  93. Lyu, K., & Barr´e, T. J. (2017). Risk aversion in crop insurance program purchase decisions evidence from maize production areas in china. China Agricultural Economic Review, 9 . doi: 10.1108/CAER-04-2015-0036
  94. Maharjan, B., Das, S., Nielsen, R., & Hergert, G. W. (2021). Maize yields from manure and mineral fertilizers in the 100-year-old knorr–holden plot. Agronomy Journal, 113 . doi: 10.1002/agj2.20713
  95. Mahul, O. (2002). Hedging in futures and options markets with basis risk (Vol. 22).
  96. doi: 10.1002/fut.2207
  97. Miao, Y., Mulla, D. J., Batchelor, W. D., Paz, J. O., Robert, P. C., & Wiebers,
  98. M. (2006). Evaluating management zone optimal nitrogen rates with a crop growth model. Agronomy Journal, 98 . doi: 10.2134/agronj2005.0153
  99. Murty, S., Russell, R. R., & Levkoff, S. B. (2012). On modeling pollution-generating technologies. Journal of Environmental Economics and Management, 64 . doi: 10.1016/j.jeem.2012.02.005
  100. of Sciences, N. A., Council, N. R., of Mathematical, A., & Sciences, P. (1979). Carbon dioxide and climate: a scientific assessment. Re- trieved from https://nap.nationalacademies.org/catalog/12181/carbon
  101. -dioxide-and-climate-a-scientific-assessment
  102. Paz, J. O., Batchelor, W. D., Babcock, B. A., Colvin, T. S., Logsdon, S. D., Kaspar,
  103. T. C., & Karlen, D. L. (1999). Model-based technique to determine variable rate nitrogen for corn. Agricultural Systems, 61 . doi: 10.1016/S0308-521X(99) 00035-9
  104. Piet, L., & Bougherara, D. (2016, 3). The impact of farmers’ risk preferences on the design of an individual yield crop insurance. WORKING PAPER SMART, INARE UMR SMART .
  105. Platt, M. L., & Huettel, S. A. (2008). Risky business: The neuroeconomics of decision making under uncertainty (Vol. 11). doi: 10.1038/nn2062
  106. Pope, R. D. (1982). Expected profit, price change, and risk aversion. American Journal of Agricultural Economics, 64 . doi: 10.2307/1240655
  107. Program, U. G. C. R. (2018). Climate science special report: Fourth national climate assessment, volume i (Vol. 1). doi: 10.7930/J0J964J6
  108. Puntel, L. A., Sawyer, J. E., Barker, D. W., Dietzel, R., Poffenbarger, H., Castellano,
  109. M. J., . . . Archontoulis, S. V. (2016). Modeling long-term corn yield response to nitrogen rate and crop rotation. Frontiers in Plant Science, 7 . doi: 10.3389/ fpls.2016.01630
  110. Quiggin, J. (1982). A theory of anticipated utility. Journal of Economic Behavior and Organization, 3 . doi: 10.1016/0167-2681(82)90008-7
  111. Raiffa, H. (1993). Decision analysis: introductory lectures on choices under un- certainty. 1968. M.D. computing : computers in medical practice, 10 . doi: 10.2307/2987280
  112. Ruszczy’ski, A. (2006, 8). Stochastic programming. John Wiley Sons, Inc. doi: 10.1002/0471667196.ess3225
  113. Schahczenski, J. (2021, 9). Crop insurance rules challenge organic and sustainable farming practices. Retrieved from https://sustainableagriculture.net/ blog/crop-insurance-rules-challenge-organic-and-sustainable
  114. -farming-practices
  115. Schnitkey, G., Batts, R., Swanson, K., Paulson, N., & Zulauf, C. (2021). Crop insurance tools. Farmdoc.
  116. Schultz, W., Preuschoff, K., Camerer, C., Hsu, M., Fiorillo, C. D., Tobler, P. N., & Bossaerts, P. (2008). Review. explicit neural signals reflecting reward uncer- tainty (Vol. 363). doi: 10.1098/rstb.2008.0152
  117. Scofield, C. (1927). Irrigated crop rotations in western nebraska. United States Department of Agriculture, Technical Bulletin, 02 .
  118. Shapiro, A., Tekaya, W., Soares, M. P., & Costa, J. P. D. (2013). Worst-case- expectation approach to optimization under uncertainty. Operations Research,
  119. 61 . doi: 10.1287/opre.2013.1229
  120. Shephard, R. W. (1970). Theory of cost and production functions. doi: 10.2307/ 2230285
  121. Sherrick, B. J., Zanini, F. C., Schnitkey, G. D., & Irwin, S. H. (2004). Crop in- surance valuation under alternative yield distributions. American Journal of Agricultural Economics, 86 . doi: 10.1111/j.0092-5853.2004.00587.x
  122. Smith, V. H., & Baquet, A. E. (1996). The demand for multiple peril crop insur- ance: Evidence from montana wheat farms. American Journal of Agricultural Economics, 78 . doi: 10.2307/1243790
  123. Steiger, R., Damm, A., Prettenthaler, F., & Pro¨bstl-Haider, U. (2021). Climate change and winter outdoor activities in austria. Journal of Outdoor Recreation and Tourism, 34 . doi: 10.1016/j.jort.2020.100330
  124. Strupczewski, G. (2019). What characterizes farmers who purchase crop insurance in poland? Problems of Agricultural Economics, 1 . doi: 10.30858/zer/103596
  125. Sulewski, P., & K-loczko-Gajewska, A. (2014). Farmers’ risk perception, risk aversion and strategies to cope with production risk: An empirical study from poland. Studies in Agricultural Economics, 116 . doi: 10.7896/j.1414
  126. Thorp, K. R., DeJonge, K. C., Kaleita, A. L., Batchelor, W. D., & Paz, J. O. (2008). Methodology for the use of dssat models for precision agriculture de- cision support. Computers and Electronics in Agriculture, 64 . doi: 10.1016/ j.compag.2008.05.022
  127. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5 . doi: 10.1007/ BF00122574
  128. Ullah, R., Shivakoti, G. P., & Ali, G. (2015). Factors effecting farmers’ risk attitude and risk perceptions: The case of khyber pakhtunkhwa, pakistan. International Journal of Disaster Risk Reduction, 13 . doi: 10.1016/j.ijdrr.2015.05.005
  129. Vajda, S., Luce, R. D., & Raiffa, H. (1958). Games and decisions: Introduction and critical survey. Journal of the Royal Statistical Society. Series A (General),
  130. 121 . doi: 10.2307/2342906
  131. Valone.T. (2021). Linear global temperature correlation to carbon dioxide level, sea level, and innovative solutions to a projected 6°c warming by 2100. Journal of
  132. Geoscience and Environment Protection. Retrieved from https://www.scirp
  133. .org/journal/paperinformation.aspx?paperid=107789
  134. Vollmer, E., Hermann, D., & Mußhoff, O. (2017). Is the risk attitude measured with the holt and laury task reflected in farmers’ production risk? European Review of Agricultural Economics, 44 . doi: 10.1093/erae/jbx004
  135. Weaver, R. (1977). The theory and measurement of provisional agricultural production decisions .
  136. Weaver, R. D. (1996). Prosocial behavior: Private contributions to agriculture’s impact on the environment. Land Economics, 72 . doi: 10.2307/3146968
  137. Weber, E. U. (1994). From subjective probabilities to decision weights: The effect of asymmetric loss functions on the evaluation of uncertain outcomes and events. Psychological Bulletin, 115 . doi: 10.1037//0033-2909.115.2.228
  138. Yaari, M. E. (1987). The dual theory of choice under risk. Econometrica, 55 . doi:
  139. 10.2307/1911158
  140. Yilmaz, H., Merkez, M., & Unlu, N. (2017). An empirical analysis on the determinants of government-subsidised crop insurance purchase in grape production in turkey. Erwerbs-Obstbau, 59 . doi: 10.1007/s10341-016-0297-3