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Mathematics and Financial Economics

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16.05.2022

Governmental incentives for green bonds investment

verfasst von: Bastien Baldacci, Dylan Possamaï

Erschienen in: Mathematics and Financial Economics | Ausgabe 3/2022

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Abstract

Motivated by the recent studies on the green bond market, we build a Principal–Agent model in which an investor trades on a portfolio of green and conventional bonds, both issued by the same governmental entity. The government provides incentives to the bondholder in order to increase the amount invested in green bonds. These incentives are, optimally, indexed on the prices of the bonds, their quadratic variation and covariation. We show numerically on a set of French governmental bonds that our methodology outperforms the current tax-incentives systems in terms of green investments. Moreover, it is robust to model specification for bond prices and can be applied to a large portfolio of bonds using classical optimisation methods.

Vorheriger Artikel Semi-analytical solution for consumption and investment problem under quadratic security market model with inflation risk

Nächster Artikel The implications of tax loss carryforwards on investment policy

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The data provided below can be found at https://www.climatebonds.net/policy/policy-areas/tax-incentives.

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We define the index as an average of the dynamics of the conventional bonds. In practice, the investor may trade a large quantity of conventional bonds and only a couple of green bonds. Thus, we argue that it is more convenient for the government to index the remuneration proposed on an average dynamics of conventional bonds in order to have more granularity for the green bonds’ incentives.

We force the control processes to be strictly positive so that the density of the canonical process in Appendix A is invertible and we can define properly the weak formulation of the control problem. Practically, this simply means that the investor ahs to invest in the index, and in at least one of the conventional and one of the green bonds.

See Appendix A for the weak formulation of the control problem, which explains how to construct \(\mathbb {P}^\pi \).

We will see later that there might be several best responses of the Agent. Thus, following the tradition in the moral hazard literature, see Mas-Colell, Whinston, and Green [33], Sannikov [43] among others, we assume that the Principal has enough bargaining power to be able to choose the best response of the Agent that maximises his own utility.

The presented methodology can also be adapted to other choices of modelling.

We use the notation \(\mathbb {E}^{({\hat{\pi }}(t,Z_t,\Gamma _t))_{t\in [0,T]}}[\cdot ]=:\mathbb {E}^{{\hat{\pi }}(Z,\Gamma )}[\cdot ]\)

In practice, we observe that for the set of parameters we choose for the numerical experiences, the function \(h^{\text {obs}}\) is strictly concave with respect to its last variable thus admits a unique maximizer \({\hat{\pi }}\).

In particular, as the bond prices do not vary drastically during the year, we use 10 time steps, 40 space steps for the cash process, 10 for the stochastic rate and 20 for the risk factors of the green bond and index of conventional bonds.

Practically, we just choose a sufficiently large grid for values of c and perform optimization on the problem of the Agent to obtain the corresponding c. In this case, We obtain \(c=0.024\).

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Titel: Governmental incentives for green bonds investment
verfasst von: Bastien Baldacci
Dylan Possamaï
Publikationsdatum: 16.05.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Mathematics and Financial Economics / Ausgabe 3/2022
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-022-00320-w

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