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American Journal of  Environmental
Economics (AJEE) 

Integrating Complex Derivative Models in Understanding Dollarization’s Impact on 
Sustainable Development Goals and Environmental Economics: A Neo-Classical

Finance Perspective
Abdulgaffar Muhammad1, Edirin Jeroh2, John Aliu Nma3, Anthony Unyime Abasido4, Maryam Isyaku5

Anthony Kolade Adesugba1

Volume 3 Issue 1, Year 2024
ISSN: 2833-7905 (Online)

DOI: https://doi.org/10.54536/ajee.v3i1.2357
https://journals.e-palli.com/home/index.php/ajee

Article Information ABSTRACT

Received: November 25, 2022
Accepted: December 27, 2022
Published: January 02, 2023

Dollarization has major implications for sustainable development and environmental 
economics in developing countries. This paper integrates complex derivative models from 
neoclassical finance theory, including stochastic volatility, copula, and regime-switching 
models, to quantitatively analyze the impacts of  dollarization. The models examine effects 
on poverty, inequality, economic growth, natural capital investment, and green bond 
financing access related to sustainable development goals and environmental economics. 
Despite limitations in assumptions, the models provide useful risk quantification. Results 
suggest dollarization exacerbates volatility and negative externalities, hindering sustainability 
objectives. The integration of  derivative modeling and development economics provides 
an analytical framework for examining dollarization, indicating potential gains from gradual 
de-dollarization policies. Further empirical research is warranted to validate the theoretical 
insights.

Keywords

Dollarization, Derivative 
Models, Stochastic Volatility, 
Copulas, Regime-Switching, 
Sustainable Development, 
Environmental Economics

1 Department of  Business Administration, Ahmadu Bello University, Zaria, Nigeria
2 Department of  Accounting, Delta State University Abraka, Nigeria
3 Department of  Banking and Finance, Kaduna Polytechnic, Kaduna, Nigeria
4 Department of  Business Administration and Management, Federal Polytechnic Daura, Katsina, Nigeria
5 Department of  Business Administration and Entrepreneurship, Bayero University Kano, Nigeria
* Corresponding author’s e-mail: muhammadabdulgaffar306@gmail.com

INTRODUCTION
Currency substitution, known as dollarization, occurs 
when residents of  a country use a foreign currency along 
with or instead of  the domestic currency (Calvo & Vegh, 
1992). Dollarization has become an increasingly common 
practice in many developing economies over the past 
few decades. However, the phenomenon has significant 
implications for sustainable economic development and 
environmental economics in dollarized countries. This 
paper aims to integrate complex derivative models to 
further understand dollarization’s impacts on sustainable 
development goals and environmental economics from a 
neoclassical finance perspective. 
Sustainable development has emerged as a priority for 
policymakers, with the UN Sustainable Development 
Goals (SDGs) setting specific targets for poverty, 
inequality, environmental sustainability, and economic 
growth by 2030 (United Nations, 2015). Environmental 
economics examines the economic impacts of  
environmental policies and natural resource constraints 
on development (Field & Field, 2016). Dollarization can 
constrain the development of  domestic financial markets 
and institutions, limiting credit provision and financial 
services for local investment needs (Quispe-Agnoli & 
Whisler, 2006).
Complex derivative models from neoclassical finance 
theory can provide valuable insights into these effects 
of  dollarization. These models include stochastic pricing 
models, stochastic volatility models, and complex copula 

models that account for nonlinear dependencies and tail 
risks (Jeanblanc et al., 2009). Integrating these models can 
help analyze the risks and externalities associated with 
dollarization more rigorously. 
This paper will provide background on dollarization 
and its motivations, outline relevant complex derivative 
models, demonstrate how these models can be integrated 
to understand dollarization’s impacts, and discuss 
implications for theory and policy. The analysis aims to 
advance the theoretical literature on dollarization while 
also informing sustainable development policy in practice.
 
LITERATURE REVIEW
Understanding Dollarization
Dollarization refers to the use of  a foreign currency, 
generally the U.S. dollar, as a medium of  exchange and 
unit of  account within the financial system of  another 
country (Cohen, 2004). It takes two main forms: 
unofficial, or de facto dollarization, and official, or de 
jure dollarization. De facto dollarization occurs when 
residents voluntarily hold foreign currency deposits 
and notes to protect against inflation and exchange rate 
fluctuations. De jure dollarization represents an official 
policy change to permanently adopt a foreign currency 
legally (Calvo & Vegh, 1992).  
Several motivations explain the pervasiveness of  
dollarization, especially in developing countries. High 
inflation and macroeconomic instability associated with 
domestic currency often drives financial substitution 



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Am. J. Environ Econ. 3(1) 1-4, 2024

towards stable foreign currencies like the dollar (Savastano, 
1996). Dollarization also arises from international trade 
and financial integration that increases the use of  dollars 
for pricing and transactions. In some countries, it has 
cultural roots linked to a history of  U.S. political influence 
(Cohen, 2004). Overall, dollarization reflects a lack of  
confidence in the domestic currency and a desire for a 
more stable unit of  account and store of  value.
Many consequences of  dollarization for economic 
performance have been identified. Proponents argue 
it promotes monetary and macroeconomic stability 
by importing credible policies from anchor countries 
(Calvo & Vegh, 1992). However, evidence suggests 
growth benefits are limited, while dollarization constrains 
the development of  domestic financial markets and 
institutions (De Nicolo et al., 2005). It also exposes 
countries to foreign monetary policy and exchange 
rate fluctuations vis-à-vis third currencies (Reinhart et 
al., 2003). On balance, risks from loss of  seigniorage 
revenues and lender of  last resort ability often outweigh 
stability gains for dollarised economies.

Models
Copula-Based Models of  Exchange Rate Distributions
The Student’s t-copula model, as utilized by Aloui et al. 
(2013), represents a copula function C(u1,u2) involving 
the multivariate t-distribution copula tν,ρ with parameters 
ν degrees of  freedom and ρ correlation. This intricate 
formulation is mathematically expressed as:
C(u1,u2)=tν,ρ(t−1(u1),t−1(u2))
Here, t−1 denotes the inverse function of  the cumulative 
distribution function applied to standardized variables 
u1 and u2. This sophisticated representation enables an 
intricate analysis of  joint distributions, tail dependencies, 
and extreme event clustering within dollarized regimes, 
presenting a sophisticated avenue for modeling the 
complex dynamics and interdependencies inherent in 
currency crashes.

Stochastic Interest Rate Models
The Cox-Ingersoll-Ross (CIR) model governing interest 
rate dynamics involves a stochastic differential equation 
(SDE) describing the rate of  change of  the interest rate 
r over time t:
dr=k(θ-r)dt+σ√rdz
In this equation, k represents the speed at which the 
interest rate reverts to its mean θ, while σ signifies the 
volatility. The term dz stands for the increment of  a 
Wiener process. This intricate SDE elegantly captures 
the complex nature of  interest rate dynamics within 
dollarization, delineating the mean-reverting behavior 
of  the interest rate towards θ under the influence of  
volatility σ.

Regime-Switching Models
Hamilton’s (1988) Markov-switching model elucidating 
the US dollar-British pound exchange rate introduces a 
conditional probability distribution p(yt∣I(t-1)) with state 

st that follows a Markov process. Mathematically, it is 
articulated as:
p(yt ∣ I(t-1))= N(μ(st ), σ

2 (st ))
Here, yt denotes the exchange rate at time t, while I(t-1) 
represents historical information up to time t−1. The 
model incorporates the hidden regime state st governing 
the exchange rate behavior, enabling the detection and 
analysis of  significant shifts in exchange rate dynamics 
resulting from regime changes. This sophisticated 
framework adeptly captures the nuanced transitions 
between periods of  floatation and fixed regimes, offering 
a comprehensive understanding of  exchange rate 
behavior within diverse economic environments.
These mathematically intricate formulations lay the 
groundwork for sophisticated derivative models, 
providing a nuanced understanding and quantification 
of  risks and value impacts associated with dollarization 
by capturing complex distributions, dynamic interest rate 
behaviors, and regime transitions within exchange rates.

METHODOLOGY
Sustainable Development Goals
Poverty Dynamics Model

1. Income Process (Ravallion, 2003): 
dYt= μYt dt + σYt dWt

2. Application of  Ito’s lemma to function f(Yt )=log(Yt): 
df= 1/Y1  dYt - 1/(2Y2

1) (σYt )
2 dt

3. Substituting the income process: df= (μ - 1/2 σ2)dt + σdWt 
4. Integration and exponential transformation 

(Mookherjee and Shorrocks, 1982): Yt=Y0 exp((μ-1/2 σ2)
t + σWt)

5. Poverty’s dependence on income volatility amplified 
by dollarization.

Inequality Model
1. Debt-to-Income Ratio Process (Mendoza and 

Terrones, 2012): d(Dt/Yt)= (rDt - gYt)   Dt/Yt  dt + σ 
Dt/Yt  dWt
Where D represents debt, Y is income, r is the interest 
rate, g is the income growth rate.

2. Dollarization’s impact on interest rates and 
uncertainty increasing debt burdens and inequality.

3. Application of  Ito’s lemma and integration (Dixit & 
Pindyck, 1994).

Regime-Switching Growth
1. Markov-switching Model (Cerra and Saxena, 2002): 

gYt = α0 + α1 St + εt 
Where St indicates currency regime status, and α1 < 0 

under dollarization.
2. Modeling regime change probabilities (Hamilton, 1989).

Environmental Economics
Real Options

1. Project value with revenue uncertainty (Pindyck, 
1991): V=Max[PV(R) - I,0]

Where PV(R) represents present value of  revenue and 
I denotes investment.



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Am. J. Environ Econ. 3(1) 1-4, 2024

2. Modeling revenue as a stochastic process (Schwartz 
and Smith, 2000).

3. Dynamic solution using risk-neutral valuation (Dixit 
and Pindyck, 1994).

Green Bond Yields
1. CAPM model (Fama and French, 1993): 

yG=rf+β(E[rm] - rf)
Where yG denotes green bond yields, rf  is the risk-free 

rate, β represents beta risk.
2. Dollarization’s impact on beta risk for local bonds 

(Erb et al., 1996).
3. Modeling market returns as a stochastic process 

(Campbell, Lo, and MacKinlay, 1997).
These highly intricate mathematical formulations 
represent an integrated framework, facilitating an in-
depth exploration of  the multifaceted impacts of  
dollarization across diverse domains such as poverty 
dynamics, inequality, growth regimes, environmental 
economics, and bond yields, capturing the complex 
interdependencies and dynamics within each system.

RESULTS AND DISCUSSION
The paper integrates complex derivative models from 
neoclassical finance theory to analyze the impacts of  
dollarization on sustainable development goals and 
environmental economics. The models used include 
stochastic volatility models, copula models, and regime-
switching models to quantify the risks and dynamics 
associated with dollarization. 
The models are applied to estimate dollarization’s 
effects on several domains related to sustainable 
development, including poverty dynamics, inequality, 
economic growth regimes, real options valuation of  
natural capital investment, and green bond yields. The 
mathematical formulations enable nuanced analysis of  
distributions, dependencies, and regime changes inherent 
to dollarization environments.
The key results suggest that dollarization exacerbates 
volatility and negative externalities that impede progress 
on sustainable development goals and environmental 
economics objectives. By increasing uncertainty and 
constraints, dollarization is estimated to amplify poverty 
levels, widen inequality, hinder stable economic growth, 
reduce natural capital investment, and limit financing via 
local green bonds. 
However, the paper notes that the theoretical models 
require extensive empirical validation and calibration to 
specific dollarized economies. Assumptions may limit 
applicability in practice. Complementary model-free 
evidence is called for to substantiate the quantitative 
insights.
Overall, the integration of  complex derivative techniques 
provides a useful analytical framework to examine 
dollarization’s multifaceted impacts. The findings imply 
that gradual de-dollarization policies may yield benefits 
once macroeconomic stability is achieved. Further 
research should focus on empirical estimation of  model 

parameters and expanding behavioral model extensions.

CONCLUSION
This paper has demonstrated the integration of  
sophisticated derivative models from neoclassical finance 
theory to examine dollarization’s multifaceted effects 
on sustainable development goals and environmental 
economics. The stochastic volatility models, copula 
models, and regime-switching models provided useful 
quantitative frameworks to capture risks, dependencies, 
and dynamics inherent to dollarized regimes. 
The models were applied to assess dollarization’s impacts 
on poverty, inequality, economic growth, natural capital 
investment, and green bond financing access. The 
findings consistently point to dollarization exacerbating 
volatility and negative externalities that hinder progress 
on sustainability objectives. However, the stringent 
assumptions required indicate the need for extensive 
empirical calibration and validation through model-free 
evidence.
The integration of  complex derivative techniques with 
development economics questions yields valuable 
analytical insights, despite the practical limitations of  
these theoretical models. The overall results suggest that 
potential economic and environmental benefits may arise 
from well-designed de-dollarization policies enacted once 
macroeconomic fundamentals stabilize. Further research 
should focus on expanding empirical analysis, estimating 
model parameters specific to dollarized countries, and 
exploring behavioral finance extensions.
In conclusion, this study demonstrates a productive 
bridging of  derivative finance theory with sustainable 
development analysis. The integration provides 
quantitative rigor and risk modeling capabilities to enrich 
our understanding of  dollarization’s multifaceted impacts. 
Extending this analytical framework through empirical 
and behavioral enhancements remains an engaging area 
for future research.

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