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This paper investigates the alternative financing instruments that can be used to hedge sovereign risks and finance development in African countries. Many heavily indebted countries are exposed to external risks especially the exchange rate shocks due to limited use of hedging instruments. We propose alternative financing instruments to minimize sovereign risks and the cost of debt. Our paper uses the standard model for pricing options, the Black-Scholes model to determine the fair value of options. The findings show that barrier options have an added advantage over plain vanilla options because of its knock-ins and knock-outs features hence they are the most affordable to use. An important aspect of the effective debt management policies should be on developing local bond market to access alternative financing instruments in the world capital market.

This paper investigates the alternative instruments of financing development and hedging risks in African countries. The limited hedging instrument in Sub-Saharan Africa has been a policy concern for foreign debt management since the 1980’s debt crisis. Many developing countries as pointed out by [

The understanding of alternative financing instruments for hedging sovereign risks is important for policymakers. Managing sovereign risks will assist the policymakers in choosing cost-effective financial instruments to avoid sovereign defaults. Efficient debt management policies as noted by [

Despite the increase in financing needs, few studies focus on innovative financing and hedging instruments in African countries. Most studies, such as [

The main contribution is to assess the cost-effective instruments for hedging sovereign risks in African countries. This paper builds on the works of [

The structure of the paper is as follows. Section 2 reviews the literature. Section 3 presents the theoretical framework. Section 4 describes data. Section 5 analyses the findings. Section 6 concludes with policy recommendations.

The literature on alternative financing instruments in Africa is relatively scarce. Most of the studies focus on the financing instruments in the emerging market economy. Alternative financing instruments issued in the international capital market are limited in African countries hence they are exposed to external shocks. Since developing countries are exposed to external shocks such as trade shocks, interest rate shocks as shown by [

Another strand of studies show that sub-Saharan Africa’s infrastructure needs are approximately USD 130 - 170 billion and a financing gap of $67.6 - $107.5 billion annually. This increasing infrastructure gap has prompted African countries to reconsider the role of private sector participation in bridging the gap. Although, most of the sub-Saharan African countries with the exception of South Africa and Nigeria have not been able to attract significant private sector investment in different economic sectors. Moreover, the capacity to effectively construct, design and manage public private partnerships is a significant challenge across Africa. Only a few countries such as South Africa, Nigeria, Zambia, and Kenya have implemented PPP frameworks, however, these countries are still experiencing challenges in terms of resources and expertise. Importantly, for PPPs to be successfully across Sub-Saharan Africa, a sound policy, legal and institutional frameworks with clear guidelines and procedures for development and implementation of PPPs should be enforced. For instance, [

Some studies have investigated the role of indexed bonds in hedging risks as a useful tool for debt management. The government can hedge risks by issuing indexed bonds or shortening the maturity of domestic debt. Indexed bonds as pointed out by [

A number of studies have investigated the issuing of bonds tied to their main export commodities. The issuing of commodity-linked bonds would reduce the debt burden along with declines in export prices. Developing countries should prefer issuing commodity-linked bonds than conventional debt to protect their export commodities from price volatilities. Commodity linked bonds such as gold-linked bonds as shown by [

A related strand of literature focus on financing instruments in which the coupon payments are tied to the GDP of the issuing country. GDP-linked bonds have potential benefits as a financing instrument. Issuing a bond whose coupon payment is indexed to GDP growth is similar to issuing a plain vanilla option. According to [

Another strand of literature show that developing countries can use options whose value depend on the value of the underlying asset to hedge commodity price risks. The simplest financial option as shown by [

Other studies focus on credit default swap which is a contract that provides insurance against a default by a sovereign entity and enhance financial stability. Credit derivatives are financial instruments managing default risk which occurs when there is a decline in the ability of the borrower to repay the debt. Credit default swap as suggested by [

A commodity derivative in the form of a plain vanilla put option should be attached to sovereign Eurobond to hedge the occurrence of a sovereign default risk. When commodity prices are increasing, [

Modern studies have shown that Artificial Intelligence can be used in forecasting the applicability of innovative financing in the capital market using intelligent algorithms such as Artificial Neural Networks. The human intelligence includes learning, reasoning and problem solving, which is accomplished by studying how human brain thinks, and how humans learn, decide and work while trying to solve a problem. The ANNs gather their knowledge by detecting the patterns and relationships in data and learn (or are trained) through experience, not from programming.

The model builds on the works of [

C t = S t N ( ∂ 1 ) − K e − r T N ( ∂ 2 ) (1)

where:

C_{t} is the price of a European call option at time t, S_{t} is the stock price, K is the strike price, r is the risk free interest rate, t is the time to option expiration, σ is the standard deviation of the option. The simplest financial option, is the European call option. If stock price is greater than the strike price at expiry, then it pays off to exercise call option. The option prices are derived using the general [

C t ( s , t , K , r , σ ) = S N ( d 1 ) − K e − r T N ( d 2 ) (2)

where N(d_{1}) and N(d_{2}) are the cumulative distribution function of a standard normal random variable.

d 1 = log ( S 0 K ) + ( r + σ 2 2 ) T T σ , d 2 = log ( S 0 K ) + ( r − σ 2 2 ) T T σ = d 1 − T σ

where C_{t} denote the price of a European call option at time t, S is the stock price, K is the option striking price, r is the risk free interest rate, t is the time to option expiration, σ is the standard deviation of the option and N(.) is the cumulative distribution function of a standard normal random variable N(0,1). For the special case of a European call or put option, Black-Scholes model indicate that a hedged position can be created consisting of a short position in the option and a long position in the underlying where option’s value will not depend on the price of the underlying. In addition, [

P t = K e − r T N ( − ∂ 2 ) − S t N ( − ∂ 1 ) (3)

where C_{t} denote the price of a European call option at time t, S is the stock price, K is the option striking price, r is the risk free interest rate, t is the time to option expiration, σ is the standard deviation of the option and N(.) is the cumulative distribution function of a standard normal random variable N(0,1).

The price P_{t} of a European put option at time t with the same expiry date T and strike price K can be obtained by the following put-call parity relationship

C t − P t = S t − K e − r ( T − t ) (4)

P_{t} is the current stock price.

Solving partial differentiation equations in closed form is difficult but in the case of Black Scholes model, the European call option at time t = 0 is

V 0 = S 0 N ( d 1 ) − K e − r t N ( d 2 ) (5)

European put option is given by:

V 0 = K e − R t N ( − d 2 ) − S 0 N ( − d 1 ) (6)

d 3 = log ( S 0 S b ) + ( r + σ 2 2 ) T T σ

d 4 = d 3 − T σ

a = ( S 0 S b ) − 1 + ( 2 r σ 2 ) , b = ( S b S 0 ) 1 + ( 2 r σ 2 )

When a financial security is traded, the buyer is said to take a long position in the security and the seller is said to take the short position in the security. The derivative pricing problem is solved by determining a fair value for a derivative. Two boundaries on s(t) are 0 and ∞ representing maximum and minimum price of the underlying asset. Black-Scholes model is also used to price barrier options which behave like a plain vanilla option as long as the underlying asset price does not fall below or predefined barrier_{.} As noted by [

d f d t + 1 2 σ 2 S 2 d 2 f d S 2 + r S d f d S − r f = 0 (7)

where r is the risk-free interest rate, σ is the volatility of the underlying asset, S(t) is the current price at time t. The value of a European option has three components, the intrinsic value, the striking price of the option and the insurance value. The intrinsic value is the difference between the price of the underlying asset, S. The striking or exercise price, K is the payoff from exercising option only on the expiration date and the option’s premium is the payment for option upfront.

The barrier option behaves like a plain vanilla option as long as the underlying asset price does not fall below or predefined barrier, S_{b}. In up-and-out options, they are active when S_{b} > S as long as the underlying asset price crosses and falls below a predefined barrier, S_{b}. The rationale for barrier options is that by putting a barrier, the payoff is limited. If both down-and-in and down-and-out are held then the effect of the barrier is cancelled and the two barrier options are equivalent to a vanilla put option.

This study employs monthly data in which the commodity prices for oil, gold and silver are from the IMF IFS for Tanzania (Gold), Copper (Zambia) and Oil (Nigeria). Commodities such as gold, oil and silver are used because they are highly volatile. The volatility and the risk free interest rate measured by the 10 year US treasury bill are from Bloomberg for the month of December 2012. The “strike” price implies percentage of the underlying price. The option prices, interpreted as the percentage of the underlying nominal amount, are derived using the Black-Scholes formula [

In vanilla options, a put option and a call option provides insurance against commodity price shocks. A put option acts as a price floor by providing insurance against price decrease. [

As shown in

These prices, OTM put options are less expensive that the ATM put options. OTM put options occur when the strike price of a put option is greater than the spot price of the underlying asset. However, risk reversals being part of the plain vanilla options, are still inefficient to reduce option costs. [

Commodity | Strike price (K) | Volatility (σ) | Price of 1-year maturity | Price of 3-year maturity |
---|---|---|---|---|

Silver | 158.16 | 26.04% | 13.66 | 14.58 |

Oil | 111.07 | 28.95% | 14.80 | 10.40 |

Gold | 137.56 | 13.78% | 11.28 | 9.65 |

Source: IMF, IFS and Bloomberg for the month of December 2012. Note that at the money put option is when the underlying is equal to the strike price at a given period of time.

Commodity | Stock price | Strike price (K) | Volatility (σ) | Price of 1-year maturity | Price of 3-year maturity |
---|---|---|---|---|---|

Silver | 158.16 | 138.16 | 26.04% | 7.86 | 8.30 |

Oil | 111.07 | 91.07 | 28.95% | 11.94 | 8.51 |

Gold | 137.56 | 117.56 | 13.78% | 9.60 | 8.01 |

Source: IMF IFS and Bloomberg for the month of December 2012. Note that out of the money put option is when the underlying is higher than the strike price at a given period of time.

Commodity | Stock price | Strike price | Volatility | Price of 1-year maturity | Price of 3-year maturity |
---|---|---|---|---|---|

Silver | 158.16 | 138.16 | 26.04% | 1.09 | 0.9 |

Oil | 111.07 | 91.07 | 28.95% | 3.85 | 7.8 |

Gold | 137.56 | 117.56 | 13.78% | 1.48 | 0.99 |

Source: IMF, IFS and Bloomberg for the month of December 2012. Note that up-and-out put option is when the underlying exceeds the barrier, H.

Up-and-out put option prices are more effective than plain vanilla put options. An up-and-out call option pays off at maturity as long as the underlying hits the barrier or exceeds the barrier at any time before expiring. [

The traditional Black-Scholes model uses partial derivatives to analyze the sensitivity of option premium to small changes in the model’s parameters known as the Greeks. These hedging parameters are considered to be useful descriptive statistics to option traders for a portfolio. Within the Black–Scholes model, these sensitivities are obtained by taking the partial derivatives of the option-pricing formula below.

If gamma is small, delta becomes less sensitive whereas if gamma is large, then delta becomes more sensitive to variations in the underlying. It implies that a 1% change in stock price, delta changes by 10%. Delta and gamma hedging are both based on the assumption that the volatility of the underlying is constant. The ρ rho is highly volatile that is a small change in interest rate leads to a significant change in the option price. Our results show that a 1% change in interest rate, the call price will vary by 8%. When interest rates increase, call prices increase

The delta of a call option (∆) | 0.90 |
---|---|

The gamma of a call option (Ґ) | 0.10 |

The rho of a call option (ρ) | 0.80 |

The theta of a call option (Φ) | 0.31 |

The vega of a call option (ϒ) | 0.39 |

Source: IMF, IFS and Bloomberg for the month of December 2012.

too but put prices decline. However, the theta, Φ which is the rate of change of option price to changes in time is less sensitive. The theta of a call option on time is 0.31 which indicates that a 1% change in time, the value of option price will vary by 31%.

Similarly, the vega, ϒ, which measures the sensitivity of option premium to changes in volatility shows that a 1% change in volatility leads to a change in option price by 39%. According to [

Developing countries depend heavily on primary commodities for their export earnings which exposes them to commodity price shocks. The commodity price shocks are persistent and highly volatile which is the most challenging issues facing policymakers in heavily indebted countries. [

These shocks to commodity prices have important implications for the many heavily indebted countries that are dependent on commodity exports. Price

fluctuations makes export earnings uncertain especially when exchange rate appreciates and interest rate increases due to inflationary pressure. [

However, [

Low levels of commodity prices in the late 1980s and in the 1990s may have played a role in some of the financial crises in commodity exporters emerging markets, deteriorating their current accounts. [

welfare implications in that the persistence of commodity price shocks affects the effectiveness of stabilization policies.

Most of the deliberate attempts to stabilize commodity prices through the buffer stocks and buffer funds, have been unsatisfactory. [

This paper investigates the alternative financing instruments that can be used in the selected African countries to minimise the default risks and finance development. Hedging instruments minimize shocks that are hitting the economy while minimizing the likelihood of sovereign risks and defaults. Most of the developing countries are exposed to interest rate shocks and commodity price fluctuations lead to debt accumulation [

The findings show that barrier options are the most cost-effective financing instruments to use especially the up-and-out barrier put options which is in line with findings by [

Our findings have several important policy implications. Firstly, African countries should mobilise domestic resources by developing their local bond market to access alternative financing instruments such as derivatives in the international capital market. As pointed out by [

The author declares no conflicts of interest regarding the publication of this paper.

Mpapalika, J. (2020) Alternative Financing Instruments for African Economies. Journal of Mathematical Finance, 10, 42-57. https://doi.org/10.4236/jmf.2020.101005