Pricing the implicit contracts in the Paris Club debt buybacks

In 2005, more than 20 billion dollars were bought back by Paris Club debtors: Russia USD 15 billion Poland USD 5.4 billion and Peru USD 1.5 billion. During the first half of 2006, more than USD 30 billion in buybacks was announced: Russia USD 22 billion, Algeria USD 8 billion dollars, Brazil USD 1.5 billion. The buybacks consisted of the prepayment of debts at par with no penalties. These transactions were carried out at a discount of more than 20% compared to their net present value. The total loss incurred by creditors in the three buybacks is estimated at more than USD 10 billion. This raises the question as to why the Paris Club creditors agreed to the buybacks voluntarily. It appears that these buybacks are the result of the exercise of specific contracts previously agreed with the debtors in the 1990s, without receiving any compensation for this and without assessing the consequences. These implicit contracts make it possible to formalise the respective interests for creditors and debtors. Their pricing requires the use of financial mathematics tools (derivatives) and stochastic models for interest rates (Vasicek), but applied in the Paris Club framework.buyback; Paris Club; par value; Vasicek model; creditor cartel

Comment on: "Sadi Carnot on Carnot's theorem"

Carnot established in 1824 that the efficiency $\eta_{C}$ of reversible engines operating between a hot bath at absolute temperature $T_{hot}$ and a cold bath at temperature $T_{cold}$ is equal to $1-T_{cold}/T_{hot}$. Carnot particularly considered air as a working fluid and small bath-temperature differences. Plugging into Carnot's expression modern experimental values, exact agreement with modern Thermodynamics is found. However, in a recently published paper ["Sadi Carnot on Carnot's theorem", \textit{Am. J. Phys.} \textbf{70}(1), 42-47, 2002], Guemez and others consider a "modified cycle" involving two isobars that they mistakenly attribute to Carnot. They calculate an efficiency considerably lower than $\eta_{C}$ and suggest that Carnot made compensating errors. Our contention is that the Carnot theory is, to the contrary, perfectly accurate.Comment: Submitted to American Journal of Physic

On Classical Ideal Gases

The ideal gas laws are derived from the democritian concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion aside from the law of energy conservation. A single corpuscle in contact with a heat bath and submitted to a $z$ and $t$-invariant force $-w$ is considered, in which case corpuscle distinguishability is irrelevant. The non-relativistic approximation is made only in examples. Some of the end results are known but the method appears to be novel. The mathematics being elementary the present paper should facilitate the understanding of the ideal-gas law and more generally of classical thermodynamics. It supplements importantly a previously published paper: The stability of ideal gases is proven from the expressions obtained for the force exerted by the corpuscle on the two end pistons of a cylinder, and the internal energy. We evaluate the entropy increase that occurs when the wall separating two cylinders is removed and show that the entropy remains the same when the separation is restored. The entropy increment may be defined at the ratio of heat entering into the system and temperature when the number of corpuscles (0 or 1) is fixed. In general the entropy is defined as the average value of $\ln(p)$ where $p$ denotes the probability of a given state. Generalization to $z$-dependent weights, or equivalently to arbitrary static potentials, is made.Comment: Generalization of previous versions to questions of stabilit