Pricing Asian options

Options are securities that are difficult to price. In particular American options, which can be exercised at any time posed a serious challenge that could only be solved in approximation with some Nobel Prize winning work. European options are simpler because they can only be exercised at maturity. Today, I learned there are also Asian options. Asia seem really to catch up in all aspects of economic life. Asian options are American options with the difference that the exercise price is some form of average of the underlying price.

Paolo Foschi, Stefano Pagliarini and Andrea Pascucci provide a way to price Asian options in a first approximation under local volatility, that is the price volatility depend on the current price level, and provide an algorithm for higher order approximations. As you may guess, it is not straightforward. Along the way, I also learned about the Greeks in option pricing. They measure various aspects of the sensitivity of option prices to underlying parameters, and they are usually represented by Greek letters. Now that I have learned that, I'll leave the actual pricing of Asian options to others.

Sweatshop equilibrium

Westerners complain about sweatshops in Asia for two reasons: they produce at much lower labor costs, thus undercutting the Western labor force; and the labor conditions are inhumane due to long hours and poor environment. One answer to these critics is that without those sweatshops, the local labor force would not have jobs and that eventually conditions and wages will improve, as it has happened during the Industrial Revolution in the West.

Nancy Chau does not seem to share this vision as she shows sweatshop conditions could be permanent due to an unfortunate outcome in a multiple equilibrium. Think of the search and matching framework used nowadays to study the labor market. People need time to explore and find new jobs. But this time is not available in a sweatshop. In other words, on-the-job search is impossible and workers end up in a situation akin to slavery. The way out? Enforce shorter hours, even if this means temporarily reducing the workers welfare. The latter may oppose it, but it is only because they do not know what their outside options are.

The scenario I describe above is only one of several possible ones, but it is somehow reminiscent of European labor history. But Chau shows that there are also equilibria where an economy can grow out of sweatshop conditions without intervention. The big question is then: in which equilibrium are Asian sweatshops currently?

The rise of Europe, the standstill of Asia

One of the big challenges of Economic history is to explain why, a thousand years ago, Asia, and in particular China, suddenly stagnated and why in the following centuries Europe started growing, leading eventually to the Industrial Revolution before any other continent. Of particular interest here is that even when you abstract from the leaders of the Industrial Revolution and look at, say, Bulgaria, Norway and Portugal, they have done much better than the rest of the world. Why?

Some of the standard answers have been that this is due to 1) cultural aspects, but within the time line we are talking about here, this is endogenous; 2) chance events (steam engine, proximity of coal), but European countries away from such events also grew faster than Asian ones; 3) resource grab from America, but would Asia really have benefited from such manna?

Cem Karayalçin argues that this divergence in growth is due to the political competition in Europe. States were fragmented and small, and people could escape there policies by migrating. This was impossible in Asia once the Ottoman, Chinese and Mughal empires were created. The latter essentially had monopoly power over fiscal matters, and thus could exploit their trapped population without further harm to the rulers. Contrast this with Europe, where sovereigns had to be careful not to tax too much, to provide services for the taxes and even had to dole out incentives to attract farmers.

A particularly important aspect of this competitive environment in Europe was that sovereigns were careful to give sufficient guarantees for ownership, that is, not expropriate at will. This made the accumulation of capital favorable. The same cannot be said for Asian empires, where for example the 122 top ranking nobles received 1/8 of the national product of India at the time of Akbar. Bequests were typically confiscated. In the Ottoman empire, wealthy traders would be stripped of their assets if not killed. It is difficult to muster any aggregate savings necessary for capital accumulation in such a hostile environment.

Karayalçin's paper has two parts: one theoretical that demonstrates his points, the other historical where he justifies the assumptions underlying his results, for example evidence on mobility in Europe since medieval times, the lack thereof in the Asian empires, and the differences in taxation burdens. This paper makes Economic history exciting.

The Economics of energy subsitution

The increase in oil prices allows nicely to highlight the mechanics of substitution. The increase in the price of most goods lead to a decrease in its use, while increasing the demand for its substitutes. This leads to an increase in the price in the other goods. We have seen this in the past month nicely with increases in electricity and food prices, although these are not pure substitution effects (oil is at least partly an input).

Another substitution effect come form the use of goods that were not used before. In the case of energy, using alternatives like solar energy or windmills becomes more economical, thus creating goods that were not in demand before. But again, this is not a pure substitution effect, because these alternative energy sources have been pushed for other reasons as well, such as pollution reduction.

For automobiles, the rise of hybrid cars is a substitution effect, although they still use some gas. What about a car that does not use energy from oil at all? Enter the AirCar, which simply runs on compressed air. The concept is ten years old, but was not economical until now (except for some cars running in Spain). Tata Motors, the major Indian car manufacturer now announced it will start producing a car based on this concept in August 2008. The MiniCAT will have a range of 300km for a maximum speed of 105km/h, the refill will come to $2.00 at a station, and an emergency compressor can be plugged into a socket to refill as well.

Note that this car does not use the air pressure per se, but rather the thermodynamic effect when you change the pressure and the volume of the air. The emissions are thus only very cold air, which can be used for air conditioning...

Politicizing markets: the India example

India is facing rising crude oil costs like other nations, but very differently. Indeed, the retail price of gas is set by the government, and as this price has been adjusted only once in 20 months, refineries that have to pay the market costs for their input face big losses. And the fact that the government is postponing meetings to solve the issue makes the problem just worse and worse. The longer it waits, the more brutal the price increase will be, and the more people will revolt. Because there, people have a reason to blame the government for price changes as the latter sets them...

Politicizing an economy is always a bad idea, and India is a prime example in this respect. For example, lobbies have been successful in enforcing protection for small manufacturers by preventing big plants to establish. This has especially hurt India in the textile sector, for which it is perfectly suited but has abandoned the world market to others to preserve inefficient mom and pop operations. By some accounts, the Indian GDP could be close to tripled by simply removing this kind of government meddling. Since this account, the Indian government has taken this seriously, deregulating substantially, leading to growth rates similar to China. But the new government ruled by the Congress Party does not seem eager to pursue this policy at all, unfortunately.