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.

Near rational agents and house price booms

House price run-ups, especially when they appear excessive, are difficult to explain. It is it even more difficult to explain how they are not coordinated across countries in a globalized world. Indeed, right now house prices are severely depressed in the United States, while you can have strong suspicions of bubbles in China, Norway and Switzerland. Bubbles are substantial deviations from fundamentals that could be due to some deviations from rationality or herd behavior, or both. But "rationalizing" this is a major challenge because of the apparent randomness of the occurrence of such house price booms.

Klaus Adam, Pei Kuang and Albert Marcet think they have a way to explain this using the concept of internally rationally agent. Such a agent, like the economist, does not know the true process of prices but tries to infer it from past observation using Bayes' rule. The belief about prices then becomes part of the state space and leads to some sort of path dependence. With shocks that are not perfectly correlated, it is then possible for different countries to experience different paths for house prices.

Econophysics: an introduction

I have criticized a number of times Econophysics as a rather naive venture of physicists into Economics, where there is too much focus on "automatic" data exploration and too little use of theory and understanding of what the data measure. But may it is just my prejudice against and my ignorance of Econophysics.

B. G. Sharma, Sadhana Agrawal, Malti Sharma, D. P. Bisen and Ravi Sharma offer in six pages an account of what Econophysics is, what its goals are, what it can contribute and where it is headed. The basic idea is that economic agents are like particles in that they are in large numbers and interact in complex ways. The dynamics of such complex processes are studied with powerful statistical tools in Physics, and physicists think that this should also apply to Economics. The focus is very much on the stock market, probably because physicists have realized where money can be made. There is no sense that there would be an attempt to improve welfare. They are also much more likely to completely discard a model in one set of observations does not corroborate it. Physicists are especially critical of how economists stick to rejected dogmas and of their inability to explain how small shocks can pan out into large crises.

The focus is really on the description of data process and documenting there statistical properties. In particular, econophysicists want to find ways to exploit even the smallest opportunities for arbitrage by finding, often through obscure and complex black box processes, the right price of an asset at any moment in time. However, there is no attempt at understanding why these arbitrage opportunities arise, say because of some form of irrationality, asymmetric information or perverse interactions in the price mechanism. From this I conclude that Econophysics can be interesting to make money on the stock market, but at least at this point, does not help us in any way in understanding why the world is like it is. Which I find rather ironic for Physics.

About very large risk aversion estimates

The equity premium puzzle is an enduring challenge to our estimates of risk aversion. Indeed, as Rajnish Mehra and Edward Prescott have highlighted, the only way to reconcile a standard model with the observed long-term equity premium is to assume a risk aversion coefficient of 10, while micro-estimate hover around two. This puzzle has been resolved a little bit in various way, most prominently by taking into habit persistence and some other deviations of the standard CRRA or CARA utility functions. But all this still boils down to a risk aversion parameter that is linked by an identity to the intertemporal elasticity of substitution (it is the inverse). But we know how to disentangle the two.

Xiaohong Chen, Jack Favilukis and Sydney Ludvigson estimate a model with the recursive preferences of Larry Epstein and Stanley Zin and Philippe Weil. This is not obvious to do because to estimate the coefficient of risk aversion in this context, one needs a measure of claims to future consumption. Here this is overcome by estimating nonparametrically the continuation value of the consumption process from within the model. The result is that the elasticity of intertemporal substitution is above one, and the coefficient of risk aversion is somewhere between 17 and 60. These are huge numbers. But they still imply a rather modest and sometimes even negative risk premium.

Razor innovation in macroeconomics

Macroeconomics is sometimes like Gillette razors. There is regularly an innovative razor that happens to have more blades than the previous one. And once it gets out of hand, the new razor goes back to fundamentals and has only one blade, before the cycle starts again. In macroeconomics, there was this fad of adding more an more shocks to models until everything became very confusing and unidentifiable. So we returned to simple models (Occam's razor was the innovation) that became more powerful because of the presence of a market friction. Now, these search frictions are appearing everywhere, one-by-one or in pairs, and the latest generation of models has three frictions.

In a pair of papers, Etienne Wasmer alone and then with Nicolas Petrosky-Nadeau introduces search frictions on labor, credit and goods markets. The first is more of an exercise of style, showing it can be elegantly solved in steady-state thanks to block-recursiveness. The second paper is more interesting, as it looks at the dynamic properties of the model and shows that is can better account for the persistence of fluctuations in the data (what frictions are good at) and the volatility of labor flows. Interesting results, especially in the light of the pronounced lag in the recovery of employment in the US these days.

I am waiting for the four-friction model now.

Inattention and bank overdrafts

It happens to everyone: you are not careful and despite having sufficient funds, your checking account is drying up at the wrong moment and you incur an overdraft fee from the bank. Oh well, you say, the penalty is somewhat stiff, but bad planning has consequences. But for those who have genuine liquidity problems or those that are really bad at planning, those fees can add up quickly and become substantial. Even on an aggregate level, it is important. Apparently, US banks earn $35 billion a year from overdraft fees, or a staggering $100 per capita.

Victor Stango and Jonathan Zinman study what can make that people avoid those fees. A lot has of course to do with education and self-discipline, thus reminders become an important tool. Indeed, they notice that people who were exposed to information about overdraft fees in surveys are less likely to incur such fees in the next month, by 12%, and this effect builds up over multiple exposures. This works best with those who need it the most: low education and low financial literacy. And as people avoid overdrafts by making fewer transactions, not increasing balances, it indicates they lower their expenses as a reaction to realizing that they may not afford that much spending. In other words, financial and economic literacy are important and should be favored.

Mission drift in microfinance?

Microfinance is based on a very simple principle. The poorest can only improve if they invest, and very small loans may be sufficient to get them started. But conventional banks do not bother with such loans, and informal money-lenders charge horrendous rates. Microfinance step in and lend small amounts, often without collateral in a community-based scheme where one's reputation is sufficient to obtain somewhat reasonable repayment rates. I am not totally convinced this scheme would work without subsidies, but it obviously serves a useful purpose, as long as it does not crowd out the regular financial system.

Beatriz Armendáriz and Ariane Szafarz point out that the latter can become a problem because of mission drift: as microfinance institutions grow, they gradually target larger loans, neglecting their original mission and becoming more like regular banks. This is like car models that grow in size through the years to follow the life-cycle of their drivers. But Armendáriz and Szafarz think that what looks like mission drift could very well be cross-subsidization, and larger and more profitable loans are made to help continue giving small and less profitable ones. The distinction is important, as donors could be put off by mission drift.

The high welfare cost of small information failures

Are stock markets efficient in the sense that stock prices reflect all available information? This question has preoccupied finance lately as many have started to doubt the efficient market hypothesis during the latest crisis. One critical aspect of this is whether current tests of the hypothesis actually give an accurate picture, and if not whether this matters in a significant way.

Tarek Hassan and Thomas Mertens
claim that it is possible for stock markets to aggregate information properly, that small errors at the household level can accumulate and amplify if these errors are correlated, and that the welfare consequences can be substantial even if the initial errors were small. This cost emerges for a portfolio misallocation due to the higher volatility of stock prices. To get to such a result, they take a standard real business cycle model, add to it that households get a noisy private signal about future total factor productivity. They then look at the stock market for additional information to form expectations. If you allow households to be on average more optimistic than rationality in some state, and more pessimistic in others, you get the above results. Interestingly, Hassan and Mertens show that households face little incentives to correct individually for these small common errors (0.01% of average consumption), but collectively the consequences are large (2.4%). Talk about an amplification.

Risk-free rate tax deductions

The Norwegian shareholder tax is rather peculiar in that it allows the deduction of risk-free interest income, thus only taxing the risky portion of capital income. This is rather counter-intuitive, as one usually wants to encourage risk-taking in the form of venture capital or plain entrepreneurship. But the idea in Norway was that this would make financing of firms neutral with respect to the source of funds.

Jan Södersten and Tobias Lindhe argue this line of reasoning is not appropriate for an open economy like Norway and 56% foreign ownership. Indeed, one needs to understand as well who is investing. Indeed, taxes are capitalized differently by different people. Indeed, for an economy that is so open, returns are largely determined on international markets, What is then determinant for Norway is the after-tax return, and this is where new distortion enter the picture: large firms are financed on international markets, and the after-tax rate is set abroad. Small firms that finance themselves domestically have provide similar after-tax returns, but domestic investors face different tax rules than their foreign counterparts. This is where new distortions can enter, and severe under-investment in domestic firms could be the consequence. But for a rather closed economy, this seems a good idea, especially as it is a neat way to prevent under-reporting of income.

Compartmentalized thinking in personal finances

Even before the crisis hit in the United States, there was talk about how foolish it is to get balloon mortgages, with low teaser rates for a few years. Yet people where going for them, either because they had expectations of strong income growth, or because they were time inconsistent or very impatient. Or people do not understand the true cost of the loan.

Johan Almenberg and Artashes Karapetyan document a phenomenon that is in some ways similar in Sweden. Mortgage interest is deductible from taxes for personal loans, but not when a co=op takes a loan. Yet people seem to favor financial situations that shift debt from personal to co-op loans. On average, the equivalent of US$540 a year are left on table. This can be explained by what is termed salience of debt. People only care about the costs they directly see, and the interest payments of the co-op are not itemized in the fees. The authors survey co-op apartment owners on how they think about their finances. It turns out people a very aware of their personal finances, but completely ignorant of the co-op finances. They never considered the trade-off between personal and co-op debt. That last point may indicate that ignorance may be more important than salience, though. This is reinforced by the fact that market price do not seem to reflect the tax difference.

As expected, lottery players are not rational

There is no mystery that under normal circumstances, homo oeconomicus does not play the lottery. Exceptions arise when there is enjoyment in playing the lottery (is this why slot machines a so popular in the US?) or when there are particular reasons. But casual observation indicates people play the lottery, and a lot. Maybe these circumstances mentioned above are met, maybe they are not rational economic agents.

Claus Bjørn Jørgensen, Sigrid Suetens and Jean-Robert Tyran would say lottery players, at least some of them, have a peculiar sense of probabilities. While many change their numbers, among those who change, many avoid numbers that have recently been drawn, as if the lottery were a drawing without replacement. But if a number is on a streak (drawn a few times in a row), then they choose it. If margins were not so high in lotteries, one could possibly make money by arbitraging against these people trying to predict the lottery numbers. But you can actually getting a positive return from lotteries by only buying tickets when large jackpots are at stake. The International Lottery Fund based in Australia is there to prove it.

Cross-border banking and financial stability

Should banks be allowed to do business across borders? The answer is not obvious. For one, it is beneficial that they have the opportunity to better diversify their risks, but they can do this without having to open branches in other states or countries. The counterpart is that doing business elsewhere increases opportunities for adverse shocks. Finally, regulatory competition in an international banking market leads to a large systemic risk.

Dirk Schoenmark and Wolf Wagner try to sort this out in the case of Europe and come to the conclusion that it depends. They argue that Germany and the UK are well diversified and thus can sustain cross-border banking, even though there appears to be overexposure to the US, as exemplified by the large negative consequences in Europe of the recent crisis in the US. For the countries on the fringes of Europe, though, there seems to be very poor diversification. Indeed, these economies seem to be very dependent on a few large foreign banks, and consequences could be dire if they run into difficulties or decide to pull out.

This analysis is entirely based on asset shares and thus diversification. This neglects a major advantage of foreign banks: they bring lending capital that would otherwise not be available. The case for cross-border banking is thus understated in this paper.

Economists did see the bubble coming

Economists have been lambasted for not alerting the public that a bubble was in the making in US real state, except for a few oddballs. Of course everyone is wiser in hindsight, but what did economists actually say? It never hurts to look at the facts.

Martha Starr analyzes statements in 24 California newspapers from 2002 to 2007. From 1998 to 2005, the state's house prices increased by more than 10% each year. This prompted the newspaper to run 379 stories with 688 statements by economists on house prices. Academics were clearly warning that house prices were not sustainable. Economists employed in the real-industry, however, were resolutely optimistic. What emerges is a mixed message that gave no guidance to the public, which was even reassured by positive messages from the Federal Reserve.

It is entirely possible opinions could have diverged based on the same evidence. But it seems more likely the professionals were not acting in good faith. They had everything to lose from predicting an end of house price growth. The media should have learned not to trust such biased speakers, yet they continue to be interviewed. Now as to why Greenspan and then Bernanke were so optimistic is beyond me. There speeches are definitively strategic and while they may have realized there was a problem, they may have tried to prevent a bubble from bursting too brutally. Then all the credit to them for trying. But one cannot postpone indefinitely a bubble from bursting, and they knew that.

Entrepreneurship and finger length

Entrepreneurship is the engine of growth, thus is it is important to understand what makes entrepreneurs tick and how to identify potential entrepreneurs. Entrepreneurship courses in BS (business schools) are often dismissed as BS (...), but they have the merit to explain the ropes of setting up a business, thus lowering the hurdle. Still not everyone has what it takes.

Luigi Guiso and Aldo Rustichini make the rather surprising discovery that people with lower second to fourth finger length ratio exhibit stronger entrepreneurial skills. There is actually some theory behind this correlation. Indeed, this finger length ratio is associated with prenatal testosterone. Thus it appears that biology has something to do with entrepreneurship and ultimately growth. Does this mean we should now adopt a policy injecting fetuses with testosterone to bolster the nation's growth rate? No, because these entrepreneurs also seem to be over-confident, tend to build empires and thus sub-optimal firm size. But I wonder when bankers will start measuring their clients' hands.

The curse of the more trustworthy gender

It sucks to be a female entrepreneur. You are more likely to repay your loan, but you still keep getting smaller loans. As a consequence, your business is smaller than that of your male counterparts. Of course, all this could be due to some common correlates that cause women to be more trustworthy and yet get smaller loans. Or it could be just plain and simple discrimination.

Isabelle Agier and Ariane Szafarz test the latter hypothesis using rich data from microfinance in Brazil. The idea is to verify whether women are discriminated against in the loan application process. Testing for discrimination is not easy as apparent inequities may make economic sense. But if across to populations a lower or equal loan default rate is associated to a higher or equal loan denial rate, then we have an ethical issue. This what Agier and Szafarz test. Sadly, the news are not good. There is significant discrimination and despite being better creditors, they get smaller loans. Even worse, repeat applicants who could thus prove their trustworthiness get even more discriminated. Of course, there could still be some unobserved variable explaining all this, but I cannot imagine what that could be.

How to finance housing in Islamic economies

Financial markets in Islamic countries face large challenges, as the law prohibits, in principle, interest. Lenders and creditors need to go through all sorts of hoops to find a legal way to allow for something that is interest in spirit but not in fact. One consequence of these hurdles is that the mortgage market is almost non-existent, and this has translated into an absolutely desolate residential stock in many Islamic countries. Clearly, improving the lives of people goes through an proper and active mortgage market. How could this be achieved in an economically and legally reasonable way?

Zubair Hasan claims to have solved this problem. The current practice is to sell the house to a bank and then buy it back with a mark-up added. This margin corresponds of course to interest, but this practice seems very controversial in case of default, as banks insist on full payment of the debt disregarding any installments already paid. This trouble arises because of the ownership structure and this is why the idea is to propose joint ownership between the "landlord" and the bank. The latter gets gradually reimbursed for the amount of the debt and also receives rent for the share of the house it owns. This solution boils down to the same outcome as for a classic, western mortgage. The trouble is that it involves three separate contracts (joint ownership, lease and buyback), and Islamic law prohibits making a contract conditional on another one. This is very constraining.

Hasan's idea is to replace the full ownership of a share of the house by the bank by a constructive ownership, much like a stock broker possesses the stocks his clients really own. The author thinks, without being certain, that this should satisfy Islamic law. But what this highlights is that Islamic law seems to put absurd hurdles on economic activity and that, maybe, it could be adapted to modern circumstances.