The fundamental theorem of asset pricing for continuous processes under small transaction costs

A version of the fundamental theorem of asset pricing is proved for continuous asset prices with small proportional transaction costs. Equivalence is established between: (a) the absence of arbitrage with general strategies for arbitrarily small transaction costs ${\varepsilon > 0}${\varepsilon > 0}, (b) the absence of free lunches with bounded risk for arbitrarily small transaction costs ${\varepsilon > 0}${\varepsilon > 0}, and (c) the existence of e{\varepsilon}-consistent price systems—the analogue of martingale measures under transaction costs—for arbitrarily small ${\varepsilon > 0}${\varepsilon > 0}. The proof proceeds through an explicit construction, as opposed to the usual separation arguments. The paper concludes comparing numéraire-free and numéraire-based notions of admissibility, and the corresponding martingale and local martingale properties for consistent price systems.     

Aktuareksamen 1927 ved Universitetet i Oslo.

1. Introduction.

The two cases where a normal distribution is “truncated” at a known point have been treated by R. A. Fisher (1) and W. L. Stevens (2), respectively. Fisher treated the case in which all record is omitted of observations below a given value, while Stevens treated the case in which the frequency of observations below a given value is recorded but the individual values of these observations are not specified. In both cases the distribution is usually termed truncated. In the first case, admittedly, the observations form a random sample drawn from an incomplete normal distribution, but in the second case we sample from a complete normal distribution in which the obtainable information in a sense has been censored, either by nature or by ourselves. To distinguish between the two cases the distributions will be called truncated and censored ¹ The term “censored” was suggested to me by Mr J. E. Kerrich. , respectively. The term “point of truncation” will be used for both.     

No arbitrage and closure results for trading cones with transaction costs

In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for , the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment, , does obey the fundamental theorem of asset pricing and, secondly, if is arbitrage-free then it is the closure of . We then conclude by showing how to represent claims.      

Paulson's gift

We calculate the costs and benefits of the largest ever US government intervention in the financial sector announced during the 2008 Columbus-day weekend. We estimate that this intervention increased the value of banks’ financial claims by $130 billion (bn) at a taxpayers’ cost of $21–$44 billion with a net benefit between $86 and $109 bn. By looking at the limited cross section, we infer that this net benefit arises from a reduction in the probability of bankruptcy, which we estimate would destroy 22% of the enterprise value. The big winners of the plan were the bondholders of the three former investment banks and Citigroup, while the losers were JP Morgan shareholders and the US taxpayers.     

Asymptotic analysis for optimal investment and consumption with transaction costs

We consider an agent who invests in a stock and a money market and consumes in order to maximize the utility of consumption over an infinite planning horizon in the presence of a proportional transaction cost . The utility function is of the form U(c) = c^1-p/(1-p) for p > 0, . We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of , and we also obtain asymptotic results on the boundary of the no-trade region.Received: July 2003, Mathematics Subject Classification (1991): 90A09, 60H30, 60G44JEL Classification: G13Work supported by the National Science Foundation under grants DMS-0103814 and DMS-0139911.     

Unintended consequences of the increased asset threshold for FDICIA internal controls: Evidence from U.S. private banks

We examine the unintended consequences of the 2005 increase from $500 million to $1 billion in the asset threshold for the Federal Deposit Insurance Corporation Improvement Act (FDICIA) internal control reporting requirements. We focus on a test sample of banks that increased their total assets from between $100 million and $500 million prior to the change in regulation to between $500 million and $1 billion within two years following the change. These “affected” banks are no longer subject to the internal control requirements but would have been had the regulation not been changed. We hypothesize that these affected banks are likely to make riskier loans, which will increase the likelihood of failure during the crisis period. We find evidence consistent with this hypothesis. Affected banks have higher likelihood of failure during the crisis period than banks from two different control samples. We also find that auditor reputation (i.e., whether the bank is audited by a Big 4 auditor or an industry specialist auditor) has a moderating effect on the likelihood of failure for these affected banks.     

Satisfying convex risk limits by trading

A random variable, representing the final position of a trading strategy, is deemed acceptable if under each of a variety of probability measures its expectation dominates a floor associated with the measure. The set of random variables representing pre-final positions from which it is possible to trade to final acceptability is characterized. In particular, the set of initial capitals from which one can trade to final acceptability is shown to be a closed half-line . Methods for computing are provided, and the application of these ideas to derivative security pricing is developed.Received: May 2004, Mathematics Subject Classification (2000): 91B30, 60H30, 60G44JEL Classification: G10Steven E. Shreve: Work supported by the National Science Foundation under grants DMS-0103814 and DMS-0139911.Reha Tütüncü: Work supported by National Science Foundation under grants CCR-9875559 and DMS-0139911.     

On irregular functionals of SDEs and the Euler scheme

We prove a sharp upper bound for the error $\mathbb {E}|g(X)-g(\hat{X})|^{p}We prove a sharp upper bound for the error in terms of moments of , where X and are random variables and the function g is a function of bounded variation. We apply the results to the approximation of a solution to a stochastic differential equation at time T by the Euler scheme, and show that the approximation of the payoff of the binary option has asymptotically sharp strong convergence rate 1/2. This has consequences for multilevel Monte Carlo methods. The author was supported by the Finnish Graduate School in Stochastics and Statistics, the Ellen and Artturi Nyyss?nen Foundation, and the Academy of Finland, project #110599.     

Foreign holdings of U.S. Treasuries and U.S. Treasury yields

Foreign official holdings of U.S. Treasuries increased from $400 billion in January 1994 to about $3 trillion in June 2010. Most of this growth is accounted for by a handful of emerging market economies that have been running large current account surpluses. These countries are channeling their savings through the official sector, which is then acquiring foreign exchange reserves. Any shift in policy to reduce their current account surpluses or dampen the rate of reserves accumulation would likely slow the pace of foreign official purchases of U.S. Treasuries. Would such a slowing of foreign official purchases of Treasury notes and bonds affect long-term Treasury yields? Most likely yes, and the effects appear to be large. By our estimates, if foreign official inflows into U.S. Treasuries were to decrease in a given month by $100 billion, 5-year Treasury rates would rise by about 40–60 basis points in the short run. But once we allow foreign private investors to react to the yield change induced by the shock to foreign official inflows, the long-run effect is about 20 basis points.     

Vector-valued coherent risk measures

We define (d,n)-coherent risk measures as set-valued maps from into satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from valued random portfolio to valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.Received: February 2004, Mathematics Subject Classification (2000): 91B30, 46E30JEL Classification: D81, G31     

Eksamen i Forsikringsvidenskab og Statistik ved Københavns Universitet

abstract

Ved et Sporvognsstoppested pas serer Linje 1 hvert 6. Minut, Linje 15 hvert 7 ½ Minut; mellem de to Linjers Afgangstider antages der ikke at bestaa nogen Forbindelse. Find Sandsynligheden for:

1^p0. At en tilfældig Passager maa vente kortere paa Linje 1 end paa Linje 15.

2^p0. At han højst maa vente 2 Minutter for at komme med en af de to Linjer.     

美国二次量化宽松货币政策研究

2010年11月3日，美联储第二轮量化宽松政策（QE2）正式启动。其主要内容为在维持0-0．25％利率水平条件下，从当日起至2011年6月份前，每月购买750亿美元的长期国债，总购买量为6000亿美元。此举意在降低长期利率，提高通胀预期，降低失业率，促进美国经济尽快复苏。本文主要分析QE2对美国的作用和对中国的影响，并从对冲流动性角度分析中国应对量化宽松政策应采取的措施。     

Efficient estimation of drift parameters in stochastic volatility models

We study the parametric problem of estimating the drift coefficient in a stochastic volatility model , where Y is a log price process and V the volatility process. Assuming that one can recover the volatility, precisely enough, from the observation of the price process, we construct an efficient estimator for the drift parameter of the diffusion V. As an application we present the efficient estimation based on the discrete sampling with δ _n →0 and n δ _n →∞. We show that our setup is general enough to cover the case of ‘microstructure noise’ for the price process as well.      

LESSONS FROM A MIDDLE MARKET LBO: THE CASE OF O.M. SCOTT

In 1986 The O.M. Scott & Sons Company, the largest producer of lawn care products in the U.S., was sold by the ITT Corporation in a divisional leveraged buyout. The company was founded in Marysville, Ohio in 1870 by Orlando McLean Scott to sell farm crop seed. In 1900, the company began to sell weedfree lawn seed through the mail. In the 1920s, the company introduced the first home lawn fertilizer, the first lawn spreader, and the first patented bluegrass seed. Today, Scott is the acknowledged leader in the “do-it-yourself” lawn care market, with sales of over $300 million and over 1500 employees. Scott remained closely held until 1971, when it was purchased by ITT. The company then became a part of the consumer products division of the huge conglomerate, and operated as a wholly-owned subsidiary for 14 years. In 1984, prompted by a decline in financial performance and rumors of takeover and liquidation, ITT began a series of divestitures. Over the next two years, total divestitures exceeded $2 billion and, after years of substandard performance, ITT's stock price significantly outperformed the market. On November 26, 1986, in the midst of this divestiture activity, ITT announced that the managers of Scott, along with Clayton & Dubilier (C & D), a private firm specializing in leveraged buyouts, had agreed to purchase the stock of Scott and another ITT subsidiary, the W. Atlee Burpee Company. The deal closed on December 30. Clayton & Dubilier raised roughly $211 million to finance the purchase of the two companies. Of that $211 million, almost $191 milion, or 91% of the total, was debt: bank loans, subordinated notes, and subordinated debentures. The $20 million of new equity was distributed as follows: roughly 62% of the shares were held by a C & D partnership, 21% by Scott's new subordinated debtholders, and 17.5% by Scott management and employees. After this radical change in financial structure and concentration of equity ownership, Scott's operating performance improved dramatically. Between the end of December 1986 and the end of September 1988, sales were up 25% and earnings before interest and taxes (EBIT) increased by 56%. As shown in Table 1, this increase in operating earnings was not achieved by cutting back on marketing and distribution or R & D. In fact, spending on marketing and distribution increased by 21% and R & D spending went up by 7%. Capital spending also increased by 23%.     

Economic impact of political barriers to cross-border acquisitions: An empirical study of CNOOC's unsuccessful takeover of Unocal

In 2005, the US Congress challenged the acquisition by CNOOC (a Chinese state-owned enterprise) of Unocal (a US firm). This challenge creates a political barrier for foreign companies to acquire US oil companies. This paper examines the stock price reaction of US oil companies to this political opposition. Using an event study methodology, we find that this political barrier resulted in a substantial decline in the market value of US oil companies. For a period of 44 days, during which six anti-CNOOC-takeover political events occurred, the cumulative decline in the market value of a portfolio of 13 US oil refining firms was $47.5 billion and that of a portfolio of 66 US oil and gas exploration firms was $11.4 billion. This study is the first to analyze and quantify the stock price reaction of US non-merging firms to political barriers to cross-border acquisitions. It also has a policy implication regarding the recent enactment of the Foreign Investment and National Security Act of 2007.     

Feeding Latin America's children.

More than US $1.6 billion is spent annually on 104 programs in 19 Latin American and Caribbean countries to subsidize or provide food for people supposedly at risk of malnutrition. This amount constitutes only 0.2% of these countries gross national product. If there is no double-counting, these programs reach more than 80 million people, or 21% of the population, at a cost of $20/beneficiary or $4 per capita. Yet some 10 million children are malnourished, which suggests that the expenditures are poorly directed or ineffective. There is little hard evidence that these programs are preventing much malnutrition; even curative results are seldom measured. THe effort is too small in some countries with great needs, while other countries have nearly eliminated malnutrition. Where coverage is high, programs--although generally targeted and with sensible criteria--do not always reach the neediest. They may also fail to provide enough food or to combine food with the health care and nutritional education necessary to attack all 3 root causes of malnutrition: poverty, disease, and ignorance. The evidence, limited mostly to program inputs rather than results, suggests that greater progress against undernourishment is possible even with current spending levels.     

Do Market Makers Suffer from Splitting Headaches?

Studies of transactions surrounding stock split ex-dates often conclude that splitting firms either experience a decline or an improvement in their stock's liquidity, based on independent measures of trading costs and trading activity. In contrast, our evidence suggests that splits from outside into what often is deemed to be the optimal stock price range of $10.00 to $39.99 are nonevents for market makers: The spread-setting behavior of the market does not change after a split. Our analysis accounts for the interdependencies between bid-ask spreads and market microstructure effects and distinguishes between optimal and all other splitting firms.