Applications of stochastic analysis in finance and statistical inference

First: A continuous-time version of Kyle's model (Kyle 1985), known as the Back's model (Back 1992), of asset pricing with asymmetric information, is studied. A larger class of price processes and of noise traders' processes are studied. The price process, as in Kyle's model, is allowed to depend on the path of the market order. The process of the noise traders' is an inhomogeneous Lévy process. Solutions are found by the Hamilton-Jacobi-Bellman equations. With the insider being risk-neutral, the price pressure is constant, and there is no equilibirium in the presence of jumps. If the insider is risk-averse, there is no equilibirium in the presence of either jumps or drifts. Also, it is analised when the release time is unknown. A general relation is established between the problem of finding an equilibrium and of enlargement of filtrations. Random announcement time is random is also considered. In such a case the market is not fully efficient and there exists equilibrium if the sensitivity of prices with respect to the global demand is time decreasing according with the distribution of the random time. Second: Power variations. it is considered, the asymptotic behavior of the power variation of processes of the form _integral_0^t u(s-)dS(s), where S_ is an alpha-stable process with index of stability 0&alpha&2 and the integral is an Itô integral. Stable convergence of corresponding fluctuations is established. These results provide statistical tools to infer the process u from discrete observations. Third: A bond market is studied where short rates r(t) evolve as an integral of g(t-s)sigma(s) with respect to W(ds), where g and sigma are deterministic and W is the stochastic Wiener measure. Processes of this type are particular cases of ambit processes. These processes are in general not of the semimartingale kind.

Prime Property Institutions for a Subprime Era: Exploring Innovative Models of Residential Development and Finance

This paper breaks new ground toward contractual and institutional innovation in models of homeownership, equity building, and mortgage enforcement. Inspired by recent developments in the affordable housing sector and in other types of public financing schemes, this paper suggests extending institutional and financial strategies such as timeand place-based division of property rights, conditional subsidies, and credit mediation to alleviate the systemic risks of mortgage foreclosure. Alongside a for-profit shared equity scheme that would be led by local governments, we also outline a private market shared equity model, one of bootstrapping home buying with purchase options.

Institutions, Public Debt and Foreign Finance

We study the role of domestic financial institutions in sustaining capital flows to the private and public sector of a country whose government can default on its debt. As in recent public debt crises, in our model public defaults weaken banks' balance sheets, disrupting domestic financial markets. This effect leads to a novel complementarity between private capital inflows and public borrowing, where the former sustain the latter by boosting the government's cost of default. Our key message is that, by shaping the direction of private capital flows, financial institutions determine whether financial integration improves or reduces government discipline. We explore the implications of this complementarity for financial liberalization and debt-financed bailouts of banks. We present some evidence consistent with complementarity.

Adjustment to Target Capital, Finance, and Growth

Does financial development result in capital being reallocated more rapidly to industries where it is most productive? We argue that if this was the case, financially developed countries should see faster growth in industries with investment opportunities due to global demand and productivity shifts. Testing this cross-industry cross-country growth implication requires proxies for (latent) global industry investment opportunities. We show that tests relying only on data from specific (benchmark) countries may yield spurious evidence for or against the hypothesis. We therefore develop an alternative approach that combines benchmark-country proxies with a proxy that does not reflect opportunities specific to a country or level of financial development. Our empirical results yield clear support for the capital reallocation hypothesis.

Malliavin calculus in finance

This article is an introduction to Malliavin Calculus for practitioners.We treat one specific application to the calculation of greeks in Finance.We consider also the kernel density method to compute greeks and anextension of the Vega index called the local vega index.

Corporate finance and the monetary transmission mechanism

This paper analyzes the transmission mechanisms of monetarypolicy in a general equilibrium model of securities marketsand banking with asymmetric information. Banks' optimal asset/liability policy is such that in equilibrium capital adequacy constraints are always binding. Asymmetric information about banks' net worth adds a cost to outside equity capital, which limits the extent to which banks can relax their capital constraint. In this context monetarypolicy does not affect bank lending through changes in bank liquidity. Rather, it has the effect of changing theaggregate composition of financing by firms. The model also produces multiple equilibria, one of which displays all the features of a "credit crunch". Thus, monetary policy can also have large effects when it induces a shift from one equilibrium to the other.

An economic theory of church strictness

This paper makes several contributions to the growing literatureon the economics of religion. First, we explicitly introduce spatial-location models into the economics of religion. Second, we offer a newexplanation for the observed tendency of state (monopoly) churches tolocate toward the "low-tension" end of the "strictness continuum" (ina one-dimensional product space): This result is obtained through theconjunction of "benevolent preferences" (denominations care about theaggregate utility of members) and asymmetric costs of going to a moreor less strict church than one prefers.We also derive implications regarding the relationship between religiousstrictness and membership. The driving forces of our analysis, religiousmarket interactions and asymmetric costs of membership, high-light newexplanations for some well-established stylized facts. The analysis opensthe way to new empirical tests, aimed at confronting the implications ofour model against more traditional explanations.

Finance versus costs for teaching hospitals in Spain

In this paper we analyse the observed systematic differences incosts for teaching hospitals (THhenceforth) in Spain. Concernhas been voiced regarding the existence of a bias in thefinancing of TH s has been raised once prospective budgets arein the arena for hospital finance, and claims for adjusting totake into account the legitimate extra costs of teaching onhospital expenditure are well grounded. We focus on theestimation of the impact of teaching status on average cost. Weused a version of a multiproduct hospital cost function takinginto account some relevant factors from which to derive theobserved differences. We assume that the relationship betweenthe explanatory and the dependent variables follows a flexibleform for each of the explanatory variables. We also model theunderlying covariance structure of the data. We assumed twoqualitatively different sources of variation: random effects andserial correlation. Random variation refers to both general levelvariation (through the random intercept) and the variationspecifically related to teaching status. We postulate that theimpact of the random effects is predominant over the impact ofthe serial correlation effects. The model is estimated byrestricted maximum likelihood. Our results show that costs are 9%higher (15% in the case of median costs) in teaching than innon-teaching hospitals. That is, teaching status legitimatelyexplains no more than half of the observed difference in actualcosts. The impact on costs of the teaching factor depends on thenumber of residents, with an increase of 51.11% per resident forhospitals with fewer than 204 residents (third quartile of thenumber of residents) and 41.84% for hospitals with more than 204residents. In addition, the estimated dispersion is higher amongteaching hospitals. As a result, due to the considerable observedheterogeneity, results should be interpreted with caution. From apolicy making point of view, we conclude that since a higherrelative burden for medical training is under public hospitalcommand, an explicit adjustment to the extra costs that theteaching factor imposes on hospital finance is needed, beforehospital competition for inpatient services takes place.

Expertise and finance: Mergers motivated by technological change

This paper argues that a large technological innovation may lead to a merger wave by inducing entrepreneurs to seek funds from technologically knowledgeable firms -experts. When a large technological innovation occurs, the ability of non-experts (banks) to discriminate between good and bad quality projects is reduced. Experts can continue to charge a low rate of interest for financing because their expertise enables them to identify good quality projects and to avoid unprofitable investments. On the other hand, non-experts now charge a higher rate of interest in order to screen bad projects. More entrepreneurs, therefore, disclose their projects to experts to raise funds from them. Such experts are, however, able to copy the projects and disclosure to them invites the possibility of competition. Thus the entrepreneur and the expert may merge so as to achieve product market collusion. As well as rationalizing mergers, the model can also explain various forms of venture financing by experts such as corporate investors and business angels.

Adjustment to target capital, finance and growth

Does financial development result in capital being reallocated more rapidly to industries where it is most productive? We argue that if this was the case, financially developed countries should see faster growth in industries with investment opportunities due to global demand and productivity shifts. Testing this cross-industry cross-country growth implication requires proxies for (latent) global industry investment opportunities. We show that tests relying only on data from specific (benchmark) countries may yield spurious evidence for or against the hypothesis. We therefore develop an alternative approach that combines benchmark-country proxies with a proxy that does not reflect opportunities specific to a country or level of financial development. Our empirical results yield clear support for the capital reallocation hypothesis.

Idiosyncratic Volatility Puzzle: Influence of Macro-Finance Factors

In this paper, we scrutinize the cross-sectional relation between idiosyncratic volatility and stock returns. As a novelty, the idiosyncratic volatility is obtained by conditioning upon macro-finance factors as well as upon traditional asset pricing factors. The macro-finance factors are constructed from a large pool of macroeconomic and financial variables. Cleaning for macro-finance e§ects reverses the puzzling negative relation between returns and idiosyncratic volatility documented previously. Portfolio analysis shows that the effects from macro-finance factors are economically strong. The relation between idiosyncratic volatility and returns does not vary with the NBER business cycles. The empirical results are highly robust. Keywords: Idiosyncratic volatility puzzle; Macro-finance predictors; Factor analysis; Business cycle. JEL Classifications: G12; G14