We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is $O(1/N^4)$ and the complexity is $O(MN\log N)$, where $N$ is the number of grid points and $M$ is the number of observation dates.

The complex networks approach has been gaining popularity in analysing investor behaviour and stock markets, but within this approach, initial public offerings (IPO) have barely been explored. We fill this gap in the literature by analysing investor clusters in the first two years after the IPO filing in the Helsinki Stock Exchange by using a statistically validated network method to infer investor links based on the co-occurrences of investors' trade timing for 14 IPO stocks. Our findings show that a rather large part of statistically similar network structures is persistent and general: they form in different securities' and persist in time for mature and IPO companies. We also find evidence of institutional herding that hints at the existence of an investor information network.

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint heavy-tailed random vectors featuring not only distinct marginal tail heaviness, but also flexible tail dependence structure. The novelty lies in that pairwise tail dependence between any two dimensions is modeled separately from their correlation, and can vary respectively according to its own parameter rather than the correlation parameter, which is an essential advantage over many commonly used methods such as multivariate $t$ or elliptical distribution. It is also intuitive to interpret, easy to track, and simple to sample comparing to the copula approach. We show its flexible tail dependence structure through simulation. Coupled with a GARCH model to eliminate serial dependence of each individual asset return series, we use this novel method to model and forecast multivariate conditional distribution of stock returns, and obtain notable performance improvements in multi-dimensional coverage tests. Besides, our empirical finding about the asymmetry of tails of the idiosyncratic component as well as the whole market is interesting and worth to be well studied in the future.

We use a rich, census-like Brazilian dataset containing information on spatial mobility, schooling, and income in which we can link children to parents to assess the impact of early education on several labor market outcomes. Brazilian public primary schools admit children up to one year younger than the national minimum age to enter school if their birthday is before an arbitrary threshold, causing an exogenous variation in schooling at adulthood. Using a Regression Discontinuity Design, we estimate one additional year of schooling increases labor income in 25.8% - almost twice as large as estimated using mincerian models. Around this cutoff there is also a gap of 9.6% on the probability of holding a college degree in adulthood, with which we estimate the college premium and find a 201% increase in labor income. We test the robustness of our estimates using placebo variables, alternative model specifcations and McCrary Density Tests.

We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution of the different components in the pool and from this we extract important information for quantities such as the loss rate in the overall pool as well as the mean impact on a given component from system wide defaults. A singular value decomposition of the adjacency matrix of the graph allows to coarse-grain the system by focusing on the highest eigenvalues which also correspond to the components with the highest contagion impact on the pool. Numerical simulations demonstrate the theoretical findings.

In this paper we construct a parsimonious causal model that addresses multiple issues researchers face when trying to use aggregate time-series shocks for policy evaluation: (a) potential unobserved aggregate confounders, (b) availability of various unit-level characteristics, (c) time and unit-level heterogeneity in treatment effects. We develop a new estimation algorithm that uses insights from treatment effects, panel, and time-series literature. We construct a variance estimator that is robust to arbitrary clustering pattern across geographical units. We achieve this by considering a finite population framework, where potential outcomes are treated as fixed, and all randomness comes from the exogenous shocks. Finally, we illustrate our approach using data from a study on the causal relationship between foreign aid and conflict conducted in Nunn and Qian [2014].

We consider a basic model of two-stage optimal decision making involving pure information learning beforehand and dynamic consumption afterwards: in stage-1 from initial time to a chosen stopping time, the individual investor has access to full market information and simply updates the underlying stock and mean-reverting drift processes by paying information costs; in stage-2 starting from the chosen stopping time, the investor terminates the costly information acquisition while the public stock prices are still available and free. Therefore, during stage-2, the investor starts the investment and consumption based on previous full information and the dynamic partial observations after the stopping time. Moreover, the investor adopts the habit formation preference, in which the past consumption affects his current decisions. Mathematically speaking, we formulate a composite optimal starting and control problem, in which the exterior problem is to determine the best time to initiate the investment-consumption decisions and the interior problem becomes a finite time stochastic control problem with partial information. The value function of the composite problem is characterized as the unique viscosity solution of some variational inequalities.

The New Keynesian model makes several anomalous predictions at the zero lower bound: collapse of output and inflation, and implausibly large effects of forward guidance and government spending. To resolve these anomalies, we introduce wealth into the utility function. The justification is that wealth is a marker of social status, and people value social status. Since people save not only for future consumption but also to accrue social status, the Euler equation is modified. As a result, when the marginal utility of wealth is sufficiently large, the dynamical system representing the equilibrium at the zero lower bound becomes a source instead of a saddle---which resolves all the anomalies.

Measurement and management of credit concentration risk is critical for banks and relevant for micro-prudential requirements. While several methods exist for measuring credit concentration risk within institutions, the systemic effect of different institutions' exposures to the same counterparties has been less explored so far. In this paper, we propose a measure of the systemic credit concentration risk that arises because of common exposures between different institutions within a financial system. This approach is based on a network model that describes the effect of overlapping portfolios. We calculate this measure of systemic network concentration on a few data sets reporting exposures of financial institutions and show that typically the effect of common exposures is not fully contained by information at the level of single portfolio concentration. As a result, we show that an optimal solution that minimizes systemic risk is to be found in a balance between these two, typically different and rather divergent, effects. Using this network measure, we calculate the additional capital corresponding to the systemic risk arising from credit concentration interconnectedness. This adjustment is additional to both the original capital requirement from Basel II and the granularity adjustment of each portfolio. We also develop an approximated methodology to avoid double counting between the granularity adjustment and the common exposure adjustment. Although approximated, our common exposure adjustment is able to capture, with only two parameters, an aspect of systemic risk that goes beyond a view over single portfolios and analyzes the complexity of the interplay among (risk-adjusted) exposures.