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Concept# State prices

Summary

In financial economics, a state-price security, also called an Arrow–Debreu security (from its origins in the Arrow–Debreu model), a pure security, or a primitive security is a contract that agrees to pay one unit of a numeraire (a currency or a commodity) if a particular state occurs at a particular time in the future and pays zero numeraire in all the other states.
The price of this security is the state price of this particular state of the world. The state price vector is the vector of state prices for all states.
See .
An Arrow security is an instrument with a fixed payout of one unit in a specified state and no payout in other states. It is a type of hypothetical asset used in the Arrow market structure model. In contrast to the Arrow-Debreu market structure model, an Arrow market is a market in which the individual agents engage in trading assets at every time period t. In an Arrow-Debreu model, trading occurs only once at the beginning of time. An Arrow Security is an as

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FIN-609: Asset Pricing

This course provides an overview of the theory of asset pricing and portfolio choice theory following historical developments in the field and putting
emphasis on theoretical models that help our understanding of financial decision
making and financial markets.

FIN-406: Macrofinance

This course provides students with a working knowledge of macroeconomic models that explicitly incorporate financial markets. The goal is to develop a broad and analytical framework for analyzing the interaction of financial decisions, macroeconomic events and policy decisions.

FIN-415: Probability and stochastic calculus

This course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. We study fundamental notions and techniques necessary for applications in finance such as option pricing, hedging, optimal portfolio choice and prediction problems.

Parametric option pricing models are largely used in Finance. These models capture several features of asset price dynamics. However, their pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches that learn and correct empirically the pricing errors. In this paper, we propose a new nonparametric method for pricing derivatives assets. Our method relies on the state price distribution instead of the state price density because the former is easier to estimate nonparametrically than the latter. A parametric model is used as an initial estimate of the state price distribution. Then the pricing errors induced by the parametric model are fitted nonparametrically. This model-guided method estimates the state price distribution nonparametrically and is called Automatic Correction of Errors (ACE). The method is easy to implement and can be combined with any model-based pricing formula to correct the systematic biases of pricing errors. We also develop a nonparametric test based on the generalized likelihood ratio to document the efficacy of the ACE method. Empirical studies based on S&P 500 index options show that our method outperforms several competing pricing models in terms of predictive and hedging abilities.

This thesis consists of three chapters on informational frictions in financial markets. The chapters analyze problems related to markets' ability to guide real investment, and what drives liquidity. Both problems are important to ensure efficient resource allocation in the economy.
The first chapter studies the interaction between financial markets and real investments. I develop a model that simultaneously study the equilibrium in financial markets, the choice of investors to produce information, and real decisions by the firm. The chapter provides a new method to overcome non-linearities in the security price, and the equilibrium is surprisingly simple. The results provide insights into when real investments have a substantial impact on market efficiency and when we can analyze equilibrium market efficiency separately. Equilibrium behavior may hide some inefficiencies from standard empirical tests. Some changes in financial markets may increase or have little effect on market efficiency, but reduce real efficiency by increasing the cost of information production.
The second chapter analyzes time-variation in liquidity. I develop a tractable model where conditions among traders vary over time. The resulting equilibrium offers several new predictions on what drives liquidity variation. For example, there may be significant reductions in liquidity from even tiny changes among the traders' conditions. Strategic behavior drives the results, and the model explains how liquidity may suddenly evaporate without a clear cause. Empirical results are in line with the predictions of the model. Surprisingly, everyone may benefit from sometimes restricting some traders from the market. Doing so can reallocate liquidity to periods with more significant liquidity needs.
The third chapter studies the choice of anonymity among traders. All traders end up revealing their identity unless doing so is costly, or the order flow is noisy. The intuition is that there is always at least one trader who prefers to reveal his or her identity. If the order flow is noisy, then there is a threshold type, and more patient traders stay anonymous. The results suggest that a fully anonymous market is most efficient, but the gains from anonymity are distributed unevenly. This result explains why different markets vary significantly in choices related to anonymity.

Damir Filipovic, Martin Larsson

We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures non-negative interest rates, (ii) easily accommodates unspanned factors affecting volatility and risk premiums, and (iii) admits semi-analytical solutions to swaptions. A parsimonious model specification within the linear-rational class has a very good fit to both interest rate swaps and swaptions since 1997 and captures many features of term structure, volatility, and risk premium dynamics-including when interest rates are close to the zero lower bound.

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