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Arbitrage Pricing

Tomas Björk

in Arbitrage Theory in Continuous Time

This chapter examines a special case of the general model derived in Chapter 6. It derives the model of a financial market, and then analyses the pricing of financial derivatives, specifically the ... More

This chapter examines a special case of the general model derived in Chapter 6. It derives the model of a financial market, and then analyses the pricing of financial derivatives, specifically the European call option. Black formulas are derived for options written on a futures contract. Practice exercises are included.Less

ARBITRAGE-FREE PRICING IN COMPLETE MARKETS

Patrick L. Anderson

in The Economics of Business Valuation: Towards a Value Functional Approach

The author describes one of the breakthrough concepts of modern finance: the use of the no arbitrage principle in complete markets as the basis for the powerful mathematics of “risk neutral” or ... More

The author describes one of the breakthrough concepts of modern finance: the use of the no arbitrage principle in complete markets as the basis for the powerful mathematics of “risk neutral” or “equivalent martingale” pricing. This neoclassical finance model relies on two intertwined assumptions: the existence of complete markets, and the assumption that market participants will act to ensure that no arbitrage profits are possible. The author then presents strong evidence that both of these assumptions are lacking for private businesses and their investors, because markets for the equity in these firms are incomplete. The author argues that this severely undermines this model as a practical valuation tool. As with other principles, this assertion is tested by applying it to three actual companies.Less

The Martingale Approach to Arbitrage Theory

Tomas Björk

in Arbitrage Theory in Continuous Time

This chapter analyses a market model made up of N + 1 a priori given asset price processes S0, S1, ..., SN. Typically, the model is specified by giving the dynamics of the asset price processes under ... More

This chapter analyses a market model made up of N + 1 a priori given asset price processes S0, S1, ..., SN. Typically, the model is specified by giving the dynamics of the asset price processes under the objective probability measure P. The main problems are: Under what conditions is the market arbitrage free? Under what conditions is the market complete? These problems are addressed using the “martingale approach” to financial derivatives.Less

The Determination of Equity Prices

Hendrik S. Houthakker and Peter J. Williamson

in The Economics of Financial Markets

Drawing on Chs. 4 and 5 (which discuss the supply and demand for securities separately), this chapter investigates whether economics has anything helpful to say about the prices of shares and related ... More

Drawing on Chs. 4 and 5 (which discuss the supply and demand for securities separately), this chapter investigates whether economics has anything helpful to say about the prices of shares and related securities by reviewing the most important ideas suggested by economic theory in this area and assessing their usefulness in the real world. In the first two sections, two fairly ancient but still popular models of equity (share) prices are examined, one of which (the steady growth model) views shares as claims to future dividends and the other (the asset model) views them as claims to the underlying net assets (corporate net worth). For the most part, these models look at the shares of individual companies in isolation, not at the market as a whole, and that is their weakness, but the asset model in particular provides important insights into aggregate equity values; as an aside to this discussion it is shown that aggregate dividends have the intriguing feature of being an approximately constant percentage of national income, which means that corporate equities offer protection (though not perfect protection) against inflation as well as participation in the real growth of the economy. The third section looks at the Capital Asset Pricing Model (CAPM) – a discovery of the 1960s that, by considering equities in relation to each other, provided important new insights into the relation between risk and return. A more recent alternative approach known as Arbitrage Pricing Theory is discussed next, and finally there is a section (an appendix) on stock indexes.Less

Arbitrage Pricing

Tomas Björk

in Arbitrage Theory in Continuous Time

In this chapter, the reader is introduced to the Black‐Scholes model and to the basic ideas behind arbitrage pricing of contingent claims. We treat European options, futures, futures options, and ... More

In this chapter, the reader is introduced to the Black‐Scholes model and to the basic ideas behind arbitrage pricing of contingent claims. We treat European options, futures, futures options, and also include a brief discussion on American options.Less

Incomplete Markets

Tomas Björk

in Arbitrage Theory in Continuous Time

This chapter provides a detailed discussion of the problems surrounding arbitrage pricing in incomplete markets.

Factor Models

Claus Munk

in Financial Asset Pricing Theory

The consumption-based asset pricing models are elegant, but tests and applications suffer from the questionable quality of the available consumption data, and at least some of these models are ... More

The consumption-based asset pricing models are elegant, but tests and applications suffer from the questionable quality of the available consumption data, and at least some of these models are unsuccessful in matching empirical facts. This motivates a search for models linking asset prices and returns to other factors than consumption. This chapter studies the so-called factor models that link the prices of the many available financial assets to a number of common observable pricing factors. The relation between state-price deflators and pricing factors is investigated. The classic CAPM and the Arbitrage Pricing Theory are reviewed. The role of mean-variance efficient returns in factor models is explored. In multi-period settings the distinction between conditional and unconditional pricing factors is emphasized. The envelope condition derived in Ch. 6 is shown to serve as a theoretical foundation for the choice of pricing factors. Finally, a brief overview of empirical studies of factor models is provided.Less

Valuing Public Policies

Anthony M. Bertelli and Peter John

in Public Policy Investment: Priority-Setting and Conditional Representation In British Statecraft

The theoretical mechanism by which the public attributes value to the attention of politicians to public policy topics is the subject of this chapter. Drawing on asset pricing theory from the ... More

The theoretical mechanism by which the public attributes value to the attention of politicians to public policy topics is the subject of this chapter. Drawing on asset pricing theory from the economics of finance, we provide the theoretical means by which policy capital takes on value for voters. Central to the approach is the responsiveness of public valuations to innovations in competence factors, which impact the value of all policy priorities in different ways. Given pricing information, politicians can select and rebalance the attention they allocate in party manifestos. Once in office, parties can rebalance their policy portfolios through the Speech from the Throne. Vital to the estimation strategy we elaborate in the next chapter are levels of risk and price signal uncertainty that policy portfolios incorporate.Less

Short Rate Models

Tomas Björk

in Arbitrage Theory in Continuous Time

Here, we present the standard theory of arbitrage pricing of interest‐rate‐related claims for short rate models.

Several Underlying Assets

Tomas Björk

in Arbitrage Theory in Continuous Time

In this chapter, the arbitrage theory from chapter 6 is extended to the case of several underlying risky assets.

Dividends

Tomas Björk

in Arbitrage Theory in Continuous Time

Here, the theory developed earlier is extended to the case of dividend‐paying assets.

Factor Models

Kerry E. Back

in Asset Pricing and Portfolio Choice Theory

The CAPM and factor models in general are explained. Factors can be replaced by the returns or excess returns that are maximally correlated (the projections of the factors). A factor model is ... More

The CAPM and factor models in general are explained. Factors can be replaced by the returns or excess returns that are maximally correlated (the projections of the factors). A factor model is equivalent to an affine representation of an SDF and to spanning a return on the mean‐variance frontier. The use of alphas for performance evaluation is explained. Statistical factor models are defined as models in which factors explain the covariance matrix of returns. A proof is given of the Arbitrage Pricing Theory, which states that statistical factors are approximate pricing factors. The CAPM and the Fama‐French‐Carhart model are evaluated relative to portfolios based on sorts on size, book‐to‐market, and momentum.Less

Valuing and Analyzing Fixed Income Derivatives

Koray D. Simsek and Halil Kiymaz

in Debt Markets and Investments

Derivatives valuation is based on the key principle of no-arbitrage pricing. This chapter presents valuation models for various types of fixed income derivatives, including forward rate agreements ... More

Derivatives valuation is based on the key principle of no-arbitrage pricing. This chapter presents valuation models for various types of fixed income derivatives, including forward rate agreements (FRAs), interest rate swaps, Eurodollar and Treasury bond futures, bond options, caps and floors, swaptions, and options on interest rate futures. Following the financial crisis that began in the summer of 2007, major changes occurred in the practice of fixed income derivatives valuation, particularly regarding the adoption of overnight indexed swaps (OIS) as a source of the risk-free rate. This chapter shows how OIS discounting is implemented in FRA pricing and swap valuation. Traditional approaches such as cost of carry valuation in futures pricing are illustrated. With respect to option valuation, this chapter explains the risk-neutral pricing approach as well as closed-form solutions such as the Black model. The chapter also provides numeric examples to illustrate the practical use of the presented models and formulas.Less

Stochastic Integrals

Tomas Björk

in Arbitrage Theory in Continuous Time

This chapter introduces the main technical tool for arbitrage pricing, namely stochastic integrals.