Semiparametric Pricing of Multivariate Contingent Claims
Semiparametric Pricing of Multivariate Contingent Claims

Author: Joshua V. Rosenberg

Publisher:

Published: 2009

Total Pages: 27

ISBN-13:

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This paper develops and implements a methodology for pricing multivariate contingent claims (MVCC s) based on semiparametric estimation of the multivariate risk-neutral density function.This methodology generates MVCC prices which are consistent with current market prices of univariate contingent claims.This method allows for completely general marginal risk-neutral densities and is compatible with all univariate risk-neutral density estimation techniques. The univariate risk-neutral densities are related by their risk-neutral correlation, which is estimated using time-series data on asset returns and an empirical pricing kernel (Rosenberg and Engle, 1999). This permits the multivariate risk-neutral density to be identified without requiring observation of multivariate contingent claims prices. The semiparametric MVCC pricing technique is used for valuation of one-month options on the better of two equity index returns. Option contracts with payoffs dependent on are four equity indexpairs are considered: Samp;P500 - CAC40, Samp;P500 - NK225, Samp;P500 - FTSE100, and Samp;P500 - DAX30. Five marginal risk-neutral densities (Samp;P500, CAC40, NK225, FTSE100, and DAX30) are estimated semiparametrically using a cross-section of contemporaneously measured equity index option prices in each market. A bivariate risk-neutral Plackett (1965) density is constructed using the given marginals and risk-neutral correlation derived using an empirical pricing kernel and the historical joint density of the index returns. Price differences from a lognormal pricing formulausing historical and risk-neutral return moments are found to be significant.

A Note on the Pricing of Multivariate Contingent Claims Under a Transformed-Gamma Distribution
A Note on the Pricing of Multivariate Contingent Claims Under a Transformed-Gamma Distribution

Author: Luiz Vitiello

Publisher:

Published: 2014

Total Pages: 18

ISBN-13:

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We develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy based on a multivariate transformed-gamma distribution. In our model, each transformed-gamma distributed underlying asset depends on two terms: a idiosyncratic term and a systematic term, where the latter is the same for all underlying assets and has a direct impact on their correlation structure. Given our distributional assumptions and the existence of a representative agent with a standard utility function, we apply equilibrium arguments and provide sufficient conditions for obtaining preference-free contingent claim pricing equations. We illustrate the applicability of our framework by providing examples of preference-free contingent claim pricing models. Multivariate pricing models are of particular interest when payoffs depend on two or more underlying assets, such as crack and crush spread options, options to exchange one asset for another, and options with a stochastic strike price in general.

Pricing Multivariate Contingent Claims Using Estimated Risk-Neutral Density Functions
Pricing Multivariate Contingent Claims Using Estimated Risk-Neutral Density Functions

Author:

Publisher:

Published: 2008

Total Pages: 24

ISBN-13:

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Many asset price series exhibit time-varying volatility, jumps, and other features inconsistent with assumptions about the underlying price process made by standard multivariate contingent claims (MVCC) pricing models. This paper develops an interpolative technique for pricing MVCCs flexible NLS pricing that involves the estimation of a flexible multivariate risk-neutral density function implied by existing asset prices. As an application, the flexible NLS pricing technique is used to value several bivariate contingent claims dependent on foreign exchange rates in 1993 and 1994. The bivariate flexible risk-neutral density function more accurately prices existing options than the bivariate lognormal density implied by a multivariate geometric Brownian motion. In addition, the bivariate contingent claims analyzed have substantially different prices using the two density functions suggesting flexible NLS pricing may improve accuracy over standard methods.

Copulae and Multivariate Probability Distributions in Finance
Copulae and Multivariate Probability Distributions in Finance

Author: Alexandra Dias

Publisher: Routledge

Published: 2013-08-21

Total Pages: 206

ISBN-13: 1317976916

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Portfolio theory and much of asset pricing, as well as many empirical applications, depend on the use of multivariate probability distributions to describe asset returns. Traditionally, this has meant the multivariate normal (or Gaussian) distribution. More recently, theoretical and empirical work in financial economics has employed the multivariate Student (and other) distributions which are members of the elliptically symmetric class. There is also a growing body of work which is based on skew-elliptical distributions. These probability models all exhibit the property that the marginal distributions differ only by location and scale parameters or are restrictive in other respects. Very often, such models are not supported by the empirical evidence that the marginal distributions of asset returns can differ markedly. Copula theory is a branch of statistics which provides powerful methods to overcome these shortcomings. This book provides a synthesis of the latest research in the area of copulae as applied to finance and related subjects such as insurance. Multivariate non-Gaussian dependence is a fact of life for many problems in financial econometrics. This book describes the state of the art in tools required to deal with these observed features of financial data. This book was originally published as a special issue of the European Journal of Finance.