Pricing Vulnerable Options with Copulas (original) (raw)

Pricing and Hedging Vulnerable Credit Derivatives with Copulas

SSRN Electronic Journal, 2000

In this paper we apply a copula function pricing technique to the evaluation of credit derivatives, namely a vulnerable default put option and a credit switch. Also in this case, copulas enable to separate the specification of marginal default probabilities from their dependence structure. Their use is based here on no-arbitrage arguments, which provide pricing bounds and easy-to-implement super-replication strategies.

Pricing and Hedging Credit Derivatives with Copulas

Economic Notes, 2003

Credit derivatives and counterparty risk pricing through copulas: recent developments

Copula functions have proven to be extremely useful in describing joint default and survival probabilities. We overview the state of the art and point out some modelling issues, such as the choice of a speci…c copula and of the amount of dependence, as well as re-mapping of models. We also discuss how to simplify credit models using factors. The survey leads us to focus on historical versus risk neutral dependence. We present an original methodology for inferring risk neutral dependence without using a single factor, provide an application to market data and explore its impact on the fees of some credit derivatives. The …rst part of the paper is a review of the copula techniques developed so far in order to evaluate credit risk in default-no default models. The review proceeds as follows: we …rst resume some basics about structural and intensity- based models, then recall how and under which conditions two models of these classes can be re-mapped into each other, using the latent va...

Bivariate option pricing with copulas

Applied Mathematical Finance, 2002

The adoption of copula functions is suggested in order to price bivariate contingent claims. Copulas enable the marginal distributions extracted from vertical spreads in the options markets to be imbedded in a multivariate pricing kernel. It is proved that such a kernel is a copula function, and that its super-replication strategy is represented by the Frechet bounds. Applications provided include

Multivariate Option Pricing With Copulas

SSRN Electronic Journal, 2000

In this paper we suggest the adoption of copula functions in order to price multivariate contingent claims. Copulas enable us to imbed the marginal distributions extracted from vertical spreads in the options markets in a multivariate pricing kernel. We prove that such kernel is a copula fucntion, and that its super-replication strategy is represented by the Fréchet bounds. As applications, we provide prices for binary digital options, options on the minimum and options to exchange one asset for another. For each of these products, we provide no-arbitrage pricing bounds, as well as the values consistent with independence of the underlying assets. As a …nal reference value, we use a copula function calibrated on historical data.

THE APPLICATION OF COPULAS IN PRICING DEPENDENT CREDIT DERIVATIVES INSTRUMENTS

2008

The aim of this paper is to use copulas functions to capture the different structures of dependency when we deal with portfolios of dependent credit risks and a basket of credit derivatives. We first present the wellknown result for the pricing of default risk, when there is only one defaultable firm. After that, we expose the structure of dependency with copulas in pricing dependent credit derivatives. Many studies suggest the inadequacy of multinormal distribution and then the failure of methods based on linear correlation for measuring the structure of dependency. Finally, we use Monte Carlo simulations for pricing Collateralized debt obligation (CDO) with Gaussian an Student copulas.

Pricing a bivariate option with copulas

International Journal of Bonds and Derivatives, 2018

The diversity of exotic-option contracts available in the market has increased significantly in recent years, and has aroused the interest to develop alternative valuation methodological approaches. Among the most interesting innovations, copulas analysis represents a major contribution to improve valuation methodologies. This paper explores the pricing of a bivariate call option on the better-of-two-markets: Mexico's Stock Exchange index, and the Standard & Poor's 500. The approach consists of a GARCH process that combines with copulas analysis and the Black and Scholes classical European call option valuation model. Copulas from the elliptical and Archimedean families provide the dependence structure among the underlying assets, and the estimated prices prove significantly different from those obtained using a static dependence assumption. The study concludes that dynamic copulas produce more robust prices than static dependence models.

Multivariate Option Pricing with Pair-Copulas

Journal of Probability, 2014

We propose a copula-based approach to solve the option pricing problem in the risk-neutral setting and with respect to a structured derivative written on several underlying assets. Our analysis generalizes similar results already present in the literature but limited to the trivariate case. The main difficulty of such a generalization consists in selecting the appropriate vine structure which turns to be of D-vine type, contrary to what happens in the trivariate setting where the canonical vine is sufficient. We first define the general procedure for multivariate options and then we will give a concrete example for the case of an option written on four indexes of stocks, namely, the S&P 500 Index, the Nasdaq 100 Index, the Nasdaq Composite Index, and the Nyse Composite Index. Moreover, we calibrate the proposed model, also providing a comparison analysis between real prices and simulated data to show the goodness of obtained estimates. We underline that our pair-copula decomposition...

Multivariate Option Pricing Using Dynamic Copula Models

SSRN Electronic Journal, 2000

This paper examines the behavior of multivariate option prices in the presence of association between the underlying assets. Parametric families of copulas offering various alternatives to the normal dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets. These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the S&P500 and Nasdaq indexes. Results show that option prices implied by dynamic copula models differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. Furthermore, the normal copula produces option prices that differ significantly from non-normal copula prices, irrespective of initial volatility levels. Within the class of non-normal copula families considered, option prices are robust with respect to the copula choice.

Pricing Vulnerable Options with Copulas (original) (raw)

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