A Universal Framework for Pricing Financial and Insurance Risks

Wang, Shaun S.

doi:10.2143/ast.32.2.1027

Cited by 202 publications

(134 citation statements)

References 12 publications

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“…It is important to note that in an incomplete market setting, such as the one related to ‡ooding, prices obtained through the forward asset speci…c pricing kernel in equation (2.6) are not unique. However, actuaries have been using complete market techniques, such as the Esscher transform and Wang transform, to calculate premiums in an incomplete market (see Buhlmann (1980), Gerber and Shiu (1994), Wang (2002Wang ( , 2003, for instance). If one accepts such constraints, the framework developed here could be used to price such payo¤s.…”

Section: Resultsmentioning

confidence: 99%

The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

Vitiello

Rebelo

2011

SSRN Journal

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In this paper we establish a Risk Neutral Valuation Relationship and develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy using a multivariate gamma distribution. In our framework, risk neutrality is obtained by using market equilibrium conditions, leading to preference-free contingent claim pricing equations. Multivariate contingent claim pricing models are of particular interest when payo¤s depend on two or more stochastic variables, such as options to exchange one asset for another, options on mutual funds, and options with a stochastic strike price in general. In our model each underlying stochastic variable depends on a systematic gamma distributed term and on an idiosyncratic one, where the former has a direct impact on the correlation structure of the underlying variables. To illustrate the applicability of our framework, we present multivariate gamma distributed versions of well-known multivariate normally/lognormally distributed contingent claim pricing formulae. The gamma distribution is particularly suitable to price stochastic variables that present implied volatilities that are an increasing function of the strike price.

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Section: Resultsmentioning

confidence: 99%

The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

Vitiello

Rebelo

2011

SSRN Journal

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“…In his seminal paper, Wang (2002) proposed a transform method to price both liabilities and contingent claims, whether traded or not. One application of the Wang Transform is in option pricing, which for example can be used in the structural modeling of defaultable bonds.…”

Section: Background and Motivationmentioning

confidence: 99%

A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk

Cohen

Costanzino²

2017

Risks

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Abstract:In this work, we introduce a general framework for incorporating stochastic recovery into structural models. The framework extends the approach to recovery modeling developed in Costanzino (2015, 2017) and provides for a systematic way to include different recovery processes into a structural credit model. The key observation is a connection between the partial information gap between firm manager and the market that is captured via a distortion of the probability of default. This last feature is computed by what is essentially a Girsanov transformation and reflects untangling of the recovery process from the default probability. Our framework can be thought of as an extension of Ishizaka and Takaoka (2003) and, in the same spirit of their work, we provide several examples of the framework including bounded recovery and a jump-to-zero model. One of the nice features of our framework is that, given prices from any one-factor structural model, we provide a systematic way to compute corresponding prices with stochastic recovery. The framework also provides a way to analyze correlation between Probability of Default (PD) and Loss Given Default (LGD), and term structure of recovery rates.

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“…Recently, Wang (2000Wang ( , 2002 proposed a pricing method based on the following transformation from G(x) to G Q (x):…”

Section: The Multivariate Wang Transformmentioning

confidence: 99%

“…In fact, some empirical studies suggest to use Student t distributions, whose CDF is denoted by t ν (x), with ν = 3 to 7 degrees of freedom for return distributions of financial and insurance assets (see, e.g., Platen and Stahl (2003) and Wang (2004)). In order to overcome this deficiency, Wang (2002) proposed the following two-parameter transformation: 2) and reported that (5.2) is much better to fit, although the two-parameter transform is not consistent with the economic premium principle (2.2) (see Kijima and Muromachi (2008)). …”

Section: Fat-tail Distributionmentioning

confidence: 99%

Pricing of CDOs based on the multivariate Wang transform

Kijima

Motomiya²,

Suzuki³

2010

Journal of Economic Dynamics and Control

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Abstract. This paper shows that the one-factor Gaussian copula model, the standard market model for valuing CDO's, can be derived from the multivariate Wang transform, which is consistent with Bühlmann's equilibrium pricing model, whence it has a sound economic interpretation. The Gaussian copula model is then extended within the Bühlmann's framework. Unlike the existing models, our model calibrates the parameter associated with risk aversion index of the representative investor, not the correlation parameter. A t-copula model is also considered to describe the fat-tail distribution observed in the actual markets.

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A Universal Framework for Pricing Financial and Insurance Risks

Cited by 202 publications

References 12 publications

The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk

Pricing of CDOs based on the multivariate Wang transform

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