scholarly journals Multidimensional Structural Credit Modeling under Stochastic Volatility

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Marcos Escobar ◽  
Tim Friederich ◽  
Luis Seco ◽  
Rudi Zagst
Keyword(s):  
Financial Crisis ◽  
Stochastic Volatility ◽  
Default Risk ◽  
Heston Model ◽  
Call Option ◽  
Fannie Mae ◽  
Structural Credit Model ◽  
Dependency Structures ◽  
Freddie Mac ◽  
A Company

This paper extends the structural credit model with underlying stochastic volatility to a multidimensional framework. The model combines the Black/Cox framework with the Heston model interpreting the equity of a company as a down-and-out barrier call option on the company's assets. This implies a combination of local and stochastic volatility on the equity as well as other stylized features. In this paper, we allow for a correlation between the asset processes of different companies to incorporate dependency structures. An estimator for the correlation parameter is derived and tested in a recovery framework. With the help of this model, we examine the default risk of the two mortgage lenders Fannie Mae and Freddie Mac before their actual placement into federal conservatorship and show that their default risk severely increased during the financial crisis.

scholarly journals HEDGING UNDER THE HESTON MODEL WITH JUMP-TO-DEFAULT

2008 ◽  
Vol 11 (04) ◽  
pp. 403-414 ◽  
Author(s):  
PETER CARR ◽  
WIM SCHOUTENS
Keyword(s):  
Orthogonal Polynomials ◽  
Stochastic Volatility ◽  
Credit Default Swap ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Call Option ◽  
Volatility Model ◽  
Credit Default ◽  
Default Swap ◽  
Special Case

In this paper, we will explain how to perfectly hedge under Heston's stochastic volatility model with jump-to-default, which is in itself a generalization of the Merton jump-to-default model and a special case of the Heston model with jumps. The hedging instruments we use to build the hedge will be as usual the stock and the bond, but also the Variance Swap (VS) and a Credit Default Swap (CDS). These instruments are very natural choices in this setting as the VS hedges against changes in the instantaneous variance rate, while the CDS protects against the occurrence of the default event. First, we explain how to perfectly hedge a power payoff under the Heston model with jump-to-default. These theoretical payoffs play an important role later on in the hedging of payoffs which are more liquid in practice such as vanilla options. After showing how to hedge the power payoffs, we show how to hedge newly introduced Gamma payoffs and Dirac payoffs, before turning to the hedge for the vanillas. The approach is inspired by the Post–Widder formula for real inversion of Laplace transforms. Finally, we will also show how power payoffs can readily be used to approximate any payoff only depending on the value of the underlier at maturity. Here, the theory of orthogonal polynomials comes into play and the technique is illustrated by replicating the payoff of a vanilla call option.

scholarly journals A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Raúl Merino ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Stock Price ◽  
Implied Volatility ◽  
Option Price ◽  
Exponential Model ◽  
Heston Model ◽  
Call Option ◽  
Itô Calculus ◽  
Decomposition Formula ◽  
Price Decomposition

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model, extending a previous decomposition formula for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used for this purpose are nonanticipative. In particular, we also see that equivalent results can be obtained by using Functional Itô Calculus. Using the same generalizing ideas, we also extend to nonexponential models the alternative call option price decomposition formula written in terms of the Malliavin derivative of the volatility process. Finally, we give a general expression for the derivative of the implied volatility under both the anticipative and the nonanticipative cases.

Book Reviews

2019 ◽  
Vol 57 (1) ◽  
pp. 187-188
Keyword(s):  
Financial Crisis ◽  
Gain Control ◽  
The Public ◽  
Fannie Mae ◽  
The Us ◽  
Us Government ◽  
National University ◽  
Federal National Mortgage Association ◽  
Freddie Mac

Sumit Agarwal of National University of Singapore reviews “Last Resort: The Financial Crisis and the Future of Bailouts,” by Eric A. Posner. The Econlit abstract of this book begins: “Argues that, in responding to the financial crisis that began in 2007, the US government violated the law and was able to gain control over AIG, the Federal National Mortgage Association (Fannie Mae), and the Federal Home Loan Mortgage Corporation (Freddie Mac) early in the critical stage of the crisis—but it did so in the public interest.”

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