scholarly journals Pricing credit default swaps under a multi-scale stochastic volatility model

2017 ◽  
Vol 468 ◽  
pp. 425-433 ◽  
Author(s):  
Wenting Chen ◽  
Xinjiang He
Keyword(s):  
Stochastic Volatility ◽  
Credit Default Swaps ◽  
Stochastic Volatility Model ◽  
Multi Scale ◽  
Volatility Model ◽  
Credit Default

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.

An explicitly solvable multi-scale stochastic volatility model: Option pricing and calibration problems

2009 ◽  
Vol 29 (9) ◽  
pp. 862-893 ◽  
Author(s):  
Lorella Fatone ◽  
Francesca Mariani ◽  
Maria Cristina Recchioni ◽  
Francesco Zirilli
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Multi Scale ◽  
Volatility Model

A non-Gaussian stochastic volatility model

1998 ◽  
Vol 2 (2) ◽  
pp. 33-47 ◽  
Author(s):  
Yuichi Nagahara ◽  
Genshiro Kitagawa
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Non Gaussian
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