scholarly journals Equity Options, Credit Default Swaps and Leverage: A Simple Stochastic-Volatility Model for Equity and Credit Derivatives

2011 ◽  
Author(s):  
Gaia Barone
Keyword(s):  
Stochastic Volatility ◽  
Credit Derivatives ◽  
Credit Default Swaps ◽  
Stochastic Volatility Model ◽  
Equity Options ◽  
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.

scholarly journals CREDIT DERIVATIVES PRICING WITH STOCHASTIC VOLATILITY MODELS

2013 ◽  
Vol 16 (04) ◽  
pp. 1350019 ◽  
Author(s):  
CARL CHIARELLA ◽  
SAMUEL CHEGE MAINA ◽  
CHRISTINA NIKITOPOULOS SKLIBOSIOS
Keyword(s):  
Interest Rates ◽  
Stochastic Volatility ◽  
Numerical Study ◽  
Credit Derivatives ◽  
Credit Default Swaps ◽  
Bond Prices ◽  
Derivatives Pricing ◽  
Defaultable Bond ◽  
Credit Default ◽  
Model Features

This paper proposes a model for pricing credit derivatives in a defaultable HJM framework. The model features hump-shaped, level dependent, and unspanned stochastic volatility, and accommodates a correlation structure between the stochastic volatility, the default-free interest rates, and the credit spreads. The model is finite-dimensional, and leads (a) to exponentially affine default-free and defaultable bond prices, and (b) to an approximation for pricing credit default swaps and swaptions in terms of defaultable bond prices with varying maturities. A numerical study demonstrates that the model captures stylized various features of credit default swaps and swaptions.

scholarly journals Asymptotic Analysis for One-Name Credit Derivatives

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yong-Ki Ma ◽  
Beom Jin Kim
Keyword(s):  
Asymptotic Analysis ◽  
Stochastic Volatility ◽  
Credit Derivatives ◽  
Approximate Solutions ◽  
Credit Default Swaps ◽  
Rate Process ◽  
Yield Curves ◽  
Defaultable Bond ◽  
Credit Default ◽  
Bond Options

We propose approximate solutions to price defaultable zero-coupon bonds as well as the corresponding credit default swaps and bond options. We consider the intensity-based approach of a two-correlated-factor Hull-White model with stochastic volatility of interest rate process. Perturbations from the stochastic volatility are computed by using an asymptotic analysis. We also study the sensitive properties of the defaultable bond prices and the yield curves.

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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