On the Heston Model with Stochastic Interest Rates

@article{Grzelak2011OnTH,
  title={On the Heston Model with Stochastic Interest Rates},
  author={Lech A. Grzelak and Cornelis W. Oosterlee},
  journal={ERN: Other Econometrics: Mathematical Methods \& Programming (Topic)},
  year={2011}
}
  • L. GrzelakC. Oosterlee
  • Published 30 July 2010
  • Mathematics
  • ERN: Other Econometrics: Mathematical Methods & Programming (Topic)
We discuss the Heston [Heston-1993] model with stochastic interest rates driven by Hull-White [Hull,White-1996] (HW) or Cox-Ingersoll-Ross [Cox, et al.-1985] (CIR) processes. A so-called volatility compensator is defined which guarantees that the Heston hybrid model with a non-zero correlation between the equity and interest rate processes is properly defined. Two different approximations of the hybrid models are presented in order to obtain the characteristic functions. These approximations… 

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References

SHOWING 1-10 OF 63 REFERENCES

Extension of stochastic volatility models with Hull-White interest rate process

In recent years the financial world has focused on accurate pricing of exotic and hybrid products that are based on a combination of underlyings from different asset classes. In this paper we present

Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility

In this paper we extend the stochastic volatility model of Schöbel and Zhu (1999) by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously

Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process

We present an extension of stochastic volatility equity models by a stochastic Hull--White interest rate component while assuming non-zero correlations between the underlying processes. We place

Incorporating an Interest Rate Smile in an Equity Local Volatility Model

The focus of this paper is on finding a connection between the interest rate and equity asset classes. We propose an equity interest rate hybrid model which preserves market observable smiles: the

Stochastic Volatility With an Ornstein-Uhlenbeck Process: An Extension

In this paper, we reexamine and extend the stochastic volatility model of Stein and Stein (S&S) (1991) where volatility follows a mean–reverting Ornstein–Uhlenbeck process. Using Fourier inversion

Markovian Projection to a Displaced Volatility Heston Model

Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian

Stochastic Interest Rates for Local Volatility Hybrids Models

This paper studies the impact of stochastic interest rates for local volatility hybrids. Our research shows that it is possible to explicitly determine the bias between the local volatility of a

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and

Using Hull-White Interest Rate Trees

This article provides more details on the ways Hull- White trees can be used and discusses the analytic results available when x = r, and makes the point that it is important to distinguish between the per-period rate over one time step on the tree and the instantaneous short rate that is used in some of these analytic results.
...