An explicitly solvable Heston model with stochastic interest rate

Maria Recchioni and Y. Sun

European Journal of Operational Research, 2016, vol. 249, issue 1, 359-377

Abstract: This paper deals with a variation of the Heston hybrid model with stochastic interest rate illustrated in Grzelak and Oosterlee (2011). This variation leads to a multi-factor Heston model where one factor is the stochastic interest rate. Specifically, the dynamics of the asset price is described through two stochastic factors: one related to the stochastic volatility and the other to the stochastic interest rate. The proposed model has the advantage of being analytically tractable while preserving the good features of the Heston hybrid model in Grzelak and Oosterlee (2011) and of the multi-factor Heston model in Christoffersen et al. (2009). The analytical treatment is based on an appropriate parametrization of the probability density function which allows us to compute explicitly relevant integrals which define option pricing and moment formulas. The moments and mixed moments of the asset price and log-price variables are given by elementary formulas which do not involve integrals. A procedure to estimate the model parameters is proposed and validated using three different data-sets: the prices of call and put options on the U.S. S&P 500 index, the values of the Credit Agricole index linked policy, Azione Più Capitale Garantito Em.64., and the U.S. three-month, two and ten year government bond yields. The empirical analysis shows that the stochastic interest rate plays a crucial role as a volatility factor and provides a multi-factor model that outperforms the Heston model in pricing options. This model can also provide insights into the relationship between short and long term bond yields.

Keywords: Finance; Option pricing; Stochastic volatility models; Calibration procedure (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221715008772
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:249:y:2016:i:1:p:359-377

DOI: 10.1016/j.ejor.2015.09.035

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().