# A series-form solution for pricing variance and volatility swaps with stochastic volatility and stochastic interest rate

Journal Article

### Abstract

• In this paper, we present analytical pricing formulae for variance and volatility swaps, when both of the volatility and interest rate are assumed to be stochastic and follow a CIR (Cox–Ingersoll–Ross) process, forming a Heston–CIR hybrid model. The solutions are written in a series form with a theoretical proof of their convergence, ensuring the accuracy of the determined swap prices. The application of the formulae in practice is also demonstrated through the designed numerical experiments.

• 2018

### Citation

• He, X. & Zhu, S. (2018). A series-form solution for pricing variance and volatility swaps with stochastic volatility and stochastic interest rate. Computers and Mathematics with Applications, 76 (9), 2223-2234.

### Scopus Eid

• 2-s2.0-85054357293

### Ro Full-text Url

• https://ro.uow.edu.au/cgi/viewcontent.cgi?article=3003&context=eispapers1

• http://ro.uow.edu.au/eispapers1/1999

• 11

• 2223

• 2234

• 76

• 9

### Place Of Publication

• United Kingdom

### Abstract

• In this paper, we present analytical pricing formulae for variance and volatility swaps, when both of the volatility and interest rate are assumed to be stochastic and follow a CIR (Cox–Ingersoll–Ross) process, forming a Heston–CIR hybrid model. The solutions are written in a series form with a theoretical proof of their convergence, ensuring the accuracy of the determined swap prices. The application of the formulae in practice is also demonstrated through the designed numerical experiments.

• 2018

### Citation

• He, X. & Zhu, S. (2018). A series-form solution for pricing variance and volatility swaps with stochastic volatility and stochastic interest rate. Computers and Mathematics with Applications, 76 (9), 2223-2234.

### Scopus Eid

• 2-s2.0-85054357293

### Ro Full-text Url

• https://ro.uow.edu.au/cgi/viewcontent.cgi?article=3003&context=eispapers1

• http://ro.uow.edu.au/eispapers1/1999

• 11

• 2223

• 2234

• 76

• 9

### Place Of Publication

• United Kingdom