Reduced-Order modeling for Heston stochastic volatility model

Sinem Kozpınar; Murat Uzunca; Bülent Karasözen

Makale detayları

Reduced-Order modeling for Heston stochastic volatility model

Yazarlar:

Sinem Kozpınar | Murat Uzunca | Bülent Karasözen

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1515-1528

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001335996

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 In this paper, we compare the intrusive proper orthogonal decomposition POD with Galerkin projection and the data-driven dynamic mode decomposition DMD, for Hestons option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.

 In this paper, we compare the intrusive proper orthogonal decomposition POD with Galerkin projection and the data-driven dynamic mode decomposition DMD, for Hestons option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.

 In this paper, we compare the intrusive proper orthogonal decomposition POD with Galerkin projection and the data-driven dynamic mode decomposition DMD, for Hestons option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.

 In this paper, we compare the intrusive proper orthogonal decomposition POD with Galerkin projection and the data-driven dynamic mode decomposition DMD, for Hestons option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.

Makale detayları

Reduced-Order modeling for Heston stochastic volatility model

Yazarlar:

Sinem Kozpınar | Murat Uzunca | Bülent Karasözen

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1515-1528

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001335996

pISSN:

2651-477X

option pricing

Heston model

discontinuous Galerkin method

reduced order modeling

proper orthogonal decomposition

dynamic mode decomposition

Sayı

Makale detayları

Reduced-Order modeling for Heston stochastic volatility model

Yazarlar: Sinem Kozpınar | Murat Uzunca | Bülent Karasözen

Yayıncı: Hacettepe University

Ana Başlıklar: Mathematical Sciences

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1515-1528

Belge Tipi: Makale

Yayın Tarihi: 12/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001335996

pISSN: 2651-477X

option pricing

Heston model

discontinuous Galerkin method

reduced order modeling

proper orthogonal decomposition

dynamic mode decomposition

Sayı

Yazarlar:

Sinem Kozpınar | Murat Uzunca | Bülent Karasözen

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 6, pp.1515-1528

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001335996

pISSN:

2651-477X