Option valuation under a multivariate Markov Chain model

Na Song; Wai Ki Ching; Tak Kuen Siu; Eric S. Fung; Michael K. Ng

doi:10.1109/CSO.2010.73

Option valuation under a multivariate Markov Chain model

Na Song, Wai Ki Ching^*, Tak Kuen Siu, Eric S. Fung, Michael K. Ng

^*Corresponding author for this work

Department of Actuarial Studies and Business Analytics

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

3 Citations (Scopus)

55 Downloads (Pure)

Abstract

In this paper, we develop an option valuation model in the context of a discrete-time multivariate Markov chain model using the Esscher transform. The multivariate Markov chain provides a flexible way to incorporate the dependency of the underlying asset price processes and price multi-state options written on several dependent underlying assets. In our model, the price of an individual asset can take finitely many values. The market described by our model is incomplete in general, hence there are more than one equivalent martingale pricing measures. We adopt conditional Esscher transform to determine an equivalent martingale measure for option valuation. We also document consequences for option prices of the dependency of the underlying asset prices described by the multivariate Markov chain model.

Original language	English
Title of host publication	3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice
Editors	Lean Yu, Yingwen Song, Wai-Ki Ching, Shouyang Wang, K. K. Lai
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	177-181
Number of pages	5
Volume	1
ISBN (Print)	9780769540306
DOIs	https://doi.org/10.1109/CSO.2010.73
Publication status	Published - 2010
Event	3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice - Huangshan, Anhui, China Duration: 28 May 2010 → 31 May 2010

Other

Other	3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice
Country/Territory	China
City	Huangshan, Anhui
Period	28/05/10 → 31/05/10

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10.1109/CSO.2010.73

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Song, N., Ching, W. K., Siu, T. K., Fung, E. S., & Ng, M. K. (2010). Option valuation under a multivariate Markov Chain model. In L. Yu, Y. Song, W.-K. Ching, S. Wang, & K. K. Lai (Eds.), 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice (Vol. 1, pp. 177-181). Article 5532981 Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/CSO.2010.73

Song, Na ; Ching, Wai Ki ; Siu, Tak Kuen et al. / Option valuation under a multivariate Markov Chain model. 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice. editor / Lean Yu ; Yingwen Song ; Wai-Ki Ching ; Shouyang Wang ; K. K. Lai. Vol. 1 Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2010. pp. 177-181

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title = "Option valuation under a multivariate Markov Chain model",

abstract = "In this paper, we develop an option valuation model in the context of a discrete-time multivariate Markov chain model using the Esscher transform. The multivariate Markov chain provides a flexible way to incorporate the dependency of the underlying asset price processes and price multi-state options written on several dependent underlying assets. In our model, the price of an individual asset can take finitely many values. The market described by our model is incomplete in general, hence there are more than one equivalent martingale pricing measures. We adopt conditional Esscher transform to determine an equivalent martingale measure for option valuation. We also document consequences for option prices of the dependency of the underlying asset prices described by the multivariate Markov chain model.",

author = "Na Song and Ching, {Wai Ki} and Siu, {Tak Kuen} and Fung, {Eric S.} and Ng, {Michael K.}",

year = "2010",

doi = "10.1109/CSO.2010.73",

language = "English",

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editor = "Lean Yu and Yingwen Song and Wai-Ki Ching and Shouyang Wang and Lai, {K. K.}",

booktitle = "3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

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Song, N, Ching, WK, Siu, TK, Fung, ES & Ng, MK 2010, Option valuation under a multivariate Markov Chain model. in L Yu, Y Song, W-K Ching, S Wang & KK Lai (eds), 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice. vol. 1, 5532981, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 177-181, 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice, Huangshan, Anhui, China, 28/05/10. https://doi.org/10.1109/CSO.2010.73

Option valuation under a multivariate Markov Chain model. / Song, Na; Ching, Wai Ki; Siu, Tak Kuen et al.
3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice. ed. / Lean Yu; Yingwen Song; Wai-Ki Ching; Shouyang Wang; K. K. Lai. Vol. 1 Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2010. p. 177-181 5532981.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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T1 - Option valuation under a multivariate Markov Chain model

AU - Song, Na

AU - Ching, Wai Ki

AU - Siu, Tak Kuen

AU - Fung, Eric S.

AU - Ng, Michael K.

PY - 2010

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N2 - In this paper, we develop an option valuation model in the context of a discrete-time multivariate Markov chain model using the Esscher transform. The multivariate Markov chain provides a flexible way to incorporate the dependency of the underlying asset price processes and price multi-state options written on several dependent underlying assets. In our model, the price of an individual asset can take finitely many values. The market described by our model is incomplete in general, hence there are more than one equivalent martingale pricing measures. We adopt conditional Esscher transform to determine an equivalent martingale measure for option valuation. We also document consequences for option prices of the dependency of the underlying asset prices described by the multivariate Markov chain model.

AB - In this paper, we develop an option valuation model in the context of a discrete-time multivariate Markov chain model using the Esscher transform. The multivariate Markov chain provides a flexible way to incorporate the dependency of the underlying asset price processes and price multi-state options written on several dependent underlying assets. In our model, the price of an individual asset can take finitely many values. The market described by our model is incomplete in general, hence there are more than one equivalent martingale pricing measures. We adopt conditional Esscher transform to determine an equivalent martingale measure for option valuation. We also document consequences for option prices of the dependency of the underlying asset prices described by the multivariate Markov chain model.

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U2 - 10.1109/CSO.2010.73

DO - 10.1109/CSO.2010.73

M3 - Conference proceeding contribution

AN - SCOPUS:77956448135

SN - 9780769540306

VL - 1

SP - 177

EP - 181

BT - 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice

A2 - Yu, Lean

A2 - Song, Yingwen

A2 - Ching, Wai-Ki

A2 - Wang, Shouyang

A2 - Lai, K. K.

PB - Institute of Electrical and Electronics Engineers (IEEE)

CY - Piscataway, NJ

T2 - 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice

Y2 - 28 May 2010 through 31 May 2010

ER -

Song N, Ching WK, Siu TK, Fung ES, Ng MK. Option valuation under a multivariate Markov Chain model. In Yu L, Song Y, Ching WK, Wang S, Lai KK, editors, 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice. Vol. 1. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). 2010. p. 177-181. 5532981 doi: 10.1109/CSO.2010.73

Option valuation under a multivariate Markov Chain model

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