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Applications of Additive Subordinati...

Li, Jing.

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Applications of Additive Subordination in Derivatives Pricing.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Applications of Additive Subordination in Derivatives Pricing./
作者:	Li, Jing.
面頁冊數:	159 p.
附註:	Source: Dissertation Abstracts International, Volume: 77-07(E), Section: A.
Contained By:	Dissertation Abstracts International77-07A(E).
標題:	Finance. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10024902
ISBN:	9781339519296

Applications of Additive Subordination in Derivatives Pricing.
Li, Jing.

Applications of Additive Subordination in Derivatives Pricing. - 159 p.

Source: Dissertation Abstracts International, Volume: 77-07(E), Section: A.

Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2015.

An important problem in mathematical finance is to develop option pricing models that are able to capture implied volatility "smile" or "skew" commonly observed in financial markets. Many existing models are based on time-homogeneous Markov processes and they often have difficulty in calibrating implied volatilities across both strikes and maturities. In this dissertation, we develop two parsimonious and analytically tractable option pricing models to evaluate VIX options and crack spread options, respectively. Our modeling approach is based on additive subordination, which is a natural generalization of classical Bochner's subordination. Probabilistically, additive subordination corresponds to a stochastic time change with respect to an independent additive subordinator. To model the VIX dynamics, we timechange a non-affine mean-reverting 3/2 diffusion with an independent additive subordinator to capture its empirical features, such as mean reversion and jumps, as well as upward-sloping implied volatility skew in VIX options. Moreover, we develop a parsimonious and analytically tractable two-factor model for crude oil and its refined product to evaluate crack spread option, where each factor is an additive subordinate Cox-Ingersoll-Ross process. This model captures key empirical features of individual commodities, such as mean-reversion and jumps, as well as of their spread. Analytical formulas for related options prices under each model are derived via an eigenfunction expansion approach. Empirical results show that our models have great flexibility in calibrating implied volatilities across strikes and maturities of each underlying with excellent performance. Our results suggest that additive subordination is a useful technique that allows one to construct a large family of jump-diffusions and/or pure jump processes with rich time- and state-dependent local characteristics, which are suited for parsimoniously reproducing empirical features with analytical tractability.

ISBN: 9781339519296Subjects--Topical Terms:

542899
Finance.

Applications of Additive Subordination in Derivatives Pricing.
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502 $a Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2015.
520 $a An important problem in mathematical finance is to develop option pricing models that are able to capture implied volatility "smile" or "skew" commonly observed in financial markets. Many existing models are based on time-homogeneous Markov processes and they often have difficulty in calibrating implied volatilities across both strikes and maturities. In this dissertation, we develop two parsimonious and analytically tractable option pricing models to evaluate VIX options and crack spread options, respectively. Our modeling approach is based on additive subordination, which is a natural generalization of classical Bochner's subordination. Probabilistically, additive subordination corresponds to a stochastic time change with respect to an independent additive subordinator. To model the VIX dynamics, we timechange a non-affine mean-reverting 3/2 diffusion with an independent additive subordinator to capture its empirical features, such as mean reversion and jumps, as well as upward-sloping implied volatility skew in VIX options. Moreover, we develop a parsimonious and analytically tractable two-factor model for crude oil and its refined product to evaluate crack spread option, where each factor is an additive subordinate Cox-Ingersoll-Ross process. This model captures key empirical features of individual commodities, such as mean-reversion and jumps, as well as of their spread. Analytical formulas for related options prices under each model are derived via an eigenfunction expansion approach. Empirical results show that our models have great flexibility in calibrating implied volatilities across strikes and maturities of each underlying with excellent performance. Our results suggest that additive subordination is a useful technique that allows one to construct a large family of jump-diffusions and/or pure jump processes with rich time- and state-dependent local characteristics, which are suited for parsimoniously reproducing empirical features with analytical tractability.
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