Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach
In this paper, we derive a pricing formula for arithmetic Asian options by using the Edgeworth series expansion. Our pricing formula consists of a Black-Scholes-Merton type formula and a finite sum with the estimation of the remainder term. Moreover, we present explicitly a method to compute each te...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
KeAi Communications Co., Ltd.
2016-03-01
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| Series: | Journal of Finance and Data Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405918816300022 |
| _version_ | 1797203669417984000 |
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| author | Weiping Li Su Chen |
| author_facet | Weiping Li Su Chen |
| author_sort | Weiping Li |
| collection | DOAJ |
| description | In this paper, we derive a pricing formula for arithmetic Asian options by using the Edgeworth series expansion. Our pricing formula consists of a Black-Scholes-Merton type formula and a finite sum with the estimation of the remainder term. Moreover, we present explicitly a method to compute each term in our pricing formula. The hedging formulas (greek letters) for the arithmetic Asian options are obtained as well. Our formulas for the long lasting question on pricing and hedging arithmetic Asian options are easy to implement with enough accuracy. Our numerical illustration shows that the arithmetic Asian options worths less than the European options under the standard Black-Scholes assumptions, verifies theoretically that the volatility of the arithmetic average is less than the one of the underlying assets, and also discovers an interesting phenomena that the arithmetic Asian option for large fixed strikes such as stocks has higher volatility (elasticity) than the plain European option. However, the elasticity of the arithmetic Asian options for small fixed strikes as trading in currencies and commodity products is much less than the elasticity of the plain European option. These findings are consistent with the ones from the hedgings with respect to the time to expiration, the strike, the present underlying asset price, the interest rate and the volatility. |
| first_indexed | 2024-04-24T08:23:00Z |
| format | Article |
| id | doaj.art-d98b0a08203f48249571c6952628f181 |
| institution | Directory Open Access Journal |
| issn | 2405-9188 |
| language | English |
| last_indexed | 2024-04-24T08:23:00Z |
| publishDate | 2016-03-01 |
| publisher | KeAi Communications Co., Ltd. |
| record_format | Article |
| series | Journal of Finance and Data Science |
| spelling | doaj.art-d98b0a08203f48249571c6952628f1812024-04-17T00:33:24ZengKeAi Communications Co., Ltd.Journal of Finance and Data Science2405-91882016-03-012112510.1016/j.jfds.2016.01.001Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approachWeiping Li0Su Chen1Southwest Jiaotong University, Chengdu, Sichuan Province 610031, PR ChinaMathematical Sciences Dept., The University of Memphis, Memphis, TN 38152, USAIn this paper, we derive a pricing formula for arithmetic Asian options by using the Edgeworth series expansion. Our pricing formula consists of a Black-Scholes-Merton type formula and a finite sum with the estimation of the remainder term. Moreover, we present explicitly a method to compute each term in our pricing formula. The hedging formulas (greek letters) for the arithmetic Asian options are obtained as well. Our formulas for the long lasting question on pricing and hedging arithmetic Asian options are easy to implement with enough accuracy. Our numerical illustration shows that the arithmetic Asian options worths less than the European options under the standard Black-Scholes assumptions, verifies theoretically that the volatility of the arithmetic average is less than the one of the underlying assets, and also discovers an interesting phenomena that the arithmetic Asian option for large fixed strikes such as stocks has higher volatility (elasticity) than the plain European option. However, the elasticity of the arithmetic Asian options for small fixed strikes as trading in currencies and commodity products is much less than the elasticity of the plain European option. These findings are consistent with the ones from the hedgings with respect to the time to expiration, the strike, the present underlying asset price, the interest rate and the volatility.http://www.sciencedirect.com/science/article/pii/S2405918816300022Arithmetic Asian optionEdgworth series expansionCumulantElasticityHedge |
| spellingShingle | Weiping Li Su Chen Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach Journal of Finance and Data Science Arithmetic Asian option Edgworth series expansion Cumulant Elasticity Hedge |
| title | Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach |
| title_full | Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach |
| title_fullStr | Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach |
| title_full_unstemmed | Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach |
| title_short | Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach |
| title_sort | pricing and hedging of arithmetic asian options via the edgeworth series expansion approach |
| topic | Arithmetic Asian option Edgworth series expansion Cumulant Elasticity Hedge |
| url | http://www.sciencedirect.com/science/article/pii/S2405918816300022 |
| work_keys_str_mv | AT weipingli pricingandhedgingofarithmeticasianoptionsviatheedgeworthseriesexpansionapproach AT suchen pricingandhedgingofarithmeticasianoptionsviatheedgeworthseriesexpansionapproach |