An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility
Timer options, which were first introduced by Société Générale Corporate and Investment Banking in 2007, are financial securities whose payoffs and exercise are determined by a random time associated with the accumulated realized variance of the underlying asset, unlike vanilla options exercised at...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024121?viewType=HTML |
| _version_ | 1797353692837445632 |
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| author | Sun-Yong Choi Donghyun Kim Ji-Hun Yoon |
| author_facet | Sun-Yong Choi Donghyun Kim Ji-Hun Yoon |
| author_sort | Sun-Yong Choi |
| collection | DOAJ |
| description | Timer options, which were first introduced by Société Générale Corporate and Investment Banking in 2007, are financial securities whose payoffs and exercise are determined by a random time associated with the accumulated realized variance of the underlying asset, unlike vanilla options exercised at the prescribed maturity date. In this paper, taking account of the correlation between the underlying asset price and volatility, we investigate the pricing of timer options under the constant elasticity of variance (CEV) model, proposed by Cox and Ross [10], taking advantage of the approach of asymptotic analysis. Additionally, we validate the pricing precision of the approximate formula for timer options using the Monte Carlo method. We conduct numerical experiments based on our corrected prices and analyze price sensitivities concerning various model parameters, with a focus on the value of elasticity. |
| first_indexed | 2024-03-08T13:34:43Z |
| format | Article |
| id | doaj.art-ceaba4f0ea38406697b599c869f7fd54 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T13:34:43Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ceaba4f0ea38406697b599c869f7fd542024-01-17T01:11:20ZengAIMS PressAIMS Mathematics2473-69882024-01-01912454247210.3934/math.2024121An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatilitySun-Yong Choi0Donghyun Kim1Ji-Hun Yoon21. Department of Financial Mathematics, Gachon University, Gyeoggi 13120, Republic of Korea2. Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea2. Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea 3. Institute of Mathematical Science, Pusan National University, Busan 46241, Republic of KoreaTimer options, which were first introduced by Société Générale Corporate and Investment Banking in 2007, are financial securities whose payoffs and exercise are determined by a random time associated with the accumulated realized variance of the underlying asset, unlike vanilla options exercised at the prescribed maturity date. In this paper, taking account of the correlation between the underlying asset price and volatility, we investigate the pricing of timer options under the constant elasticity of variance (CEV) model, proposed by Cox and Ross [10], taking advantage of the approach of asymptotic analysis. Additionally, we validate the pricing precision of the approximate formula for timer options using the Monte Carlo method. We conduct numerical experiments based on our corrected prices and analyze price sensitivities concerning various model parameters, with a focus on the value of elasticity.https://www.aimspress.com/article/doi/10.3934/math.2024121?viewType=HTMLtimer optionsstochastic volatilityconstant elasticity of varianceasymptotic analysismonte-carlo simulation |
| spellingShingle | Sun-Yong Choi Donghyun Kim Ji-Hun Yoon An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility AIMS Mathematics timer options stochastic volatility constant elasticity of variance asymptotic analysis monte-carlo simulation |
| title | An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility |
| title_full | An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility |
| title_fullStr | An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility |
| title_full_unstemmed | An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility |
| title_short | An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility |
| title_sort | analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility |
| topic | timer options stochastic volatility constant elasticity of variance asymptotic analysis monte-carlo simulation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024121?viewType=HTML |
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