An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility

Sun-Yong Choi; Donghyun Kim; Ji-Hun Yoon; Sun-Yong Choi; Donghyun Kim; Ji-Hun Yoon

doi:10.3934/math.2024121

AIMS Mathematics

2024, Volume 9, Issue 1: 2454-2472. doi: 10.3934/math.2024121

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An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility

1.
Department of Financial Mathematics, Gachon University, Gyeoggi 13120, Republic of Korea
2.
Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea
3.
Institute of Mathematical Science, Pusan National University, Busan 46241, Republic of Korea

Received: 14 November 2023 Revised: 14 December 2023 Accepted: 18 December 2023 Published: 25 December 2023
MSC : 91G20, 91G60

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.
- timer options,
- stochastic volatility,
- constant elasticity of variance,
- asymptotic analysis,
- Monte-Carlo simulation
Citation: Sun-Yong Choi, Donghyun Kim, Ji-Hun Yoon. An analytic pricing formula for timer options under constant elasticity of variance with stochastic volatility[J]. AIMS Mathematics, 2024, 9(1): 2454-2472. doi: 10.3934/math.2024121

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Abstract

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.

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