• East Asian mathematical journal
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• 제40권1호
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• pp.63-74
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• 2024

Timer options are financial instruments proposed by Société Générale Corporate and Investment Banking in 2007. Unlike vanilla options, where the expiry date is fixed, the expiry date of timer options is determined by the investor's choice, which is in linked to a variance budget. In this study, we derive a pricing formula for hybrid options that combine timer options, digital options, and power options, considering an environment where volatility of an underlying asset follows a fast-mean-reverting process. Additionally, we aim to validate the pricing accuracy of these analytical formulas by comparing them with the results obtained from Monte Carlo simulations. Finally, we conduct numerical studies on these options to analyze the impact of stochastic volatility on option's price with respect to various model parameters.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.296-309
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• 2022

Timer options are one of the contingent claims that, for given the variance budget, its payoff depends on a random maturity in terms of the realized variance unlike the standard European vanilla option with a fixed time maturity. Since it was first launched by Société Générale Corporate and Investment Banking in 2007, the valuation of the timer options under several stochastic environment for the volatility has been conducted by many researches. In this study, we propose the pricing of timer power options combined with standard timer options and the index of the power to the underlying asset for the investors to actualize lower risks and higher returns at the same time under the uncertain markets. By using the asymptotic analysis, we obtain the first-order approximation of timer power options. Moreover, we demonstrate that our solution has been derived accurately by comparing it with the solution from the Monte-Carlo method. Finally, we analyze the impact of the stochastic volatility with regards to various parameters on the timer power options numerically.

• 한국정보처리학회논문지
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• 제1권3호
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• pp.357-366
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• 1994

IEEE 802.4 토큰버스 방식이 산업용 네트워크에 있어서 표준으로 넓게 받아들여지 고 있다. 802.4에서는 정보의 교환을 제어하기 위해 일종의 타이머를 사용하여 트래 픽의 다중 클래스를 지원한다. 실시간 처리를 위한 802.4 기능의 시간 할당방법은 실제 생산 공정에서 요구되는 실시간 제어응용에서 최악의 상태 억세스 요구를 만족하 도록 타이머들이 설정되어야 한다. 물론 시간에 제약을 받지 않은 다른 응용들도 동시 에 지원될 수 있다. 본 논문에서는 실시간 처리를 위하여 토큰 버스 네트워크 운영시 타이머 할당 구조에 따른 최소한의 대역폭 할당을 위하여 알고리즘을 제안하고 해석 적 방법과 이의 시뮬레이션을 수행하여 타이머 할당과 유용도 산출에 대한 성능을 해 석하였다.