• East Asian mathematical journal
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• v.40 no.1
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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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• v.26 no.4
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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.

• The Transactions of the Korea Information Processing Society
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• v.1 no.3
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• pp.357-366
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• 1994

The IEEE 802.4 token bus has been widely accepted as the standard for factory local area networks. The priority option of the 802.4 standard supports multiple classes of traffic by using a set of timers to control information exchange. The performance of the 802.4 priority mechanism in industrial real time control is examined. A timer assignment technique is presented for such applications. The timers are set to satisfy the worst case access delay requirements of real time control applications. Other applications that are not time constrainted can be supported simultaneously. In fact under certain conditions, such applications can also be guaranteed a minimum bandwidth allocation. Simulation results are used to evaluate the timer assignment and utililization.