Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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THE VALUATION OF TIMER POWER OPTIONS WITH STOCHASTIC VOLATILITY

  • MIJIN, HA (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY) ;
  • DONGHYUN, KIM (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY) ;
  • SERYOONG, AHN (DIVISION OF BUSINESS ADMINISTRATION, PUKYONG NATIONAL UNIVERSITY) ;
  • JI-HUN, YOON (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
  • Received : 2022.11.05
  • Accepted : 2022.12.20
  • Published : 2022.12.25
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Abstract

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.

Keywords

Acknowledgement

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea(NRF-2021S1A5A2A03063960).

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