Asia-Pacific Financial Markets

, Volume 26, Issue 4, pp 553–565 | Cite as

A Numerical Scheme for Expectations with First Hitting Time to Smooth Boundary

  • Yuji Hishida
  • Yuta Ishigaki
  • Toshiki OkumuraEmail author


In the present paper, we propose a numerical scheme to calculate expectations with first hitting time to a given smooth boundary, in view of the application to the pricing of options with non-linear barriers. To attack the problem, we rely on the symmetrization technique in Akahori and Imamura (Quant Finance 14(7):1211–1216, 2014) and Imamura et al. (Monte Carlo Methods Appl 20(4):223–235, 2014), with some modifications. To see the effectiveness, we perform some numerical experiments.


Barrier option price First hitting time Non-linear smooth boundary Reflection principle Symmetrization of multi-dimensional diffusion 



The authors are grateful to Professor Jiro Akahori for many valuable comments and for careful reading of the manuscript and suggesting several improvements.


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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mizuho Securities Asia LimitedHong KongThe People’s Republic of China
  2. 2.COSMEDIA. CO., LTDTokyoJapan
  3. 3.The Dai-ichi Life Insurance Company, LimitedTokyoJapan

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