A systematic and efficient simulation scheme for the Greeks of financial derivatives

Yuh Dauh Lyuu, Huei-Wen Teng*, Yao Te Tseng, Sheng Xiang Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Greeks are the price sensitivities of financial derivatives and are essential for pricing, speculation, risk management, and model calibration. Although the pathwise method has been popular for calculating them, its applicability is problematic when the integrand is discontinuous. To tackle this problem, this paper defines and derives the parameter derivative of a discontinuous integrand of certain functional forms with respect to the parameter of interest. The parameter derivative is such that its integration equals the differentiation of the integration of the aforesaid discontinuous integrand with respect to that parameter. As a result, unbiased Greek formulas for a very broad class of payoff functions and models can be systematically derived. This new method is applied to the Greeks of (1) Asian options under two popular Lévy processes, i.e. Merton's jump-diffusion model and the variance-gamma process, and (2) collateralized debt obligations under the Gaussian copula model. Our Greeks outperform the finite-difference and likelihood ratio methods in terms of accuracy, variance, and computation time.

Original languageEnglish
Pages (from-to)1199-1219
Number of pages21
JournalQuantitative Finance
Issue number7
StateAccepted/In press - 1 Jan 2019


  • Credit derivatives
  • Dirac delta function
  • Greeks
  • Jump-diffusion processes
  • Monte Carlo simulation
  • Variance-gamma processes


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