Volume 7, Issue 2
Uncertainty Quantification of Derivative Instruments

Xianming Sun & Michèle Vanmaele

East Asian J. Appl. Math., 7 (2017), pp. 343-362.

Published online: 2018-02

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  • Abstract

Model and parameter uncertainties are common whenever some parametric model is selected to value a derivative instrument. Combining the Monte Carlo method with the Smolyak interpolation algorithm, we propose an accurate efficient numerical procedure to quantify the uncertainty embedded in complex derivatives. Except for the value function being sufficiently smooth with respect to the model parameters, there are no requirements on the payoff or candidate models. Numerical tests carried out quantify the uncertainty of Bermudan put options and down-and-out put options under the Heston model, with each model parameter specified in an interval.

  • Keywords

Parameter uncertainty, Derivative pricing, Smolyak algorithm, Monte Carlo, Entropy.

  • AMS Subject Headings

62P05, 65C05, 65C50, 68U20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-343, author = {}, title = {Uncertainty Quantification of Derivative Instruments}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {343--362}, abstract = {

Model and parameter uncertainties are common whenever some parametric model is selected to value a derivative instrument. Combining the Monte Carlo method with the Smolyak interpolation algorithm, we propose an accurate efficient numerical procedure to quantify the uncertainty embedded in complex derivatives. Except for the value function being sufficiently smooth with respect to the model parameters, there are no requirements on the payoff or candidate models. Numerical tests carried out quantify the uncertainty of Bermudan put options and down-and-out put options under the Heston model, with each model parameter specified in an interval.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.100316.270117a}, url = {http://global-sci.org/intro/article_detail/eajam/10753.html} }
TY - JOUR T1 - Uncertainty Quantification of Derivative Instruments JO - East Asian Journal on Applied Mathematics VL - 2 SP - 343 EP - 362 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.100316.270117a UR - https://global-sci.org/intro/article_detail/eajam/10753.html KW - Parameter uncertainty, Derivative pricing, Smolyak algorithm, Monte Carlo, Entropy. AB -

Model and parameter uncertainties are common whenever some parametric model is selected to value a derivative instrument. Combining the Monte Carlo method with the Smolyak interpolation algorithm, we propose an accurate efficient numerical procedure to quantify the uncertainty embedded in complex derivatives. Except for the value function being sufficiently smooth with respect to the model parameters, there are no requirements on the payoff or candidate models. Numerical tests carried out quantify the uncertainty of Bermudan put options and down-and-out put options under the Heston model, with each model parameter specified in an interval.

Xianming Sun & Michèle Vanmaele. (2020). Uncertainty Quantification of Derivative Instruments. East Asian Journal on Applied Mathematics. 7 (2). 343-362. doi:10.4208/eajam.100316.270117a
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