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COS Option Pricing: Scaling, Truncation Intervals, and Calibration

Article Quant Q&A · Author: Math122
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Summary

The document raises implementation questions about the COS method for option pricing. It asks why a reference formulates characteristic functions and cumulants for a log price relative to the strike, rather than relative to the initial price, and how that choice affects the truncation interval used in the Fourier expansion.

It also asks how to select the interval and expansion size when calibrating a model, since model parameters are changing and cumulants may not be available as fixed inputs. The text offers no answers, derivation, numerical comparison, or calibration guidance; it is a focused statement of issues a practitioner must resolve when applying COS pricing. Its value is identifying the dependence between coordinate scaling, interval construction, and calibration setup, while leaving the recommended choices open.

Key ideas

  • The COS method can express the log-price variable relative to the strike or the initial asset price.
  • Changing the reference level affects the cumulants and may shift the truncation interval.
  • Calibration complicates interval selection because model parameters vary during the search.
  • The document poses these questions but does not provide a solution or empirical guidance.

Tags

OptionsDerivatives pricingStatistics
Full text
# Two questions about COS method


# Two questions about COS method












Hey I have some problem with COS method. Here is the paper of Fang and Oosterlee https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.466.267&rep=rep1&type=pdf

- Why in table 1.1 they write characteristic functions for $\ln(S_t/K)$ instead of $\ln(S_t/S_0)$ and where is this $K$? Is it hidden in $\mu$ term? And why cumulants are also calculated for $\ln(S_t/K)$? Then the interval $[a,b]$ which depends on the cumulants would be different for different values ​​of $K$.

- How to use this method for calibration procedure? What interval $[a,b]$ should I use for different models and what value of $N$? Since in calibration we are searching for model parameter we can't use cumulant to determine this interval.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.