Here is the soluton to determine if the given option exist in the page (select item) or not

public boolean isSelectOptionPresent(WebDriver webdriver, String selectLocator, String optionToCheck) {
    if (webdriver == null) {
        throw new NullPointerException("WebDriver instance is null.");
    }

    if (null == optionToCheck || optionToCheck.isEmpty()) {
        throw new IllegalArgumentException("Invalid value
    }

    String[] availableOptions = webdriver.getSelectOptions(selectLocator);
    for(String option: availableOptions) {
        if (optionToCheck.equals(option) {
            return true;
        }
    }
    return false;
}