**Core Concept**
Nihilistic delusions are a type of psychotic symptom characterized by a person's belief that they, their loved ones, or the world are insignificant, worthless, or non-existent. This concept is rooted in the realm of psychiatric diagnosis and the classification of mood disorders.

**Why the Correct Answer is Right**
Nihilistic delusions are more commonly associated with severe and endogenous forms of depression. This is because endogenous depression is thought to be more biologically driven and less influenced by external factors, which can contribute to the development of psychotic symptoms like nihilistic delusions. The presence of nihilistic delusions often indicates a more severe level of depression, which may require more intensive treatment.

**Why Each Wrong Option is Incorrect**
**Option A:** While endogenous depression is a correct association, nihilistic delusions are not exclusive to this condition. Other forms of depression can also manifest with psychotic symptoms.
**Option B:** Double depression refers to the co-occurrence of dysthymia and major depressive disorder. While patients with double depression may experience severe depressive symptoms, nihilistic delusions are not a hallmark feature.
**Option C:** Depression in involutional psychosis is a type of depression that occurs in middle-aged adults, often in the context of a psychotic break. However, nihilistic delusions are more commonly seen in endogenous depression than in involutional psychosis.
**Option D:** Cyclothymia is a mood disorder characterized by periods of hypomania and depression, but it is not typically associated with nihilistic delusions.
**Option E:** Dysthymia is a mild, chronic form of depression that does not usually involve psychotic symptoms like nihilistic delusions.

**Clinical Pearl / High-Yield Fact**
Nihilistic delusions are a red flag for severe depression, and their presence in a patient should prompt a thorough evaluation for potential suicidal risk and the need for intensive psychiatric treatment.

**Correct Answer: A. Endogenous depression**