Inclusion Criteria:

          -  Willing and able to provide signed informed consent.

          -  Males aged 18 years of age and above.

          -  Histological or cytologic proof of adenocarcinoma of the prostate.

          -  Known castration-resistant disease, defined according to Prostate Cancer Working Group
             3 (PCWG3) criteria as:

               -  Castrate serum testosterone level: ≤ 50 ng/dL (≤ 1.7 nmol/L).

               -  Subjects who have failed initial hormonal therapy, either by orchiectomy or by
                  using a gonadotropin-releasing hormone (GnRH) agonist in combination with an
                  anti-androgen, must first progress through anti-androgen withdrawal prior to
                  being eligible. The minimum time frame to document failure of anti-androgen
                  withdrawal will be four weeks.

               -  Serum Prostate Specific Antigen (PSA) progression defined as two consecutive
                  increases in PSA over a previous reference value within 6 months of first study
                  treatment, each measurement at least one week apart.

        Or

          -  Documented bone lesions by the appearance of ≥ 2 new lesions by bone scintigraphy or
             dimensionally-measureable soft tissue metastatic lesion assessed by CT or MRI.

               -  Absolute PSA ≥ 2.0 ng/mL at screening.

               -  Must have PSA and/or radiographic progression on AT LEAST 1 novel AR targeted
                  therapy (abiraterone acetate, enzalutamide). One prior chemotherapy agent for
                  metastatic castration-resistant prostate cancer (mCRPC) will be allowed.

               -  Prior treatment with abiraterone, enzalutamide, bicalutamide, and/or ketoconazole
                  is allowed. There is no limit on the maximum number or types of prior hormonal
                  therapies received.

               -  Must be maintained on a GnRH analogue or have undergone orchiectomy.

               -  Radiographic evidence of metastatic disease by CT scan and bone scan, performed
                  within the prior 4 weeks.

               -  Must have a soft tissue metastatic lesion available for biopsy collection to
                  perform tumor tissue analysis.

               -  Karnofsky Performance Status (KPS): ≥ 70% within 14 days before start of study
                  treatment (ECOG ≤ 2).

               -  Participants must have normal organ and bone marrow function measured within 28
                  days prior to administration of study treatment as defined below:

          -  Hemoglobin ≥ 9.0 g/dL with no blood transfusion in the past 28 days.

          -  Absolute neutrophil count (ANC) ≥ 1.0 x 10^9/L

          -  Platelet count ≥ 100 x 10^9/L

          -  Total bilirubin within institutional upper limit of normal (ULN) (In patients with
             Gilbert's syndrome, total bilirubin < 1.5x institutional ULN will be acceptable).

          -  Aspartate aminotransferase (AST) (Serum Glutamic Oxaloacetic Transaminase (SGOT)) /
             Alanine aminotransferase (ALT) (Serum Glutamic Pyruvate Transaminase (SGPT)) within
             institutional upper limit of normal.

          -  Participants must have creatinine clearance estimated ≥ 40 mL/min.

               -  Participants must have a life expectancy ≥ 6 months.

               -  Male participants and their partners, who are sexually active and of childbearing
                  potential, must agree to the use of two highly effective forms of contraception
                  in combination, throughout the period of taking study treatment and for 7 months
                  after the last dose of nivolumab to prevent pregnancy in a partner.

               -  No evidence (within 5 years) of prior malignancies (except successfully treated
                  basal cell or squamous cell carcinoma of the skin).

        Exclusion Criteria:

          -  Has received external-beam radiotherapy within the last 2 weeks prior to start of
             study treatment.

          -  Prior oral anti-androgen (e.g. bicalutamide, nilutamide, enzalutamide, apalutamide),
             or androgen synthesis inhibitor (e.g. abiraterone, orteronel) within the past 2 weeks
             is not permitted. 5-alpha reductase inhibitor therapy (e.g. finasteride, dutasteride)
             is allowed, as long as subject has been stable on medication for past 6 months.

          -  Prior treatment with chemotherapy for the treatment of metastatic hormone sensitive
             prostate cancer is allowed if the last dose of chemotherapy was greater than 6 months
             prior to enrollment. In addition, one chemotherapy agent for mCRPC will be allowed.

          -  Patients who have received prior treatment with bipolar androgen therapy (e.g.
             testosterone, BAT) are excluded.

          -  Pain due to metastatic prostate cancer requiring opioid therapy.

          -  Patients with an intact prostate AND urinary obstructive symptoms are excluded (which
             includes patients with urinary symptoms from benign prostatic hyperplasia (BPH)).

          -  Patients receiving anticoagulation therapy with Coumadin are not eligible for study.
             (Patients on non-coumadin anticoagulants (Lovenox, Xarelto, etc.) are eligible for
             study. Patients on Coumadin who can be transitioned to Lovenox or Xarelto prior to
             starting study treatments will be eligible).

          -  Patients with prior history of an arteriovenous thromboembolic event within the last
             12 months are excluded.

          -  Patients allergic to sesame seed oil or cottonseed oil are excluded.

          -  Involvement in the planning and/or conduct of the study (applies to both BMS staff
             and/or staff at the study site).

          -  Participation in another clinical study with an investigational product during the
             last 4 weeks/28 days.

          -  Patients should be excluded if they have had prior systemic treatment with an
             anti-Programmed Cell Death Protein (PD)-1, anti-PD-L1, anti-PD-L2, anti-Cytotoxic
             T-lymphocyte-Associated Protein (CTLA)-4 antibody, or any other antibody or drug
             specifically targeting T-cell costimulation or immune checkpoint pathways (e.g. immune
             checkpoint antagonists).

          -  Evidence of disease in sites or extent that, in the opinion of the investigator, would
             put the patient at risk from therapy with testosterone (e.g. femoral metastases with
             concern over fracture risk, severe and extensive spinal metastases with concern over
             spinal cord compression, extensive liver metastases).

          -  Concurrent use of other anticancer agents or treatments, with the following
             exceptions:

               -  Ongoing treatment with leutinizing hormone-releasing hormone (LHRH) agonists or
                  antagonists, denosumab (Prolia) or bisphosphonate (e.g. zoledronic acid) is
                  allowed. Ongoing treatment should be kept at a stable schedule; however, if
                  medically required, a change of dose, compound, or both is allowed.

          -  Any treatment modalities involving major surgery within 4 weeks prior to the start of
             study treatment.

          -  Symptomatic nodal disease, i.e. scrotal, penile or leg edema (≥ CTCAE Grade 3).

          -  Patients are excluded if they have active known brain metastases or leptomeningeal
             metastases. Subjects with brain metastases are eligible if metastases have been
             treated and there is no magnetic resonance imaging (MRI) evidence of progression for
             at least 4 weeks after treatment is complete and within 28 days prior to the first
             dose of testosterone administration. There must also be no requirement for
             immunosuppressive doses of systemic corticosteroids (> 10 mg/day prednisone
             equivalents) for at least 2 weeks prior to study drug administration.

          -  Patients should be excluded if they have an active, known or suspected autoimmune
             disease (e.g. inflammatory bowel disease, rheumatoid arthritis, autoimmune hepatitis,
             lupus, celiac disease). Subjects are permitted to enroll if they have vitiligo, type I
             diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring
             hormone replacement, psoriasis not requiring systemic treatment, or conditions not
             expected to recur in the absence of an external trigger.

          -  Patients should be excluded if they have a condition requiring systemic treatment with
             either corticosteroids (> 10 mg daily prednisone equivalents) or other
             immunosuppressive medications within 14 days of study drug administration. Inhaled or
             topical steroids and adrenal replacement doses > 10 mg daily prednisone equivalents
             are permitted in the absence of active autoimmune disease.

          -  Permitted therapies include topical, ocular, intra-articular, intranasal, and
             inhalational corticosteroids (with minimal systemic absorption). Physiologic
             replacement doses of systemic corticosteroids are permitted, even if > 10 mg/day
             prednisone equivalents. A brief course of corticosteroids for prophylaxis (e.g.
             contrast dye allergy) or for treatment of non-autoimmune conditions (e.g. delayed-type
             hypersensitivity reaction caused by contact allergen) is permitted.

          -  As there is potential for hepatic toxicity with nivolumab, drugs with a predisposition
             to hepatotoxicity should be used with caution in patients treated with
             nivolumab-containing regimen.

          -  Patients should be excluded if they have a positive test for hepatitis B virus surface
             antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating
             acute or chronic infection.

          -  Patients should be excluded if they have known history of testing positive for human
             immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS).

          -  History of allergy to study drug components.

          -  History of severe hypersensitivity reaction to any monoclonal antibody.

          -  Other primary tumor (other than CRPC) including hematological malignancy present
             within the last 5 years (except non-melanoma skin cancer or low-grade superficial
             bladder cancer).

          -  Has imminent or established spinal cord compression based on clinical findings and/or
             MRI.

          -  Any other serious illness or medical condition that would, in the opinion of the
             investigator, make this protocol unreasonably hazardous, including, but not limited
             to:

               -  Any uncontrolled major infection.

               -  Cardiac failure New York Heart Association (NYHA) Class III or IV.

               -  Crohn's disease or ulcerative colitis.

               -  Bone marrow dysplasia.

               -  Known allergy to any of the compounds under investigation.

               -  Unmanageable fecal incontinence.

          -  Persistent toxicities (> CTCAE Grade 2) caused by previous cancer therapy, excluding
             alopecia.

          -  Poor medical risk due to a serious, uncontrolled medical disorder, non-malignant
             systemic disease or active, uncontrolled infection. Examples include, but are not
             limited to, uncontrolled ventricular arrhythmia, recent (within 6 months) myocardial
             infarction, uncontrolled major seizure disorder, extensive interstitial bilateral lung
             disease, or any psychiatric disorder that prohibits obtaining informed consent.