Black-Scholes MCP Server

import unittest import math from calculators.black_scholes_charm import calculate_charm_value from calculators.black_scholes_common import calculate_d1_d2, norm_pdf, norm_cdf class TestBlackScholesCharm(unittest.TestCase): def test_calculate_charm_call_at_the_money(self): # Test charm with at-the-money call option S, K, T, r, q, vol = 100, 100, 1, 0.05, 0.02, 0.2 d1, d2 = calculate_d1_d2(S, K, T, r, q, vol) # Calculate expected value common_term = -math.exp(-q * T) * norm_pdf(d1) / (2 * T) expected_charm = common_term * (2 * (r - q) / (vol * math.sqrt(T)) - d2 / (2 * T)) - q * math.exp(-q * T) * norm_cdf(d1) charm = calculate_charm_value(S, K, T, r, q, vol, "call") self.assertAlmostEqual(charm, expected_charm, places=8) def test_calculate_charm_put_at_the_money(self): # Test charm with at-the-money put option S, K, T, r, q, vol = 100, 100, 1, 0.05, 0.02, 0.2 d1, d2 = calculate_d1_d2(S, K, T, r, q, vol) # Calculate expected value common_term = -math.exp(-q * T) * norm_pdf(d1) / (2 * T) expected_charm = common_term * (2 * (r - q) / (vol * math.sqrt(T)) - d2 / (2 * T)) + q * math.exp(-q * T) * norm_cdf(-d1) charm = calculate_charm_value(S, K, T, r, q, vol, "put") self.assertAlmostEqual(charm, expected_charm, places=8) def test_calculate_charm_call_in_the_money(self): # Test charm with in-the-money call option S, K, T, r, q, vol = 110, 100, 1, 0.05, 0.02, 0.2 d1, d2 = calculate_d1_d2(S, K, T, r, q, vol) # Calculate expected value common_term = -math.exp(-q * T) * norm_pdf(d1) / (2 * T) expected_charm = common_term * (2 * (r - q) / (vol * math.sqrt(T)) - d2 / (2 * T)) - q * math.exp(-q * T) * norm_cdf(d1) charm = calculate_charm_value(S, K, T, r, q, vol, "call") self.assertAlmostEqual(charm, expected_charm, places=8) def test_calculate_charm_put_out_of_the_money(self): # Test charm with out-of-the-money put option S, K, T, r, q, vol = 110, 100, 1, 0.05, 0.02, 0.2 d1, d2 = calculate_d1_d2(S, K, T, r, q, vol) # Calculate expected value common_term = -math.exp(-q * T) * norm_pdf(d1) / (2 * T) expected_charm = common_term * (2 * (r - q) / (vol * math.sqrt(T)) - d2 / (2 * T)) + q * math.exp(-q * T) * norm_cdf(-d1) charm = calculate_charm_value(S, K, T, r, q, vol, "put") self.assertAlmostEqual(charm, expected_charm, places=8) def test_charm_short_maturity(self): # Test with very short time to maturity S, K, T, r, q, vol = 100, 100, 0.01, 0.05, 0.02, 0.2 # For call option charm_call = calculate_charm_value(S, K, T, r, q, vol, "call") self.assertTrue(math.isfinite(charm_call), f"Charm calculation for short maturity call resulted in {charm_call}") # For put option charm_put = calculate_charm_value(S, K, T, r, q, vol, "put") self.assertTrue(math.isfinite(charm_put), f"Charm calculation for short maturity put resulted in {charm_put}") def test_charm_long_maturity(self): # Test with long time to maturity S, K, T, r, q, vol = 100, 100, 5, 0.05, 0.02, 0.2 # For call option charm_call = calculate_charm_value(S, K, T, r, q, vol, "call") self.assertTrue(math.isfinite(charm_call), f"Charm calculation for long maturity call resulted in {charm_call}") # For put option charm_put = calculate_charm_value(S, K, T, r, q, vol, "put") self.assertTrue(math.isfinite(charm_put), f"Charm calculation for long maturity put resulted in {charm_put}") def test_put_call_parity_relation(self): # Test that put-call parity relation holds for Charm: # Charm_call - Charm_put = q * e^(-qT) # (with a small difference due to floating point precision) S, K, T, r, q, vol = 100, 100, 1, 0.05, 0.02, 0.2 charm_call = calculate_charm_value(S, K, T, r, q, vol, "call") charm_put = calculate_charm_value(S, K, T, r, q, vol, "put") # The difference should be approximately q * e^(-qT) expected_diff = q * math.exp(-q * T) actual_diff = charm_call - charm_put self.assertAlmostEqual(actual_diff, -expected_diff, places=8) if __name__ == '__main__': unittest.main()