def test_model_cache(self):
opt = Option(opt_type=OptionType.CALL,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.025)
self.assertEquals(0, len(opt.model_cache))
self.assertAlmostEquals(
3.19,
opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
self.assertEquals([OptionModel.BINOMIAL_TREE], opt.model_cache.keys())
self.assertAlmostEquals(
3.19,
opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
opt.model_cache[OptionModel.BINOMIAL_TREE][OptionMeasure.VALUE] = 42.42
self.assertAlmostEquals(
42.42,
opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
opt.vol = 0.55
self.assertAlmostEquals(
6.76,
opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
def test_binomial_tree_discrete_dividend_valuation(self):
mat = 9.0 / 12
num_steps = 9 * 4
self.assertAlmostEquals(13.93, Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10) \
.run_model(model=OptionModel.BINOMIAL_TREE, num_steps=num_steps)[OptionMeasure.VALUE], delta=0.01)
self.assertAlmostEquals(13.93, Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, yield_=lambda t1, t2: 0) \
.run_model(model=OptionModel.BINOMIAL_TREE, num_steps=num_steps)[OptionMeasure.VALUE], delta=0.01)
self.assertAlmostEquals(14.77, Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, yield_=0.04) \
.run_model(model=OptionModel.BINOMIAL_TREE, num_steps=num_steps)[OptionMeasure.VALUE], delta=0.01)
def div1_fn(t1, t2): # $2.50 dividend after about a one month
n = t2 / (mat / num_steps)
return 2.50 if n == 4 else 0
self.assertAlmostEquals(15.45, Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, yield_=div1_fn) \
.run_model(model=OptionModel.BINOMIAL_TREE, num_steps=num_steps)[OptionMeasure.VALUE], delta=0.01)
def div_monthly_fn(t1, t2): # $2.50 dividend every month
n = t2 / (mat / num_steps)
return 2.50 if (n % 4) == 0 else 0
self.assertAlmostEquals(3.57, Option(opt_type=OptionType.CALL, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, yield_=div_monthly_fn) \
.run_model(model=OptionModel.BINOMIAL_TREE, num_steps=num_steps)[OptionMeasure.VALUE], delta=0.01)
self.assertAlmostEquals(24.51, Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, yield_=div_monthly_fn) \
.run_model(model=OptionModel.BINOMIAL_TREE, num_steps=num_steps)[OptionMeasure.VALUE], delta=0.01)
def test_implied_volatility(self):
self.assertAlmostEquals(0.30,
Option.imply_volatility(
10.10,
opt_type=OptionType.PUT,
spot0=90,
strike=100,
mat=1.0 / 12,
riskless_rate=0.10),
delta=0.01)
self.assertAlmostEquals(0.52,
Option.imply_volatility(
2.25,
opt_type=OptionType.CALL,
spot0=90,
strike=100,
mat=1.0 / 12,
riskless_rate=0.10),
delta=0.01)
premium = 10.10
opt_kwargs = {
'opt_type': OptionType.PUT,
'spot0': 90,
'strike': 100,
'mat': 1.0 / 12,
'riskless_rate': 0.10,
}
self.assertAlmostEquals(0.30,
Option.imply_volatility(premium, **opt_kwargs),
delta=0.01)
opt_kwargs['vol'] = Option.imply_volatility(premium, **opt_kwargs)
self.assertAlmostEquals(
premium,
Option(**opt_kwargs).run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
def test_monte_carlo_valuation(self):
self.assertAlmostEquals(2.51, Option(opt_type=OptionType.CALL, spot0=90, strike=100, mat=3.0 / 12,
vol=0.35, riskless_rate=0.10, yield_=0.05, exer_type=OptionExerciseType.EUROPEAN) \
.run_model(model=OptionModel.MONTE_CARLO, random_seed=12345)[OptionMeasure.VALUE], delta=0.01)
self.assertAlmostEquals(3.60, Option(opt_type=OptionType.CALL, spot0=90, strike=100, mat=3.0 / 12,
vol=0.35, riskless_rate=0.10, yield_=0.05, exer_type=OptionExerciseType.AMERICAN) \
.run_model(model=OptionModel.MONTE_CARLO, random_seed=12345)[OptionMeasure.VALUE], delta=0.01)
mat = 9.0 / 12
num_steps = 9 * 4
def div_monthly_fn(t1, t2): # $2.50 dividend every month
n = t2 / (mat / num_steps)
return 2.50 if (n % 4) == 0 else 0
self.assertAlmostEquals(10.16, Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, exer_type=OptionExerciseType.EUROPEAN) \
.run_model(model=OptionModel.MONTE_CARLO, num_steps=num_steps, random_seed=12345)[OptionMeasure.VALUE], delta=0.01)
self.assertAlmostEquals(23.39, Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, yield_=div_monthly_fn, exer_type=OptionExerciseType.EUROPEAN) \
.run_model(model=OptionModel.MONTE_CARLO, num_steps=num_steps, random_seed=12345)[OptionMeasure.VALUE], delta=0.01)
self.assertAlmostEquals(1.40, Option(opt_type=OptionType.CALL, spot0=90, strike=100, mat=mat,
vol=0.35, riskless_rate=0.10, yield_=div_monthly_fn, exer_type=OptionExerciseType.EUROPEAN) \
.run_model(model=OptionModel.MONTE_CARLO, num_steps=num_steps, random_seed=12345)[OptionMeasure.VALUE], delta=0.01)
greek_put_opt_results = Option(opt_type=OptionType.PUT, spot0=90, strike=100, mat=3.0 / 12,
vol=0.35, riskless_rate=0.10, yield_=0.05, exer_type=OptionExerciseType.EUROPEAN) \
.run_model(model=OptionModel.MONTE_CARLO, random_seed=12345)
self.assertAlmostEqual(-0.6442,
greek_put_opt_results[OptionMeasure.DELTA],
delta=0.0001)
self.assertAlmostEqual(-6.7226,
greek_put_opt_results[OptionMeasure.THETA],
delta=0.0001)
self.assertAlmostEqual(-17.0219,
greek_put_opt_results[OptionMeasure.RHO],
delta=0.0001)
self.assertAlmostEqual(+15.2718,
greek_put_opt_results[OptionMeasure.VEGA],
delta=0.0001)
self.assertAlmostEqual(+0.0254,
greek_put_opt_results[OptionMeasure.GAMMA],
delta=0.0001)
greek_call_opt_results = Option(opt_type=OptionType.CALL, spot0=90, strike=100, mat=3.0 / 12,
vol=0.35, riskless_rate=0.10, yield_=0.05, exer_type=OptionExerciseType.AMERICAN) \
.run_model(model=OptionModel.MONTE_CARLO, random_seed=12345)
self.assertAlmostEqual(+0.4217,
greek_call_opt_results[OptionMeasure.DELTA],
delta=0.0001)
self.assertAlmostEqual(+60.4526,
greek_call_opt_results[OptionMeasure.THETA],
delta=0.0001)
self.assertAlmostEqual(+6.4028,
greek_call_opt_results[OptionMeasure.RHO],
delta=0.0001)
self.assertAlmostEqual(-55.4468,
greek_call_opt_results[OptionMeasure.VEGA],
delta=0.0001)
self.assertAlmostEqual(+0.0163,
greek_call_opt_results[OptionMeasure.GAMMA],
delta=0.0001)
def test_black_scholes_valuation(self):
self.assertAlmostEquals(
13.70,
Option(opt_type=OptionType.CALL,
spot0=100,
strike=95,
mat=3.0 / 12,
vol=0.50,
riskless_rate=0.10,
exer_type=OptionExerciseType.EUROPEAN).run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.VALUE],
delta=0.01)
self.assertAlmostEquals(
10.03,
Option(opt_type=OptionType.PUT,
spot0=90,
strike=100,
mat=1.0 / 12,
vol=0.35,
riskless_rate=0.10,
exer_type=OptionExerciseType.EUROPEAN).run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.VALUE],
delta=0.01)
self.assertAlmostEquals(
3.45,
Option(opt_type=OptionType.CALL,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
exer_type=OptionExerciseType.EUROPEAN).run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.VALUE],
delta=0.01)
self.assertAlmostEquals(
3.06,
Option(opt_type=OptionType.CALL,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.05,
exer_type=OptionExerciseType.EUROPEAN).run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.VALUE],
delta=0.01)
greek_call_opt = Option(opt_type=OptionType.CALL,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.05,
exer_type=OptionExerciseType.EUROPEAN)
greek_put_opt = Option(opt_type=OptionType.PUT,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.05,
exer_type=OptionExerciseType.EUROPEAN)
self.assertAlmostEquals(
+0.3248,
greek_call_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.DELTA],
delta=0.0001)
self.assertAlmostEquals(
-0.6628,
greek_put_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.DELTA],
delta=0.0001)
self.assertAlmostEquals(
-12.4048,
greek_call_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.THETA],
delta=0.0001)
self.assertAlmostEquals(
-7.0958,
greek_put_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.THETA],
delta=0.0001)
self.assertAlmostEquals(
+6.5405,
greek_call_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.RHO],
delta=0.0001)
self.assertAlmostEquals(
-17.8422,
greek_put_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.RHO],
delta=0.0001)
self.assertAlmostEquals(
+16.0714,
greek_call_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.VEGA],
delta=0.0001)
self.assertAlmostEquals(
+16.0714,
greek_put_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.VEGA],
delta=0.0001)
self.assertAlmostEquals(
+0.0227,
greek_call_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.GAMMA],
delta=0.0001)
self.assertAlmostEquals(
+0.0227,
greek_put_opt.run_model(
model=OptionModel.BLACK_SCHOLES)[OptionMeasure.GAMMA],
delta=0.0001)
def test_binomial_tree_valuation(self):
self.assertAlmostEquals(
10.32,
Option(opt_type=OptionType.PUT,
spot0=90,
strike=100,
mat=1.0 / 12,
vol=0.35,
riskless_rate=0.10).run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
self.assertAlmostEquals(
10.01,
Option(opt_type=OptionType.PUT,
spot0=90,
strike=100,
mat=1.0 / 12,
vol=0.35,
riskless_rate=0.10,
exer_type=OptionExerciseType.EUROPEAN).run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
self.assertAlmostEquals(
10.40,
Option(opt_type=OptionType.PUT,
spot0=90,
strike=100,
mat=1.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.025).run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
self.assertAlmostEquals(
3.19,
Option(opt_type=OptionType.CALL,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.025).run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VALUE],
delta=0.01)
greek_call_opt = Option(opt_type=OptionType.CALL,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.05,
exer_type=OptionExerciseType.AMERICAN)
greek_put_opt = Option(opt_type=OptionType.PUT,
spot0=90,
strike=100,
mat=3.0 / 12,
vol=0.35,
riskless_rate=0.10,
yield_=0.05,
exer_type=OptionExerciseType.AMERICAN)
self.assertAlmostEquals(
+0.3205,
greek_call_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.DELTA],
delta=0.0001)
self.assertAlmostEquals(
-0.6973,
greek_put_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.DELTA],
delta=0.0001)
self.assertAlmostEquals(
-12.6706,
greek_call_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.THETA],
delta=0.0001)
self.assertAlmostEquals(
-8.3641,
greek_put_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.THETA],
delta=0.0001)
self.assertAlmostEquals(
+6.4561,
greek_call_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.RHO],
delta=0.0001)
self.assertAlmostEquals(
-10.9031,
greek_put_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.RHO],
delta=0.0001)
self.assertAlmostEquals(
+14.1128,
greek_call_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VEGA],
delta=0.0001)
self.assertAlmostEquals(
+13.7077,
greek_put_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.VEGA],
delta=0.0001)
self.assertAlmostEquals(
+0.0268,
greek_call_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.GAMMA],
delta=0.0001)
self.assertAlmostEquals(
+0.0178,
greek_put_opt.run_model(
model=OptionModel.BINOMIAL_TREE)[OptionMeasure.GAMMA],
delta=0.0001)
