def test_deep_otm_put():
strike = 0
fwd = 0.1
expiry = 0.5
vol = 0.005
put = Bachelier(K=strike, F=fwd, T=expiry, vol=vol, is_call=False)
assert (put.price(), put.delta(), put.vega()) == pytest.approx(
(0, 0, 0), abs=ERROR_MAX)
def test_atm_put():
fwd = 0.02
expiry = 2
vol = 0.005
put = Bachelier(K=fwd, F=fwd, T=expiry, vol=vol, is_call=False)
assert (put.price(), put.delta(), put.vega()) == pytest.approx(
(vol * sqrt(expiry / 2 / pi), -0.5, sqrt(expiry / 2 / pi)),
abs=ERROR_MAX)
def test_deep_otm_call():
strike = 0
fwd = -0.1
expiry = 0.5
vol = 0.005
call = Bachelier(K=strike, F=fwd, T=expiry, vol=vol, is_call=True)
assert (call.price(), call.delta(), call.vega()) == pytest.approx(
(0, 0, 0), abs=ERROR_MAX)
def test_atm_call():
fwd = 0.02
expiry = 2
vol = 0.005
call = Bachelier(K=fwd, F=fwd, T=expiry, vol=vol, is_call=True)
assert (call.price(), call.delta(), call.vega()) == pytest.approx(
(vol * sqrt(expiry / 2 / pi), 0.5, sqrt(expiry / 2 / pi)),
abs=ERROR_MAX)
def test_call_put_parity():
strike = 0.02
fwd = 0.03
expiry = 2
vol = 0.005
call = Bachelier(K=strike, F=fwd, T=expiry, vol=vol, is_call=True)
put = Bachelier(K=strike, F=fwd, T=expiry, vol=vol, is_call=False)
assert (call.price() - put.price(), call.delta() - put.delta(),
call.vega() - put.vega()) == pytest.approx((fwd - strike, 1, 0),
abs=ERROR_MAX)
def test_negative_vol():
with pytest.raises(ValueError):
Bachelier(K=0.02, F=0.03, T=1, vol=-0.005, is_call=True)
def test_no_vol_otm_put():
put = Bachelier(K=0.02, F=0.03, T=1, vol=0, is_call=False)
assert (put.price(), put.delta(), put.vega()) == pytest.approx(
(0, 0, 0), abs=ERROR_MAX)
def test_no_vol_otm_call():
call = Bachelier(K=0.04, F=0.03, T=1, vol=0, is_call=True)
assert (call.price(), call.delta(), call.vega()) == pytest.approx(
(0, 0, 0), abs=ERROR_MAX)
def test_expired_itm_put():
put = Bachelier(K=0.04, F=0.03, T=0, vol=0.005, is_call=False)
assert (put.price(), put.delta(), put.vega()) == pytest.approx(
(0.01, -1, 0), abs=ERROR_MAX)
def test_expired_itm_call():
call = Bachelier(K=0.02, F=0.03, T=0, vol=0.005, is_call=True)
assert (call.price(), call.delta(), call.vega()) == pytest.approx(
(0.01, 1, 0), abs=ERROR_MAX)