def test_swaption_price():
kappa = 0.03
swaption_expiry = 4
swap_maturity = 5
swap_freq = 0.5
initial_curve = LiborCurve.from_constant_rate(0.06)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
sigma_r = LinearLocalVolatility.from_const(swap_maturity, 0.4, 0.1, 0)
piterbarg_approx = PiterbargExpectationApproximator(sigma_r, swap_pricer)
swap = Swap(swaption_expiry, swap_maturity, swap_freq)
displaced_diffusion = DisplacedDiffusionParameterApproximator(sigma_r, swap_pricer, swap, piterbarg_approx)
coupon = swap_pricer.price(swap, 0, 0, 0)
swaption = Swaption(swaption_expiry, coupon, swap)
b_s = displaced_diffusion.calculate_bs
lambda_s_bar, b_bar = calculate_vola_skew(swaption.expiry, displaced_diffusion.calculate_lambda_square, b_s)
swaption_value, black_implied_vola = lognormalimpliedvola(swaption, swap_pricer, lambda_s_bar, b_bar)
print(lambda_s_bar, b_bar)
print(swaption_value, black_implied_vola)
def test_approx():
kappa = 0.03
initial_curve = LiborCurve.from_constant_rate(0.06)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
sigma_r = LinearLocalVolatility.from_const(15, 0.4, 0.06, 0.2)
swaption_expiry = 4
swap = Swap(swaption_expiry, 5, 0.5)
coupon = swap_pricer.price(swap, 0, 0, 0)
swaption = Swaption(swaption_expiry, coupon, swap)
xyapproximator = RungeKuttaApproxXY
#xyapproximator = PitergargDiscreteXY
for xyapproximator in [RungeKuttaApproxXY, PitergargDiscreteXY]:
for k in [16]:
grid_size = 2**k + 1
#xy_calculator = PitergargDiscreteXY(grid_size, swap_pricer, sigma_r, swap)
xy_calculator = xyapproximator(grid_size, swap_pricer, sigma_r, swap)
integration_approx = DiscreteParameterAveraging(grid_size, swap_pricer, sigma_r, swap, xy_calculator)
lambda_avg, beta_avg = integration_approx.calculate_average_param()
swaption_value, black_implied_vola = lognormalimpliedvola(swaption, swap_pricer, lambda_avg, beta_avg)
print(lambda_avg, beta_avg)
print(swaption_value, black_implied_vola)
def test_runge_kutta_approx():
kappa = 0.3
t = 10
initial_curve = LiborCurve.from_constant_rate(0.06)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
sigma_r = LinearLocalVolatility.from_const(t, 0.4, 0.1, 0)
swap = Swap(4, 5, 0.5)
swap0 = swap_pricer.price(swap, 0, 0, 0)
integration_grid_size = 2*10 + 1
rk_approx = RungeKuttaApproxXY(integration_grid_size, swap_pricer, sigma_r, swap)
res = rk_approx.calculate_xy()
piterbarg_approx = PiterbargExpectationApproximator(sigma_r, swap_pricer)
time_grid = res.t
xbar = []
ybar = []
for t in time_grid:
ybar.append(piterbarg_approx.ybar_formula(t))
xbar.append(piterbarg_approx.xbar_formula(t, ybar[-1], swap, swap0, 0))
print("As")
def test_swap_pricer():
swap = Swap(1, 20, 0.25)
initial_curve = LiborCurve.from_constant_rate(0.04)
swap_pricer = SwapPricer(initial_curve, kappa=0.2)
price = swap_pricer.price(swap, 0, 0, 0)
print("pas")
def test_forward_rate_pricer_from_constant_curve():
bond = Bond(10)
initial_curve = LiborCurve.from_constant_rate(0.04)
bond_pricer = BondPricer(initial_curve, 0.2)
expected_price = bond_pricer.price(bond, 0, 0, 0)
actual_price = bond_pricer.calculate_price_from_forward(bond)
np.testing.assert_approx_equal(expected_price, actual_price)
def test_bond_pricer():
rate = 0.04
maturity = 5
bond = Bond(maturity)
initial_curve = LiborCurve.from_constant_rate(rate)
bond_pricer = BondPricer(initial_curve, 0.2)
actual_price = bond_pricer.price(bond, x=0, y=0, t=0)
expected_price = np.exp(-rate * maturity)
np.testing.assert_approx_equal(actual_price, expected_price)
def test_forward_rate_pricer_from_file():
bond = Bond(10)
tmp_file = r"C:\Users\d80084\Google Drive\01oxford\7 Thesis\code\quasigaussian\data\market_data\libor_curve\usd_libor\sofr_curve.csv"
initial_curve = LiborCurve.from_file(tmp_file, "2013-05-20")
bond_pricer = BondPricer(initial_curve, 0.2)
expected_price = bond_pricer.price(bond, 0, 0, 0)
actual_price = bond_pricer.calculate_price_from_forward(bond)
np.testing.assert_approx_equal(expected_price, actual_price)
def test_piterbarg_y_bar():
kappa = 0.001
t = 15
initial_curve = LiborCurve.from_constant_rate(0.06)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
sigma_r = LinearLocalVolatility.from_const(t, 0.1, 0.1, 0)
piterbarg_approx = PiterbargExpectationApproximator(sigma_r, swap_pricer)
y_bar_actual = piterbarg_approx.calculate_ybar(t)
y_bar_expected = np.exp(-2*kappa*t)*(np.exp(2*kappa*t) - 1)/(2*kappa)*0.0001
np.testing.assert_approx_equal(y_bar_actual, y_bar_expected)
def test_linear_local_volatility_approximation():
kappa = 0.001
t = 15
initial_curve = LiborCurve.from_constant_rate(0.06)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
sigma_r = LinearLocalVolatility.from_const(t, 0.1, 0.1, 0)
piterbarg_approx = PiterbargExpectationApproximator(sigma_r, swap_pricer)
swap = Swap(4, 5, 0.5)
displaced_diffusion = DisplacedDiffusionParameterApproximator(sigma_r, swap_pricer, swap, piterbarg_approx)
pass
def test_piterbarg_ksi():
kappa = 0.001
t = 15
initial_curve = LiborCurve.from_constant_rate(0.06)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
sigma_r = LinearLocalVolatility.from_const(t, 0.5, 0.5, 0.2)
piterbarg_approx = PiterbargExpectationApproximator(sigma_r, swap_pricer)
swap = Swap(4, 5, 0.5)
swap_value = swap_pricer.price(swap, 0.01717964, 0.0025, 0.04)
ksi = piterbarg_approx.calculate_ksi(0.04, swap_value, swap)
np.testing.assert_approx_equal(ksi, 0.01717964, significant=4)
def test_black_swaption_pricer():
# see John Hull ex 28.4, page 661
kappa = 0.3
swap = Swap(5, 8, 0.5)
initial_curve = LiborCurve.from_constant_rate(0.06)
bond_pricer = BondPricer(initial_curve, kappa=kappa)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
coupon = 0.062
swaption = Swaption(expiry=5, coupon=coupon, swap=swap)
swaption_pricer = Black76Pricer(lambda_s=0.2,
b_s=1,
swap_pricer=swap_pricer,
bond_pricer=bond_pricer)
swaption_value = 100 * swaption_pricer.black76_price(swaption)
np.testing.assert_approx_equal(swaption_value, 2.07, significant=4)
def test_implied_black_vola():
kappa = 0.3
swap = Swap(5, 8, 0.5)
initial_curve = LiborCurve.from_constant_rate(0.06)
bond_pricer = BondPricer(initial_curve, kappa=kappa)
swap_pricer = SwapPricer(initial_curve, kappa=kappa)
coupon = 0.062
swaption = Swaption(expiry=5, coupon=coupon, swap=swap)
swaption_pricer = Black76Pricer(lambda_s=0.2,
b_s=1,
swap_pricer=swap_pricer,
bond_pricer=bond_pricer)
swaption_value = swaption_pricer.black76_price(swaption)
implied_vola = find_implied_black_vola(swaption_value, swaption,
swap_pricer, bond_pricer)
np.testing.assert_approx_equal(implied_vola, 0.2, significant=4)
def process_bond_fd(input_file):
output_fd = pd.read_hdf(input_file, key="data")
meta_data = pd.read_hdf(input_file, key="metadata").iloc[0]
xmesh = pd.read_hdf(input_file, key="xmesh")
ymesh = pd.read_hdf(input_file, key="ymesh")
xgrid = pd.read_hdf(input_file, key="xgrid")
ugrid = pd.read_hdf(input_file, key="ygrid")
bond = Bond(meta_data["maturity"])
curve = LiborCurve.from_constant_rate(meta_data["curve_rate"])
bond_pricer = BondPricer(curve, meta_data["kappa"])
bond_value = bond_pricer.price(bond, xmesh, ymesh, 0)
#relative_diff = (output_fd - bond_value)/bond_value
analytics_bond = extract_x0_result(bond_value.values,
np.array(xgrid[0].values),
ugrid[0].values)
fd_bond = extract_x0_result(output_fd.values, np.array(xgrid[0].values),
ugrid[0].values)
return fd_bond, analytics_bond, output_fd, bond_value, meta_data, xgrid, ugrid
def get_mock_yield_curve_const(rate=0.04):
return LiborCurve.from_constant_rate(rate)
def get_mock_yield_curve_from_file():
tmp_file = r"C:\Users\d80084\Google Drive\01oxford\7 Thesis\code\quasigaussian\data\market_data\libor_curve\usd_libor\sofr_curve.csv"
initial_curve = LiborCurve.from_file(tmp_file, "2013-05-20")
return initial_curve
def calculate_swaption_prices():
output_path = os.path.join(output_data_raw_approx, date_timestamp,
"result")
output_file = os.path.join(output_path, "swaption_approximation.hdf")
file_path = get_nonexistant_path(output_file)
grid_size = 2**12 + 1
swap_freq = 0.5
curve_rate = 0.06
initial_curve = LiborCurve.from_constant_rate(curve_rate)
kappa_grid = [0.03]
vola_parameters = [(i, curve_rate, j) for i in [0.6, 0.8]
for j in [0.05, 0.2]]
vola_grid_df = pd.DataFrame(vola_parameters,
columns=["lambda", "alpha", "beta"])
vola_grid_df = vola_grid_df.iloc[[0, 3]]
#coupon_grid = [0, +0.0025, -0.0025, +0.005, -0.005, +0.01, -0.01, 0.015, -0.015, 0.02, -0.02, 0.025, -0.025]
XYApproximator = PitergargDiscreteXY
XYApproximator = RungeKuttaApproxXY
swap_ls = [(20, 21)]
coupon_grid = [0, +0.005, -0.005, +0.01, -0.01, 0.015, -0.015]
#vola_grid_df = vola_grid_df.iloc[9:10]
for swap_T0_TN in swap_ls:
print(swap_T0_TN)
T0, TN = swap_T0_TN
for kappa in kappa_grid:
swap_pricer = SwapPricer(initial_curve, kappa)
swap = Swap(T0, TN, 1 / 2)
for index, vola_grid_row in vola_grid_df.iterrows():
sigma_r = LinearLocalVolatility.from_const(
swap.TN, vola_grid_row["lambda"], vola_grid_row["alpha"],
vola_grid_row["beta"])
swap = Swap(T0, TN, swap_freq)
atm_swap_price = swap_pricer.price(swap, 0, 0, 0)
strike_grid = [
atm_swap_price + coupon for coupon in coupon_grid
]
#strike_grid = [0.01, 0.015, 0.02, 0.025, 0.03]
xy_calculator = XYApproximator(grid_size, swap_pricer, sigma_r,
swap)
integration_approx = DiscreteParameterAveraging(
grid_size, swap_pricer, sigma_r, swap, xy_calculator)
lambda_avg, beta_avg = integration_approx.calculate_average_param(
)
for strike in strike_grid:
swaption = Swaption(T0, strike, swap)
swaption_value, black_implied_vola = lognormalimpliedvola(
swaption, swap_pricer, lambda_avg, beta_avg)
output_data = pd.DataFrame({
'expiry': [T0],
"maturity": [TN],
"atm strike":
atm_swap_price,
"swaption_value": [swaption_value],
"kappa": [kappa],
"vola_lambda": [vola_grid_row["lambda"]],
"vola_alpha": [vola_grid_row["alpha"]],
"vola_beta": [vola_grid_row['beta']],
"strike": [strike],
'moneyness': [strike - atm_swap_price],
"curve_rate": [curve_rate],
"implied_black_vola": [black_implied_vola],
'integration_grid': [grid_size],
"xy_approximation": [str(xy_calculator)]
})
try:
all_output_data = pd.read_hdf(file_path, key="data")
except:
all_output_data = pd.DataFrame()
all_output_data = pd.concat([all_output_data, output_data])
all_output_data.to_hdf(file_path, key="data", complevel=9)