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 plot_model_vs_market_data(market_data, res, approximator):
expiry = market_data["Expiry"].iloc[0]
tenor = market_data["Tenor"].iloc[0]
curve_rate = market_data["Rate"].iloc[0]
kappa = 0.03
initial_curve = get_mock_yield_curve_const(rate=curve_rate)
swap_pricer = SwapPricer(initial_curve, kappa)
swaption_pricer = SwaptionPricer(swap_pricer)
swap = Swap(expiry, expiry + tenor, frequency=0.5)
atm_swap_price = swap_pricer.price(swap, 0, 0, 0)
sigma_r = LinearLocalVolatility.from_const(int(swap.TN), res.x[0],
curve_rate, res.x[1])
xy_calculator = approximator(grid_size, swap_pricer, sigma_r, swap)
aprox_type = str(xy_calculator)
integration_approx = DiscreteParameterAveraging(grid_size, swap_pricer,
sigma_r, swap,
xy_calculator)
lambda_avg, beta_avg = integration_approx.calculate_average_param()
moneyness_ls = []
market_implied_vola_ls = []
black_implied_vola_ls = []
swaption_value_fd_ls = []
for row_id, inp_data in market_data.iterrows():
expiry = inp_data["Expiry"]
coupon = inp_data["moneyness"] + atm_swap_price
if coupon < 0:
continue
swaption = Swaption(expiry, coupon, swap)
market_implied_vola_ls.append(inp_data["implied black vola"])
swaption_value_fd = price_fd(swaption_pricer, sigma_r, swaption)
swaption_value_fd_ls.append(swaption_value_fd)
swaption_value, black_implied_vola = lognormalimpliedvola(
swaption, swap_pricer, lambda_avg, beta_avg)
black_implied_vola_ls.append(black_implied_vola)
print(swaption_value_fd_ls)
moneyness_ls.append(inp_data["moneyness"])
fig = plt.figure()
plt.plot(moneyness_ls, market_implied_vola_ls, "g-x", label="Market data")
plt.plot(moneyness_ls,
black_implied_vola_ls,
"r-x",
label="Approximate solution")
plt.plot(moneyness_ls,
swaption_value_fd_ls,
"b-x",
label="Finite Difference repricing")
plt.legend()
return fig
def minimize_func(x):
print("run minimize")
lambda_param = x[0]
beta_param = x[1]
sigma_r = LinearLocalVolatility.from_const(int(swap.TN), lambda_param,
curve_rate, beta_param)
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()
error = 0
for row_id, inp_data in market_data.iterrows():
expiry = inp_data["Expiry"]
coupon = inp_data["moneyness"] + atm_swap_price
swaption = Swaption(expiry, coupon, swap)
market_implied_vola = inp_data["implied black vola"]
swaption_value, black_implied_vola = lognormalimpliedvola(
swaption, swap_pricer, lambda_avg, beta_avg)
error += (black_implied_vola - market_implied_vola)**2
return error
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)