def price_Loss(beta, df, coupons_cf, streak_data,
rho=0.2, weight_scheme='rev_span', tau=None):
'''
Parameters
---------------
beta: array-like
Nelson-Siegel's vector of parameters
df: Pandas Dataframe
Dataframe of bonds' data
coupons_cf: Pandas Dataframe
Dataframe containing bonds' payment cash flows
streak_data: Pandas Dataframe
Dataframe containing bonds' payment calendar
rho: float from 0 to 1, default 0.2
Weight of oldest deal - only used in
'vol_time', 'full_vol_time', 'volume_kzt', 'complex_volume' weight schemes
weight_scheme: str, default 'no_weight'
weight function used to weight deals
tau: float, default None
Use this parameter if only you do 3-variablie minimization.
Parameter is only used in grid search optimization
'''
#if tau is given, then beta is array
if tau is not None:
assert beta.shape[0] == 3
beta = np.append(beta, [tau])
ind = df.index
Price = (D(streak_data[ind], beta) * coupons_cf[ind]).sum().values
Loss = np.linalg.norm(weight(beta, df=df, rho=rho, weight_scheme=weight_scheme) *
(df.stand_price.values - Price))
return Loss
def naive_yield_Loss(beta, df, coupons_cf, streak_data, rho=0.2,
weight_scheme='no_weight', tau=None):
'''
Parameters
---------------
beta: array-like
Nelson-Siegel's vector of parameters
df: Pandas Dataframe
Dataframe of bonds' data
coupons_cf: Pandas Dataframe
Dataframe containing bonds' payment cash flows
streak_data: Pandas Dataframe
Dataframe containing bonds' payment calendar
rho: float from 0 to 1, default 0.2
Weight of oldest deal - only used in
'vol_time', 'full_vol_time', 'volume_kzt', 'complex_volume' weight schemes
weight_scheme: str, default 'no_weight'
weight function used to weight deals
tau: float, default None
Use this parameter if only you do 3-variablie minimization.
Parameter is only used in grid search optimization
'''
#if tau is given, then beta is array
if tau is not None:
assert beta.shape[0] == 3
beta = np.append(beta, [tau])
#estimating price
#calculatting Loss
W = weight(beta, df=df, rho=rho, weight_scheme=weight_scheme)
Loss = (W * np.square(df.ytm.values - Z(df.span / 365, beta))).sum()
return Loss
def grad(beta,
data,
coupons_cf,
streak_data,
rho=0.2,
weight_scheme='no_weight'):
m = data['span']
grad_z = []
teta_m = m / beta[3]
grad_z.append(1)
grad_z.append((1 / teta_m) * (1 - np.exp(-teta_m)))
grad_z.append((1 / teta_m) * (1 - np.exp(-teta_m)) - np.exp(-teta_m))
teta_m_der = m / (beta[3]**2)
grad_z.append(
((beta[1] + beta[2]) *
((1 / m) * (1 - np.exp(-teta_m)) - np.exp(-teta_m) / beta[3]) -
beta[2] * np.exp(-teta_m) * teta_m_der))
#calculatting Loss
W = weight(beta, df=data, rho=rho, weight_scheme=weight_scheme)
non_grad = W * (data['ytm'] / 100 - Z(m, beta))
loss_grad = np.zeros_like(beta)
for i in range(beta.shape[0]):
loss_grad[i] = -2 * (non_grad * grad_z[i]).sum()
return loss_grad
def yield_Loss(beta,
df,
coupons_cf,
streak_data,
rho=0.2,
weight_scheme='no_weight',
tau=None):
'''
Parameters
---------------
beta: array-like
Nelson-Siegel's vector of parameters
df: Pandas Dataframe
Dataframe of bonds' data
coupons_cf: Pandas Dataframe
Dataframe containing bonds' payment cash flows
streak_data: Pandas Dataframe
Dataframe containing bonds' payment calendar
rho: float from 0 to 1, default 0.2
Weight of oldest deal - only used in
'vol_time', 'full_vol_time', 'volume_kzt', 'complex_volume' weight schemes
weight_scheme: str, default 'no_weight'
weight function used to weight deals
tau: float, default None
Use this parameter if only you do 3-variablie minimization.
Parameter is only used in grid search optimization
'''
#if tau is given, then beta is array
if tau is not None:
assert beta.shape[0] == 3
beta = np.append(beta, [tau])
ind = df.index
#estimating price
Price = (D(streak_data[ind], beta) * coupons_cf[ind]).sum().values
if (Price <= 0).any():
Loss = 1e100
else:
ytm_hat = np.array([
newton_estimation(df.iloc[i],
Price[i],
coupons_cf,
streak_data,
maxiter=200) for i in range(df.shape[0])
])
#calculatting Loss
W = weight(beta, df=df, rho=rho, weight_scheme=weight_scheme)
Loss = (W * np.square(df['ytm'].values - ytm_hat)).sum()
return Loss
#Parameters bounds for constraint optimization
bounds = ((0, 1), (None, None), (None, None), (CONFIG.TETA_MIN, CONFIG.TETA_MAX))
#Maturity limit for Zero-curve plot
longest_maturity_year = max([max_deal_span, 20])
theor_maturities = np.linspace(0.001, longest_maturity_year, 10000)
options = {'maxiter': 500, 'eps': 9e-5, 'disp': True}
#Tuple of arguments for loss function
loss_args = (filtered_data, coupons_cf, streak_data, CONFIG.RHO, CONFIG.WEIGHT_SCHEME)
#defining loss
loss = yield_Loss
filtered_data['weight'] = weight([1, 1, 1, 1], filtered_data, CONFIG.WEIGHT_SCHEME)
###### OPTIMIZATION
print('start optimization\n')
res_ = iter_minimizer(Loss=loss, beta_init=x0,
loss_args=loss_args, method='SLSQP',
bounds=bounds,
constraints=constr,
max_deal_span=max_deal_span, options=options)
beta_best = res_.x
print('end optimization\n')
### Showing results of work
draw(beta_best, filtered_data, theor_maturities, f'{CONFIG.SETTLE_DATE:%d.%m.%Y}',
longest_maturity_year, draw_points=True,
def draw(beta,
df,
theor_maturities,
title_date,
longest_maturity_year,
weight_scheme=None,
ax=None,
draw_points=True,
label=None,
shift=False,
**kwargs):
'''
Drawing spot curve based on beta
Parameters
------------
beta: list-like
Should be length of 4. Nelson-Siegel's vector of parameters
df: Pandas Dataframe
Dataframe of bonds' data
theor_maturities: list-like
Vector of maturities
title_date: str or datetime
Settle date of the curve's construction
longest_maturity_year: int
Maximum tenor on which plot will be drawn
weight_scheme: 'str', default: None
Weights of deals
ax: Matplotlib Axes, default: None
draw_points: bool
Whether to draw deals' ytm on plot or not
label: str, default: None
shift: bool, default: False
If shift true transforms spot rate curve from discrete to continuous
'''
#defining zero curbe
beta = beta.copy()
spot_rates = spot_nelson(theor_maturities, beta)
if shift:
spot_rates = (np.exp(spot_rates) - 1)
#setting axes
if ax is None:
fig, ax = plt.subplots(figsize=(15, 10))
if label is None:
beta[:3] *= 100
label = f'{beta.round(2)}'
ax.plot(theor_maturities, spot_rates, label=label, **kwargs)
#draw scatterplot of deals or not?
if draw_points:
y_scatter = df['ytm'].values
x_scatter = df['span'].values / 365
#size of points; depends on weight of transaction
s = (weight(beta, df, weight_scheme=weight_scheme) /
weight(beta, df, weight_scheme=weight_scheme).sum())
ax.scatter(x_scatter,
y_scatter,
s=s * 15 * 1e3,
facecolors='none',
edgecolors='grey',
alpha=0.9)
#setting labels, ticks, legend and title
ax.set_title(f'Curves at {title_date} for {df.shape[0]} deals')
ax.set_ylabel('%')
ax.set_xlabel('Tenor in years')
ax.set_xticks(np.arange(0, longest_maturity_year + 1, 1))
ax.legend()