def test_heston_pricer(self):
trade_date = date(2011, 1, 24)
spot = 1290.58
# option definition
options = ds.option_quotes_template().reindex(index=range(2))
options[nm.OPTION_TYPE] = ['C', 'P']
options[nm.STRIKE] = [1290, 1290]
options[nm.EXPIRY_DATE] = [date(2015, 1, 1), date(2015, 1, 1)]
options[nm.SPOT] = [spot] * 2
# interest rate and dividend yield
rates = ds.riskfree_dividend_template().reindex(
index=[date(2011, 3, 16), date(2013, 3, 16), date(2015, 3, 16)])
rates[nm.DIVIDEND_YIELD] = [.021, .023, .024]
rates[nm.INTEREST_RATE] = [.010, .015, .019]
# heston model
heston_params = dict(v0=0.051965,
kappa=0.977314, theta=0.102573,
sigma=0.987796, rho=-0.747033
)
results = heston_pricer(trade_date, options,
heston_params, rates, spot=1290.58)
price_call = results[nm.PRICE][0]
price_put = results[nm.PRICE][1]
self.assertAlmostEqual(price_call, 194.6, 1)
self.assertAlmostEqual(price_put, 218.9, 1)
def test_heston_pricer(self):
trade_date = date(2011, 1, 24)
spot = 1290.58
# option definition
options = ds.option_quotes_template().reindex(index=range(2))
options[nm.OPTION_TYPE] = ['C', 'P']
options[nm.STRIKE] = [1290, 1290]
options[nm.EXPIRY_DATE] = [date(2015, 1, 1), date(2015, 1, 1)]
options[nm.SPOT] = [spot] * 2
# interest rate and dividend yield
rates = ds.riskfree_dividend_template().reindex(
index=[date(2011, 3, 16), date(2013, 3, 16), date(2015, 3, 16)])
rates[nm.DIVIDEND_YIELD] = [.021, .023, .024]
rates[nm.INTEREST_RATE] = [.010, .015, .019]
# heston model
heston_params = dict(v0=0.051965,
kappa=0.977314, theta=0.102573,
sigma=0.987796, rho=-0.747033
)
results = heston_pricer(trade_date, options,
heston_params, rates, spot=1290.58)
price_call = results[nm.PRICE][0]
price_put = results[nm.PRICE][1]
self.assertAlmostEqual(price_call, 194.6, 1)
self.assertAlmostEqual(price_put, 218.9, 1)
def options_to_rates(options, t_min=1. / 12., n_min=6):
"""
Extract implied risk-free rates and dividend yield from
standard European option quote file.
ignore data:
- with time to maturity < tMin (in fraction of years)
- with fewer than nMin quotes per maturity date
Parameters
----------
t_min: float (default: 1 month)
Minimum time to maturity in fraction of years
n_min: int (default: 6)
minimum number of quotes per maturity date
"""
grouped = options.groupby(nm.EXPIRY_DATE)
expiry_dates = []
implied_interest_rates = []
implied_dividend_yields = []
for spec, group in grouped:
# implied vol for this type/expiry group
index = group.index
trade_date = group[nm.TRADE_DATE][index[0]]
expiry_date = group[nm.EXPIRY_DATE][index[0]]
spot = group[nm.SPOT][index[0]]
days_to_expiry = (expiry_date - trade_date).days
time_to_maturity = days_to_expiry / 365.0
# exclude groups with too short time to maturity
if time_to_maturity < t_min:
continue
# extract the put and call quotes
calls = group[group[nm.OPTION_TYPE] == nm.CALL_OPTION]
puts = group[group[nm.OPTION_TYPE] == nm.PUT_OPTION]
# exclude groups with too few data points
if (len(calls) < n_min) | (len(puts) < n_min):
continue
# calculate forward, implied interest rate and implied div. yield
call_premium = DataFrame(
(calls[nm.PRICE_BID] + calls[nm.PRICE_ASK]) / 2.,
columns=[CALL_PREMIUM])
call_premium.index = np.array(calls[nm.STRIKE])
put_premium = DataFrame((puts[nm.PRICE_BID] + puts[nm.PRICE_ASK]) / 2.,
columns=[PUT_PREMIUM])
put_premium.index = np.array(puts[nm.STRIKE])
# use 'inner' join because some strikes are not quoted for C and P
all_quotes = call_premium.join(put_premium, how='inner')
all_quotes[nm.STRIKE] = all_quotes.index
all_quotes['C-P'] = all_quotes[CALL_PREMIUM] - all_quotes[PUT_PREMIUM]
y = np.array(all_quotes['C-P'])
x = np.array(all_quotes[nm.STRIKE])
A = np.vstack([x, np.ones(len(x))]).T
a_1, a_0 = np.linalg.lstsq(A, y)[0]
# intercept is last coef
interest_rate = -np.log(-a_1) / time_to_maturity
dividend_yield = np.log(spot / a_0) / time_to_maturity
implied_interest_rates.append(interest_rate)
implied_dividend_yields.append(dividend_yield)
expiry_dates.append(expiry_date)
rates = ds.riskfree_dividend_template().reindex(index=expiry_dates)
rates[nm.INTEREST_RATE] = implied_interest_rates
rates[nm.DIVIDEND_YIELD] = implied_dividend_yields
return rates
def test_riskfree_dividend(self):
x = df.riskfree_dividend_template().reindex(
index=[date(2000, 1, 1) + timedelta(days=k) for k in range(10)])
x[nm.DIVIDEND_YIELD] = np.linspace(.01, .03, 10)
x[nm.INTEREST_RATE] = np.linspace(.02, .04, 10)
self.assertTrue(True)
def test_riskfree_dividend(self):
x = df.riskfree_dividend_template().reindex(
index=[date(2000,1,1)+timedelta(days=k) for k in range(10)])
x[nm.DIVIDEND_YIELD] = np.linspace(.01, .03, 10)
x[nm.INTEREST_RATE] = np.linspace(.02, .04, 10)
self.assertTrue(True)
def options_to_rates(options, t_min=1./12., n_min=6):
"""
Extract implied risk-free rates and dividend yield from
standard European option quote file.
ignore data:
- with time to maturity < tMin (in fraction of years)
- with fewer than nMin quotes per maturity date
Parameters
----------
t_min: float (default: 1 month)
Minimum time to maturity in fraction of years
n_min: int (default: 6)
minimum number of quotes per maturity date
"""
grouped = options.groupby(nm.EXPIRY_DATE)
expiry_dates = []
implied_interest_rates = []
implied_dividend_yields = []
for spec, group in grouped:
# implied vol for this type/expiry group
index = group.index
trade_date = group[nm.TRADE_DATE][index[0]]
expiry_date = group[nm.EXPIRY_DATE][index[0]]
spot = group[nm.SPOT][index[0]]
days_to_expiry = (expiry_date-trade_date).days
time_to_maturity = days_to_expiry/365.0
# exclude groups with too short time to maturity
if time_to_maturity < t_min:
continue
# extract the put and call quotes
calls = group[group[nm.OPTION_TYPE] == nm.CALL_OPTION]
puts = group[group[nm.OPTION_TYPE] == nm.PUT_OPTION]
# exclude groups with too few data points
if (len(calls) < n_min) | (len(puts) < n_min):
continue
# calculate forward, implied interest rate and implied div. yield
call_premium = DataFrame(
(calls[nm.PRICE_BID] + calls[nm.PRICE_ASK]) / 2.,
columns=[CALL_PREMIUM])
call_premium.index = np.array(calls[nm.STRIKE])
put_premium = DataFrame(
(puts[nm.PRICE_BID] + puts[nm.PRICE_ASK]) / 2.,
columns=[PUT_PREMIUM])
put_premium.index = np.array(puts[nm.STRIKE])
# use 'inner' join because some strikes are not quoted for C and P
all_quotes = call_premium.join(put_premium, how='inner')
all_quotes[nm.STRIKE] = all_quotes.index
all_quotes['C-P'] = all_quotes[CALL_PREMIUM] - all_quotes[PUT_PREMIUM]
y = np.array(all_quotes['C-P'])
x = np.array(all_quotes[nm.STRIKE])
A = np.vstack([x, np.ones(len(x))]).T
a_1, a_0 = np.linalg.lstsq(A, y)[0]
# intercept is last coef
interest_rate = -np.log(-a_1)/time_to_maturity
dividend_yield = np.log(spot/a_0)/time_to_maturity
implied_interest_rates.append(interest_rate)
implied_dividend_yields.append(dividend_yield)
expiry_dates.append(expiry_date)
rates = ds.riskfree_dividend_template().reindex(index=expiry_dates)
rates[nm.INTEREST_RATE] = implied_interest_rates
rates[nm.DIVIDEND_YIELD] = implied_dividend_yields
return rates