def objective(chain, x):
T = chain.Time_to_exp / 252
Rf = chain.Rf
c_total = len(chain.Call_Strike)
p_total = len(chain.Put_Strike)
w = x[0]
F1 = x[1]
sigma1 = x[2]
F2 = x[3]
sigma2 = x[4]
c_market = (chain.Call_Ask + chain.Call_Bid) / 2
p_market = (chain.Put_Ask + chain.Put_Bid) / 2
S1 = F1 * math.exp(-1 * Rf * T)
S2 = F2 * math.exp(-1 * Rf * T)
c_the =np.array([w*(american_option('c',S1,chain.Call_Dummy_Strike[i],T,Rf,sigma1)[0])\
+ (1-w)*(american_option('c',S2,chain.Call_Dummy_Strike[i],T,Rf,sigma2)[0])\
for i in range(c_total)])
p_the = np.array([w*(american_option('p',S1,chain.Put_Dummy_Strike[i],T,Rf,sigma1)[0])\
+ (1-w)*(american_option('p',S2,chain.Put_Dummy_Strike[i],T,Rf,sigma2)[0])\
for i in range(p_total)])
c_sse = np.sum((c_market - c_the)**2)
p_sse = np.sum((p_market - p_the)**2)
return c_sse + p_sse
def __init__(self, asset, final_dataset):
self.Name = asset
self.lot_size = 100
setattr(self, "Time_to_exp", days_to_expiry)
asset_df = final_dataset[final_dataset['Group'] == asset]
asset_df["Dummy_Strike"] = asset_df.loc[:, "Strike"]
filtered = asset_df.groupby('Strike')['Strike'].filter(
lambda x: len(x) == 2)
not_common = asset_df[~asset_df['Strike'].isin(filtered)]
records = not_common.to_dict('records')
to_add = list()
for record in records:
new = record.copy()
if record["Option_type"] == "CALL":
for keys, value in new.items():
if type(value) == str:
if keys in ["Symbol", "Description"]:
new[keys] = "Dummy"
if keys == "Option_type":
new[keys] = "PUT"
else:
if keys in ["Bid", "Ask"]:
option_type = 'p'
fs = new['stock_Last']
x = new['Strike']
t = self.Time_to_exp / 252
r = rf_value
v = new['Impl Vol']
new[keys] = american_option(
option_type, fs, x, t, r, v)[0]
if keys[:5] != "stock" and (keys not in [
"Strike", "Dummy_Strike", "Ask", "Bid",
"Impl Vol"
]):
new[keys] = 0
new["Strike"] = -1000000
else:
for keys, value in new.items():
if type(value) == str:
if keys in ["Symbol", "Description"]:
new[keys] = "Dummy"
if keys == "Option_type":
new[keys] = "CALL"
else:
if keys in ["Bid", "Ask"]:
option_type = 'p'
fs = new['stock_Last']
x = new['Strike']
t = self.Time_to_exp / 252
r = rf_value
v = new['Impl Vol']
new[keys] = american_option(
option_type, fs, x, t, r, v)[0]
if keys[:5] != "stock" and (keys not in [
"Strike", "Dummy_Strike", "Ask", "Bid",
"Impl Vol"
]):
new[keys] = 0
new["Strike"] = 1000000
to_add.append(new)
df_dummy_options = pd.DataFrame(to_add)
asset_df = asset_df.append(df_dummy_options)
asset_df = asset_df.sort_values(by=['Option_type', 'Dummy_Strike'])
greeks = ["Delta", "Gamma", "Theta", "Vega", "Rho"]
for greek in greeks:
setattr(self, "Var_" + greek, np.std(asset_df[greek].values))
self.call_df = asset_df[asset_df['Option_type'] == "CALL"]
self.put_df = asset_df[asset_df['Option_type'] == "PUT"]
cols = [
"Bid", "Ask", "Last", "Delta", "Gamma", "Theta", "Vega", "Rho",
"Impl Vol", "Strike", "Dummy_Strike"
]
for col in cols:
setattr(self, "Call_" + col, self.call_df[col].values)
setattr(self, "Put_" + col, self.put_df[col].values)
setattr(self, "Call_total", len(self.Call_Strike))
setattr(self, "Put_total", len(self.Put_Strike))
setattr(self, "Stock_Last", asset_df["stock_Last"].iloc[0])
setattr(self, "Description", asset_df["stock_Description"].iloc[0])
setattr(self, "Stock_Volt", asset_df["stock_Impl_Vol"].iloc[0])
std = self.Stock_Last * (self.Stock_Volt *
((self.Time_to_exp / 252)**0.5))
self.sigma = std
self.Rf = rf_value
vol_day = (self.Stock_Volt) * math.sqrt(1 / 252)
ln_S_0 = math.log(self.Stock_Last)
rt = self.Rf * (self.Time_to_exp / 252)
s_term = -0.5 * (vol_day**2) * (self.Time_to_exp)
mu_n = ln_S_0 + rt + s_term
sigma_n = vol_day * math.sqrt(self.Time_to_exp)
s = sigma_n
scale = math.exp(mu_n)
self.lognormal_s = s
self.lognormal_scale = scale
S = self.Stock_Last
#self.S_space = np.linspace(self.Stock_Last - 4*self.sigma, self.Stock_Last + 4*self.sigma, 20)
self.S_space = np.arange(S - 0.5 * S, S + 0.5 * S, 0.1)
self.S_density = stats.lognorm.pdf(self.S_space, s, loc=0, scale=scale)
## for optimization
variables = [
"Ask", "Bid", "Strike", "Delta", "Gamma", "Theta", "Vega", "Rho"
]
for variable in variables:
cal_cont = getattr(self, "Call_" + variable)
put_cont = getattr(self, "Put_" + variable)
array = np.hstack((cal_cont[:, np.newaxis], put_cont[:,
np.newaxis]))
setattr(self, variable + "_List",
[[array[i, j] for j in range(array.shape[1])]
for i in range(array.shape[0])])
from american_option_pricing import american_option option_type = 'c' fs = 98.95 x = 104 t = 9 / 252 r = 0.103 / 100 b = 0 v = 0.2793 ans = american_option(option_type, fs, x, t, r, v) #actual = 5.75 #print(actual) print((0.62 + 0.35) / 2) print(ans[0])