def bsm_geometric_asian_price(self,
otype=1,
strike=110,
marturity=1,
num_step=4):
m = num_step
n = m + 1
sigma = self.vol_ratio
S0 = self.init_state
T = marturity
K = strike
r = self.drift_ratio
mu = r - 0.5 * sigma**2
mu_hat = 0.5 * mu
sigma_hat_s = sigma**2 * (2 * m + 1) / (6 * (m + 1))
r_hat = mu_hat + 0.5 * sigma_hat_s
sigma_hat = np.sqrt(sigma_hat_s)
if otype == 1:
option = VanillaOption(otype=1,
strike=K,
maturity=T,
market_price=15.)
return np.exp([
(r_hat - r) * T
]) * Gbm_1d(init_state=S0, drift_ratio=r_hat,
vol_ratio=sigma_hat).bsm_price(option)
else:
option = VanillaOption(otype=-1,
strike=K,
maturity=T,
market_price=15.)
return np.exp([
(r_hat - r) * T
]) * Gbm_1d(init_state=S0, drift_ratio=r_hat,
vol_ratio=sigma_hat).bsm_price(option)
def bsm_geometric_asian_price(
self,
otype=1,
strike=110,
maturity=1,
num_step=4 #partition number
):
s0 = self.init_state
sigma = self.vol_ratio
r = self.drift_ratio
n = num_step
#NOTE: This price assumes a uniform partition time steps, for ease of coding.
#Compute mu-hat
#mu-hat = mu/2 (we are assuming uniform partition as stated above)
mu = r - 0.5 * (sigma**2)
mu_hat = (mu / 2)
#Compute sigma-hat
#Sigma-hat^2 = (sigma^2 * (2m + 1))/(6*(m+1)) where m is the number of steps.
#Recall that the vol_ratio is sigma, not sigma^2. Thus we need both.
sigma_hat_squared = ((sigma**2) * ((2 * n) + 1)) / (6 * (n + 1))
sigma_hat = sigma_hat_squared**0.5
#With mu-hat and sigma-hat calculated, we can find r-hat.
r_hat = mu_hat + (0.5 * sigma_hat_squared)
#Create a separate GBM variable to store the new sigma and r, for the sake of
#computing the price.
gao_internal_gbm = Gbm_1d(init_state=s0,
drift_ratio=r_hat,
vol_ratio=sigma_hat)
return np.exp((r_hat - r) * maturity) * gao_internal_gbm.bsm_price(
VanillaOption(otype, strike, maturity))
# In[5]:
if __name__ == '__main__':
'''============
test:
plot Gbm paths
=============='''
gbm1 = Gbm_1d(init_state=10., drift_ratio=.03, vol_ratio=.25)
grid = np.linspace(0, 1, 100)
plt.figure()
plt.title('test Gbm_1d.euler')
plt.xlabel('time')
plt.ylabel('state')
for i in range(5):
xh = gbm1.euler(grid)
plt.plot(grid, xh)
'''===============
Test bsm_price
================='''
gbm1 = Gbm_1d(init_state=100., drift_ratio=.0475, vol_ratio=.2)
option1 = VanillaOption(otype=1,
strike=110.,
maturity=1.,
market_price=15.)
print('>>>>>>>>>>call value is ' + str(gbm1.bsm_price(option1)))
option2 = VanillaOption(otype=-1)
print('>>>>>>>>>>put value is ' + str(gbm1.bsm_price(option2)))