def pricer(self, S0, K, r, T, N, sigma,
is_call=True, div=0., is_eu=False):
model = BinomialCRROption(S0, K, r, T, N,
{"sigma": sigma,
"div": div,
"is_call": is_call,
"is_eu": is_eu})
return model.price()
def _option_valuation_( self, K, sigma, model ):
""" Do valuation based on given model:
Binomial, CRR...
"""
if model.upper() == "CRR":
option = BinomialCRROption(
self.S0, K, self.r, self.T, self.N,
{ "sigma":sigma,
"is_call":self.is_call,
"div": self.div } )
else:
option = BinomialTreeOption(
self.S0, K, self.r, self.T, self.N,
{ "sigma":sigma,
"is_call":self.is_call,
"div": self.div } )
return option.price()
======
This file contains Python codes.
======
"""
""" Price an option by the binomial CRR model """
from BinomialTreeOption import BinomialTreeOption
import math
class BinomialCRROption(BinomialTreeOption):
def _setup_parameters_(self):
self.u = math.exp(self.sigma * math.sqrt(self.dt))
self.d = 1./self.u
self.qu = (math.exp((self.r-self.div)*self.dt) -
self.d)/(self.u-self.d)
self.qd = 1-self.qu
if __name__ == "__main__":
from BinomialCRROption import BinomialCRROption
eu_option = BinomialCRROption(
50, 50, 0.05, 0.5, 2,
{"sigma": 0.3, "is_call": False})
print ("European put: %s" % eu_option.price())
am_option = BinomialCRROption(
50, 50, 0.05, 0.5, 2,
{"sigma": 0.3, "is_call": False, "is_eu": False})
print ("American put: %s" % am_option.price()
import math
class BinomialCRROption(BinomialTreeOption):
def _setup_parameters_(self):
self.u = math.exp(self.sigma * math.sqrt(self.dt))
self.d = 1. / self.u
self.qu = (math.exp(
(self.r - self.div) * self.dt) - self.d) / (self.u - self.d)
self.qd = 1 - self.qu
if __name__ == "__main__":
from BinomialCRROption import BinomialCRROption
eu_option = BinomialCRROption(50, 50, 0.05, 0.5, 2, {
"sigma": 0.3,
"is_call": False
})
print("European put: %s" % eu_option.price())
am_option = BinomialCRROption(50, 50, 0.05, 0.5, 2, {
"sigma": 0.3,
"is_call": False,
"is_eu": False
})
print("American put: %s" % am_option.price())
# ### Leisen-Reimer tree:
# #### Dr. Dietmar Leisen and Matthias Reimer proposed a binomial tree model with the purpose of approximating to the Black-Scholes solution as the number of steps increases. It is known as the Leisen-Reimer (LR) tree, and the nodes do not recombine at every alternate step. It uses an inversion formula to achieve better accuracy during tree transversal. A detailed explanation of the formulas is given in the paper Binomial Models For Option Valuation - Examining And Improving Convergence, March 1995, which is available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=5976.
# In[8]:
""" Price an option by the Leisen-Reimer tree """
