Simple "Binomial Non-Arbitrage Pricing model (BNPM)" simulator, based upon the first 2 paragraphs of the book of Steven Shreve.

BNPM.py

# A simple "Binomial Non-Arbitrage Pricing model (BNPM)" simulator. Requires python 2.x
import sys;
steps = ("--steps" in sys.argv); # if --steps is included, BNPM.py will show all V-values.
PUT = "p"; CALL = "c";

class Stock:
	tail = head = None;
	val = -1.0;
	period = 0;
	
	def __init__(self,price):
		self.price = price;	
	
	def delta(self):
		return (self.head.val-self.tail.val)/(self.head.price-self.tail.price);
	
	def eval(self):
		if self.val < 0.0:
			p = float(((1.0+r)-(self.tail.price/self.price))/((self.head.price-self.tail.price)/self.price))
			q = 1.0 - p
			self.val = 1.0/(1.0+r)*(p*self.head.eval()+q*self.tail.eval());
			if steps: print "V" + str(self.period) + ": " + str(self.val) + " with p = " + str(p) + ", q = " + str(q) + ", delta = " + str(self.delta()) + " and price = " + str(self.price);
		return self.val

# input ###############
r = (1.0/4.0);
model = Stock(10.0);
u = d = None;
## If only the above is specified, BNPM.py will ask for up/down-factors.
model.head = Stock(20.0);
model.tail = Stock(5.0);
model.head.head = Stock(35.0);
model.head.tail = Stock(15.0);
model.tail.head = Stock(10.0);
model.tail.tail = Stock(2.5);
#######################

# Setup option
assert model
type = raw_input("(c)all or (p)ut?: ");
assert type == CALL or type == PUT;
K = float(raw_input("Strike price: "))
e = int(raw_input("Expiration time: "));
if not model.head and (u == None or d == None):
	u = float(raw_input("up-factor: "));
	d = float(raw_input("down-factor: "));

# find leafs of the model.
tmp = []; stocks = [model]; # starting point
for i in range(1,e+1):		
	for s in stocks:
		assert s.head and s.tail;
		if u is not None:
			s.head = Stock(s.price * u)
			s.tail = Stock(s.price * d)
		s.head.period = s.tail.period = i;
		tmp += [s.head,s.tail];
	stocks = tmp;
	tmp = [];
	
# Calculate Ve
for s in stocks:
	s.val = max(s.price - K,0.0) if type == CALL else max(K - s.price,0.0);
	if steps: print "V" + str(str(s.period)) + ": " + str(s.val) + " (leaf)";
if not steps: print "\nV0: " + str(model.eval()) + " and delta: " + str(model.delta());