Binomial Tree

Question 1

What is the formula for risk neutral probability of going up p?

Answer 1

e^(rT) _ d
P= —————– for non div stock
u - d

   e^(r-q)t  _   d P= -------------------   q is dividend
      u - d

   e^(r - rf)t  _  d P = ------------------  rf-foreign risk free
     u - d

    1 - d p = ------------  for futures
   u -  d

Question 2

Put call parity?

Answer 2

(0,S-X) + X= (0,X-S) + S
Call + PV of Cash = Put + share at time 0
Share - C = Cash - Put

This portfolio is used for calculating the value of derivative ie no arbitrage method

Question 3

What if annual volatility is given, then u ~? d~?

Answer 3

u= e^(st.dev•sqrt of time)

d= 1/u