Chapter 4

Question 1

What are the steps for binomial option pricing

Answer 1

1. Draw the diagram for the share prices at time 0 and time 1 (up and down)
2. Draw one for Call option: ST-K =CT
3. Get the hedge ratio by doing (h x ST)-CT and equate both in the specific times.
4. Equate the current (h x S0) - C0 with upper bound (hxS0)-C0 x discount rate(exp-(risk free rate x t).
5. If there is one step then t=1/12 as per month, if two steps then both have to be a total of a month so each is two weeks. so each t=1/24.
6. If two steps then the value we have obtained is the C0 and the one below is zero as we wont need to exercise if K>ST

Question 2

What is the formula for risk neutral binomial pricing

Answer 2

C0 = [πu × Pay-off upper + (1 − πu) × payoff lower] × e(−rf×t)

Question 3

What is the formula for put call parity

Answer 3

S + P = PV(k) + C

Question 4

What is the formula for Black scholes

Answer 4

C = P(X=x1)S − Ke(rf ×t)P(X=x2) where
x1 =(1/σ√t)(ln S/K+(rf +σ^2/2)t)
x2 = x1 − σ√t