Question

You have a stock in the one-period binomial model such that S0 = 4,S1(H) = 8,S1(T) = 2, and r = 1.5. Show how to extract arbitrage by explicitly defining a portfolio (X, ∆) such that X0 < 0 while X1 ≥ 0.

Answer 1

First claculate Hedge ratio

Hedge Ratio= (Return to the Option Buyer if Price Goes Up- return to the option buyer if the price goes down)/ Upper Price- Lower Price

Or Swing of call/ Swing of stock

Hedge ratio= (S1(H)- E( Strike Price)) -0/( S1(H)-S1(T)

= (8-4)-0/8-2= (4-0)/6= 4/6= 2/3

Which represent that Call writer should write an option on 3 shares & buy 2 shares to partly cover themselves.

An Option writer shall buy the share equal to the numerator of Hedge ratio before writing a call option and he shall write an call option in the number share equal to the denominator of the hedge ratio.