Let?s say that stock in Amalgamated Boll Weevils (ABW) has an expected annual re

Question

Let?s say that stock in Amalgamated Boll Weevils (ABW) has an expected annual return of 9%, an annual volatility of 30%, and a current price of 60 dollars per share. The risk free interest rate is 4%. Let?s say you own a call on ABW with a strike of 79 dollars per share and an expiration 3/4 of a year from now.

If you own the call option on ABW described above, how much ABW stock would you need to buy or sell to keep the total delta of your portfolio equal to zero? (This means that you will have completely ?delta hedged? your portfolio, which is also called making your portfolio ?delta neutral?.)

Explanation / Answer

Spot Price (S)=60

Strike Price (K)=79

Time to maturity (t)=3/4=0.75 years

Risk free rate (Rf) =0.04

S.D=0.3

D1=(ln(S/k)+(r+S.D^2/2)*t)/(S.D*(t^0.5))

D1=(ln(60/79)+(0.04+(0.3^2)/2)*0.75)/(0.3*(0.75^0.5))

D1=-0.813499193

N(d1)= 0.207965954

Delta =N(d1)= 0.207965954

So no of stock that we need to sell per unit of long call option =0.207965954 shares

Delta Neutral Portfolio =1 unit of Long call Option + 0.207965954 unit of Short underlying

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