2) Using Binomial Model:
Facts:
Spot price = $100, term = 6 months, Exercise price = $110, FSP = $120 or $90, interest rate=6%
Step 1:
situation FSP Value of call
1 120 -10
2 90 0
change Δ 30 10
Step 2: Calculation of Δ shares
Δ shares = change in value of call/change in FSP = 10/30 = 0.3333 shares
step 3: future value of portfolio
Situation FSP share value value of call portfolio value
1 120 (120*0.333)= 40 -10 30
2 90 (90*0.333)= 30 0 30
Step 4: P.V of portfolio:
present value = 30*1/1.03 = 29.126
Step 5: P.V of Δ shares
= Δ shares*spot price
= 0.3333*$100
= $33.33
Step 6: Value of call
value of portfolio = value of call + value of Δ shares
29.126 = value of call + 33.33
value of call = $4.206
The strategy is write 1 call option and hold 0.333 shares
3) Calculation of value of call option:
Step 1:
situation FSP Value of call
1 60 -12
2 45 0
change Δ 15 12
Δ shares = change in value of call/change in FSP = 12/15 =0.8 shares
step 2: future value of portfolio
Situation FSP share value value of call portfolio value
1 60 (60*0.8)= 48 -12 36
2 45 (45*0.8)=36 0 36
Step 3: P.V of portfolio:
present value = 36*1/1.02 = 35.29
Step 4: P.V of Δ shares
= Δ shares*spot price
= 0.80*$50
=$40
Step 5: Value of call
value of portfolio = value of call + value of Δ shares
35.29 = value of call + 40
value of call = $4.71
strategy is write 1 call option and hold 0.8 shares
If the call is trading at $3 then hold a call as it was less than equilibrium price
4) Black Schole's model:
2. A stock has two possible ending prices six months from now: $120 or $90. A...
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