1.) Binomial Model The current price of a stock is $14. In 6 months, the price w
ID: 2736955 • Letter: 1
Question
1.) Binomial Model
The current price of a stock is $14. In 6 months, the price will be either $20 or $12. The annual risk-free rate is 7%. Find the price of a call option on the stock that has a strike price of $13 and that expires in 6 months. (Hint: Use daily compounding.) Round your answer to the nearest cent. Assume a 365-day year. Do not round your intermediate calculations.
2.) Binomial Model
The current price of a stock is $19. In 1 year, the price will be either $28 or $14. The annual risk-free rate is 5%. Find the price of a call option on the stock that has a strike price is of $23 and that expires in 1 year. (Hint: Use daily compounding.) Round your answer to the nearest cent. Assume 365-day year. Do not round your intermediate calculations.
Explanation / Answer
FACTS:QUESTION-------1
SPOT PRICE=$14
STRIKE PRICE=$13
FUTURE SPOT PRICE=$20-$12
RATE OF INTEREST-7%
STEP-1
SITUATION FSP VALUE OF CALL
1 20 7
2 12 0
CHANGE 8 7
STEP-2
CALUCATION OF
CHANGE IN VALUE OF CALL/CHANGE IN FSP=7/8=0.875
STEP-3 MATURITY VALUE OF PORTFOLIO
SITUATION FSP SHAREVALUE VALUE OF CALL PORTFOLIOVALUE
1 20 20*0.875=17.5 (7) 10.5
2 12 12*0.875=10.5 0 10.5
STEP-4 PRESENT VALUE OF PORTFOLIO:
10.5/1.035=10.14
STEP-5 PRESENT VALUE OF DELTA SHARES
=14*0.875 HARES
=12.25
STEP-6 PRESENT VALUE OF PORTFOLIO=
VALUEOF CALL+ VALUE OF DELTA SHARES
10.14 =VALUE OF CALL+12.25
VALUE OF CALL=12.25-10.14=2.11
FACTS OF THE QUESTION-2
STEP-1
SITUATION FSP VALUE OF CALL
1 28 5
2 14 0
CHANGE 14 5
STEP-2 CALCULATION OF DELTA SHARE
= CHANGE IN VALUE OF CALL/CHANGE IN FSP
=5/14=0.357
STEP-3 MATURITY VALUE OF PORTFOLIO
SITUATION FSP SHAREVALUE VALUE OF CALL PORTFOLIO VALUE
1 28 28*0.357=9.99 (5) 4.99
2 14 14*0.357=4.99 0 4.99
STEP-4 PRESENT VALUE OF PORTFOLIO
4.99/1.05=4.752
STEP-5 PRESEMT VALUE OF DELTA SHARES
=0.357SHARES*19=6.78
STEP-6 VALUE OF PORTFOLIO=VALUE OF CALL+VALUE OF VALUE OF DELTA SHARES
4.752=VALUE OF CALL+6.78
VALUE OF CALL=6.78-4.752=2.028
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.