# Answer to Question #13019 in Finance for heidi

Question #13019
The current price of a stock is $22, and at the end of one year its price will be either$27 or $17. The annual risk-free rate is 6.0%, based on daily compounding. A 1-year call option on the stock, with an exercise price of$22, is available. Based on the binominal model, what is the option's value
1
2012-08-14T09:21:00-0400
Current price& $22.00& Price at end of year: Exercise price&$22.00& High& $27.00 RF& 6.00%& Low&$17.00
&
Step 1.& Payoff range, stock:& $27.00 &minus;$17.00 = $10.00 Step 2.& Payoff range, option: & If stock is high: Price &minus; Exercise = 27 &minus; 22 =$ 5.00
& If stock is low:
(Price &minus; Exercise) or $0 = & 0.00 & Option range:$5 &minus; $0 =$ 5.00
Step 3.& Equalize the ranges to find the number of shares of stock:
& Option range/Stock range = $5/$10 = shares of stock = 0.5

Step 4.& The payoff from 0.5 shares of stock will be either:& $13.50& or&$ 8.50
& The payoff from the option will be either: 5.00& or 0.00
& The portfolio's payoff will be either:& $8.50& or&$ 8.50
& So the portfolio's payoff is riskless, $8.50 regardless of which choice materializes. Step 5.& The present value of$8.50 at the daily compounded risk-free rate is:
& PV = $8.50/(1 + (0.06/365)) & 365 & =$8.005.
Step 6.& The option price is the cost of the stock purchased for the portfolio minus the PV of
the payoff:
V = 0.5($22) &minus;$8.01 = \$2.99
& PTS:& 1& DIF:& Medium& OBJ:& 8.2& NAT:& AACSB: C; P
TOP:& Option price based on binomial model MSC:& Problem

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!