Question
In: Finance
The following four (4) problems are based on the following information: AMZN closed at $1,162.35 on...
The following four (4) problems are based on the following information:
AMZN closed at $1,162.35 on 2017.12.01. A 2018.03.16 call option with a strike price of $1,000 sells for $182.30.
1. What is the intrinsic value of this option?
2. What is the time value of this option?
3. Your fancy computer estimates the volatility of AMZN as σ = 20.00 % and the risk free rate is r = 3.00 %. Given this information, what is the Black-Scholes value of this option? Feel free to use Excel or R to answer this problem.
4. Given the Black-Scholes value obtained in the previous problem, would you enter a long (buy) or short (sell/write) position in this option?
Solutions
Expert Solution
1) Intrinsic Value = Spot price of underlying - Strike price of option = $1,162.35 - $1000 = $162.35
2) Time Value = Call Premium - Intrinsic Value = $182.30 -$162.35 = $19.95
3) Days between 2018-03-16 and 2017-12-1 is 105 (Using DAYS formula in excel)
t = 105/365 =0.2877 years
| Current Price | S | 1162.35 |
| Strike Price | X | 1000 |
| Risk free | r | 3.00% |
| Time | t | 0.287671233 |
| Dividend Yield | q | 0% |
| Standard Dev. | σ | 20% |
d1 = [ln(1162.35/1000)+0.2877*(0.03+0.2*0.2/2)] / (0.2*0.28770.5)
d1 = [ 0.15044 + 0.014384] / 0.1072 = 1.536565
d2 = 1.536565 - 0.1072 = 1.42929
N(d1) = Norm.s.dist(1.536565) = 0.9378
N(d2) = Norm.s.dist (1.42929) = 0.9235
C = 1162.35*0.9378 - 1000 * exp(-0.03*0.2877)*0.9235 = 174.4476
4) Since Black Scholes Price is $174.45 and current price is $182.30. So it is overpriced. There we need to go Short on Option
jeff jeffy answered 1 year agoRelated Solutions
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