*I need step by step explanation on how the answer in bold were gotten.* The fol
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Question
*I need step by step explanation on how the answer in bold were gotten.* The following quotes were observed for options on a given stock on November 1 of a given year. These are American calls except where indicated. Use the information to answer questions 12 through 20. Cells Puts Strike Nov Dec Jen Nov Dec Jan 105 8.40 10 11.50 5.30 1.30 2.00 110 4.40 7.10 8.30 0.90 2.50 3.80 115 1.50 3.90 5.30 2.80 4.80 4.80 The stock price was 113.25. The risk -free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The times to expiration were 0.0384 (November), 0.1342 (December), and 0.211 (January). Assume no dividends unless indicated. 12. What is the time value of the November 115 put? a. 1.75 b. 2.80 C. 1.10 d. 0.00 e. none of the above 14. What is the time value of the January 115 call? a. 5.30 b. 0.00 c. 3.50 d. 1.70 e. none of the above 15. What is the European lower bound of the December 105 call? a. 9.86 b. 0.00 c. 8.25 d. 9.26 e. none of the above 16. What is the European lower bound of the November 115 call? a. 1.44 b. 0.00 c. 1.75 d. 2.06 e. none of the aboveExplanation / Answer
12. Intrinsic value of a put = strike price - underlying price
if strike price is greater than underlying price
Thus, intrinsic value of 115 put = 115 - 113.25 = 1.75
Option price = Intrinsic value + time value
2.80 = 1.75 + time value
Thus, time value = 2.80 - 1.75 = $1.05
14. intrinsic value of a call = underlying price - strike price
if underlying price is greater than strike price else 0. as underlying price is lower than the strike price, i.e call is out of the money, its intrinsic value is 0.
Thus, time value = $5.30
15. European lower bound of Dec 105 call
Strike price, K = 105
Current Stock price, S0 = 113.25
r = 7.50% and T = 0.1342
Lower bound of european call = S0 - K*exp(-r*T)
= 113.25 - 105*exp(-0.075*0.1342)
= 113.25 - 105*0.9899
= 113.25 - 103.95
= 9.30
16. Strike price, K = 115
S0 = 113.25, r = 7.30%, T = 0.0384
Lower bound of european call = S0 - K*exp(-r*T)
= 113.25 - 115*exp(-0.073*0.0384)
= 113.25 - 115 * 0.9972
= 113.25 - 114.68 = -1.43
But, the price of a call can never be negative. Thus, lower bound = 0.
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