Cash compensation at the end of the 5th year = $5,000(1+6.02%)^5
To equal $6,697.44, the stock price must increase to at least $37.23 at the end of the 5th year. The stock price has to be higher than $35 in order to be exercised and make a gain, otherwise she will leave it expire worthlessly. However, from Exhibit 2, Telstar stock price has increased higher than $35 only once and 10-year average stock price is $21.17. Therefore, the chance that the value of option is greater than the cash compensation is very rare. The options will even worth nothing to Ms. Jameson if the stock price is below $35 at the maturity date.
If Sally holds options until maturity, she should choose cash compensation. Second scenario Because, Ms. Jameson is free to sell options at any time after her joins Telstar, she may sell her option immediately after receiving (at the time that the value of option is greatest) We price the value of stock option by using Black and Schole’s Model and compare it with cash compensation of $5,000. [pic]
[pic] and [pic]
S0 = 18.75 K = 35 T = 5 (refer in case) rf = 6.02% (use 5 year T-bond yield, which match with time to maturity of the option) For volatility, we calculate both historical volatility and implied volatility. (1) Historical volatility : calculate from historical stock returns for 10 years. V = 0.3687 or 36.87%
V comes from: The return of stocks = ln(stock priceT/stock priceT-1 Standard deviation of stock return = 0.023 per day, Convert to per annum = [pic] (253 = number of trading days per annum) So, V = 0.3687 or 36.87%
Put variables into the equation
[pic] ; [pic]
Hence, by using historical volatility, we get the price of call option at $4.07 per option. There are 3,000 call options, so the value of option equals to $4.07*3000 = $12,209.50. If Sally can sell the option as soon as she receives them, she will get $12,209.50 which obviously worth more than cash $5,000. (2) Implied volatility: Calculated from call options currently traded in the market Implied Volatility
|Strike Price |Call Expiration Date | | |June 20, 1992 |July 18, 1992 |Oct 17, 1992 |Jan 22, 1994 | |$12.50 | | | |0.37 | |$17.50 |0.27 |0.36 |0.35 |0.36 | |$20.00 |0.27 |0.31 |0.35 |0.39 | |$22.50 | |0.33 |0.34 | |
Max: 0.39, Min: 0.27, Average: 0.34
Value per option
|Strike Price |Call Expiration Date | | |June 20, 1992 |July 18, 1992 |Oct 17, 1992 |Jan 22, 1994 | |$12.50 | | | |$4.09 | |$17.50 |$2.43 |$3.92 |$3.76 |$3.92 | |$20.00 |$2.43 |$3.09...