Premium Essay

Submitted By financejake2015

Words 1595

Pages 7

Words 1595

Pages 7

Next, we calculated d1 and d2 in order to evaluate the price of the call option. D1 and d2 were both calculated at 0.63427 and -0.17406, respectively. This was determined by using the formulas to find d1 and d2 using the Black-Scholes method of valuation.

Lastly, using the Black-Scholes method, the price of the call following all of these conditions was determined to by $29.31. So, the value of 70 million options is simply 70 million multiplied by the price of the call, $29.31. This was found to be $2,052,045,496.29. This data can be seen in Table 1 in the appendix.

Next, I examined the value of the 70 million options when T followed the distribution of: 10% at 4 years, 20% at 5 years, 40% at 6 years, 20% at 7 years, and 10% at 8 years. Following this distribution set, and calculating the summation of all 70 million options at each different time, T, gave a smaller valuation when compared to the value of all 70 million options at one time, T=6 ($2,040,710,000.00 vs all at T=6, $2,052,045,496.29). The following distribution of the call options at different times, their values at those times, and the summation of all the values can be found in Table 2 of the appendix. The Black-Scholes valuation of the options was then recalculated using two different historical volatilities calculated using the daily return data for Microsoft in 1999 and in 2000-2005. To determine this volatility, the continuously