Question

An option to buy a stock is priced at $200. If the stock closes above 30 on May 15, the option will be worth $900. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $200 A trader thinks there is a 40% chance that the stock will close in the 20-30 range, a 30% chance that it will close above 30, and a 30% chance that it will fall below 20 on May 15. Complete parts (a) through (c)

Help on A and B

A) How much does she expect to​ gain?

​(Round to the nearest dollar as​ needed.)

B)  The standard deviation of gain is

Answer 1

Excel work:

700 0.3 -200 0.3 0 0.4 p x*p x^2 * p Total 1 150 159000 210 147000 -60 12000 0

A) So, expected gain = sum(x*p) = 150

B)

SD = (Στ2 και p) – (Στ και γ)2 = V159000 - 1502 = $369.46

Standard deviation is $369.46 which I rounded to the nearest cent. If we need to round to nearest dollar to this also then that will be $369. So, please check the rounding info they ask.

Please comment if any doubt. Thank you.