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 ​$500. 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 50​% chance that the stock will close in the​ 20-30 range, a 40​% chance that it will close above​ 30, and a 10​%chance that it will fall below 20 on May 15. Complete parts​ (a) through​ (b).

a. How much does she expect to​ gain

b. What is the standard deviation of her gain?

Answer 1

The probability mass function of gain is,

P(X = 500 - 200 = 300) = 0.4 => P(X = 300) = 0.4

P(X = 0 - 200 = -200) = 0.4 => P(X = -200) = 0.1

P(X = 200 - 200 = 0) = 0.5 => P(X = 0) = 0.5

(a)

Expected Gain = E(X) =

= 300 * 0.4 - 200 * 0.1 + 0 * 0.5

= $100

(b)

= 40000

Standard deviation of her gain =

$173.21