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

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