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*Learning objectives: Explain put-call parity and apply it to the valuation of European and American stock options. Explain the early exercise features of American call and put options.*

**Questions:**

726.1. The price of a dividend-paying stock is $44.00 while the riskfree rate is 3.0%. Consider a European call option and a European put option with identical strike prices, K = $40.00, and identical times to expiration of nine months, T = 0.75 years. The call has a price of $8.95 and the put has a price of $5.36. What is the present value of the dividends expected during the life of the option?

a. Zero

b. $0.19

c. $1.30

d. $4.75

726.2. Assume an option has a strike price of $50.00 and its time to expiration is six months (0.5 years) while the stock pays a dividend. Each of the following implications is true, ceteris paribus, if the risk-free rate reduces from 3.0% to zero

**EXCEPT**which is FALSE if the risk-free rate reduces to zero?

a. If the option is put (either American or European), its price will increase

b. If the option is a call (either American or European), its price will decrease

c. If the option is American (either a call or a put), the early exercise feature becomes relatively LESS attractive

d. If the option is European (either a call or a put), the lower bound (aka, minimum value) simplifies to the option's intrinsic value

726.3. A non-dividend-paying stock currently trades at a price of $21.00 while the risk-rate is 4.0%. The stock's is highly uncertain, with a volatility of 50.0%. Two deeply in-the-money one-year European put options on this stock are trading at the following prices:

- The put with a strike price of $40.00 has a price (premium) of $18.20
- The put with a strike price of $45.00 has a price (premium) of $25.20

a. No

b. Yes, and it exploited with a straddle

c. Yes, and it is exploited with a bull spread

d. Yes, and it is exploited with a bear spread

**Answers here:**

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