FMP13 - Properties of Options

Question 1

Identify six factors that affect an options price

Answer 1

1. price of underlying stock
2. strike price
3. risk-free rate
4. volatility of stock price
5. time to maturity
6. dividends to be paid over the life of the option

Question 2

Identify and compute upper and lower bounds for option prices on non-dividend and dividend paying stocks

Answer 2

• Non-div call = [S - PV(K), S]
• Non-div put = [max(PV(K) - S, 0), PV(K)]
• Div call = [S - PV(K) - PV(Div), S]
• Div put = [max(PV(K) + PV(Div) - S, 0), PV(K)

Question 3

Explain put-call parity and apply it to the valuation of European and American stock options, with dividends and without dividends, and express it in terms of forward prices

Answer 3

Put-call parity: C + PV(K) + PV(Div) = P + S
where C and P are prices of call and puts

In terms of forward prices:
C + PV(K) = P + PV(F)

Question 4

Explain and assess the potential rationales for using the early exercise features of American call and put options

Answer 4

Calls: stock paying no dividends should never be exercised before maturity. When dividends, may be optimal to exercise just before ex-dividend date

Puts: can be optimal to exercise at any time before maturity