課程名稱︰財務工程
課程性質︰研究所選修
課程教師︰黃以達
開課學院：
開課系所︰經濟系\所
考試日期（年月日）︰
考試時限（分鐘）：
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1. For a 4-month European call option on a stock, you are given:
(i) The stock’s price is 52.
(ii) The strike price is 60.
(iii) The stock pays no dividends.
(iv) The stock’s annual volatility is 25%
(v) The continuously compounded risk-free rate is 5%
Determine the Black-Scholes premium for the option.
2. For a 6-month European put option on a stock, you are given:
(i) The stock’s price is 45.
(ii) The strike price is 44.
(iii) The continuous dividend rate for the stock is 3%.
(iv) The stock’s annual volatility is 10%
(v) The continuously compounded risk-free rate is 4%
Determine the Black-Scholes premium for the option.
3. For a 1-year European call option on a stock, you are given:
(i) The 1-year forward price for the stock’s price is 50.
(ii) The strike price is 45.
(iii) The continuous dividend rate for the stock is 2%.
(iv) The stock’s annual volatility is 0.4
(v) The continuously compounded risk-free rate is 5%
Determine the Black-Scholes premium for the option.
4. For a 3-month European put option on a stock, you are given:
(i) The stock’s price is 41.
(ii) The strike price is 45.
(iii) The stock pays a dividend of 2 in one month.
(iv) The annual volatility of a prepaid forward on the stock is 0.25.
(v) The continuously compounded risk-free rate is 0.05.
Determine the Black-Scholes premium for the option.
5. For a 1-year European call option on a stock, you are given:
(i) The stock’s 1-year forward price is 60.
(ii) The strike price is 55.
(iii) The continuously compounded risk-free rate is 0.04.
(iv) The annual volatility of a prepaid forward on the stock is 0.3.
(v) The stock pays a dividend of 1 every 3 months, starting immediately after
the call option is written. The dividend at the end of one year is paid
before the option may be exercised .
Determine the Black-Scholes premium for the option.
6. For the dollar-euro exchange rate, you are given:
(i) The spot exchange rate is 0.85 ＄/€.
(ii) The strike price is 0.9 ＄/€.
(iii) The continuously compounded risk-free rate for dollar is 0.05.
(iv) The continuously compounded risk-free rate for euro is 0.02.
(v) The annual volatility of the exchange rate is 10%.
Determine the Garman-Kohlhagen premium for a dollar-denominated 1-year
European call option on euros
7. For the yen-dollar exchange rate, you are given:
(i) The spot exchange rate is 130 ￥/＄.
(ii) The strike price is 125 ￥/＄.
(iii) The continuously compounded risk-free rate for dollar is 0.05.
(iv) The continuously compounded risk-free rate for yen is 0.03.
(v) The annual volatility of the exchange rate is 10%.
Determine the Garman-Kohlhagen premium for a yen-denominated 6-month
European put option on dollars.
8. For the dollar-pound exchange rate, you are given:
(i) The spot exchange rate is 1.3＄/￡.
(ii) The strike price is 0.7￡/＄.
(iii) The continuously compounded risk-free rate for dollar is 0.04.
(iv) The continuously compounded risk-free rate for pound is 0.05.
(v) The annual volatility of the exchange rate is 0.2.
Determine the Garman-Kohlhagen premium for a pound-denominated 6-month
European call option on dollars.