课程名称︰财务工程 课程性质︰研究所选修 课程教师︰黄以达 开课学院： 开课系所︰经济系\所 考试日期（年月日）︰ 考试时限（分钟）： 是否需发放奖励金：yes （如未明确表示，则不予发放） 试题 : 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. --

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