期权期货考试大题

四、基于同一股票的看跌期权有相同的到期日.执行价格为$70、$65和$60，市场价格分为$5、$3和$2. 如何构造蝶式差价期权.请用一个表格说明这种策略带来的盈利性.股票价格在什么范围时，蝶式差价期权将导致损失？

五、 基于同一股票的有相同的到期日敲定价为 $70的期权市场价格为 $4. 敲定价$65 的看跌期权的市场价格为 $6。解释如何构造底部宽跨式期权.请用一个表格说明这种策略带来的盈利性.股票价格在什么范围时，宽跨式期权将导致损失？

答案： buy a put with the strike prices $65 and buy a call with the strike prices $70, this portfolio would need initial cost $10.

当 50

时，组合会带来损失

六、远期/期货价格公式及其价值公式，B-S 公式的使用

()()12()()q T t r T t c Se N d Xe N d ----=>=-

()()21()()r T t q T t p Xe N d Se N d ----=---

21d = 21d d =-1).What is the price of a European call option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months?

()()

()()()r T t r T t r q T t F Se S I e Se ----==-=)()(t T r t T q Ke

Se f -----=)()(,t T r t T r Ke I S f Ke S f ------=-=

2). Suppose the current value of the index is 500, continuous dividend yields of index is 4% per annum, the risk-free interest rate is 6% per annum . if the price of three-month European index call option with exercise price 490is $20, What is the price of a three-month European index put option with exercise price 490?

by put-call parity

3) What is the price of a European futures put option ：current futures price is $19, the strike price is $20, the risk-free interest rate is 12% per annum, the volatility is 20% per annum, and the time to maturity is five months? （保留2位小数）

Solution: In this case F=19,X=20, r=0.12, σ=0.20, T -t=0.42,

210.33d ==-

210.46d d =-=-

(0.33)0.6293,(0.46)0.6772N N ==

12()(0.33)0.6293,()(0.46)0.6772N d N N d N -==-==

The price of the European put is

()()210.120.420.120.42()()

200.6772190.6293 1.51r T t r T t p Xe N d Fe N d e e -----⨯-⨯=---=⨯-⨯=

4) A one-year-long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding.

(a)What are the forward price and the initial value of the forward contract?

(b)Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract?

The forward price, 21.44401.0)(===-e Se F t T r ， The initial value of the forward contract is zero.0=f (a)The delivery price K in the contract is $44.21. The value of the forward contract after six months is given:

95.221.44455.01.0)(=-=-=⨯---e Ke S f t T r

The forward price, 31..47455.01.0)(===⨯-e Se F t T r