期权与风险模型真题练习及详情解析-金程FRM

期权与风险模型真题练习及详情解析

行业资讯 | 2020-04-15

在给大家公布期权与风险模型真题练习及详情解析之前首先金程FRM小编给大家讲一讲什么是期权？齐全的标志物是什么？到期日是什么意思？齐全的执行是什么？希望可以帮助大家更好的认识期权？》》对期权有不明白的点我咨询

期权，是指一种合约，源于十八世纪后期的美国和欧洲市场，该合约赋予持有人在某一特定日期或该日之前的任何时间以固定价格购进或售出一种资产的权利。期权定义的要点如下：

1、期权是一种权利。期权合约至少涉及买家和出售人两方。持有人享有权利但不承担相应的义务。

2、期权的标的物。期权的标的物是指选择购买或出售的资产。它包括股票、政府债券、货币、股票指数、商品期货等。期权是这些标的物“衍生”的，因此称衍生金融工具。值得注意的是，期权出售人不一定拥有标的资产。期权是可以“卖空”的。期权购买人也不一定真的想购买资产标的物。因此，期权到期时双方不一定进行标的物的实物交割，而只需按价差补足价款即可。

3、到期日。双方约定的期权到期的那一天称为“到期日”，如果该期权只能在到期日执行，则称为欧式期权；如果该期权可以在到期日及之前的任何时间执行，则称为美式期权。

4、期权的执行。依据期权合约购进或售出标的资产的行为称为“执行”。在期权合约中约定的、期权持有人据以购进或售出标的资产的固定价格，称为“执行价格”。

Q-1.Jeff is an arbitrage trader,and he wants to calculate the implied dividend yield on a stock while looking at the over-the-counter price of a 5-year put and call(both European-style)on that same stock.He has the following data:

•Initial stock price=USD 85

•Strike price=USD 90

•Continuous risk-free rate=5%

•Underlying stock volatility=unknown

•Call price=USD 10

•Put price=USD 15

What is the continuous implied dividend yield of that stock?

A.2.48%

B.4.69%

C.5.34%

D.7.71%

Solution:C

Solving for q,we get 5.34%.

Q-2.The price of a six-month,USD 25 strike price,European call option on a stock is USD 3.The stock price is USD 24.A dividend of USD 1 is expected in three months.The continuously compounded risk-free rate for all maturities is 5%per year.Which of the following is closest to the value of a put option on the same underlying stock with a strike price of USD 25 and a time to maturity of six months?

A.USD 3.60

B.USD 2.40

C.USD 4.37

D.USD 1.63

Solution:C

From the equation for put-call parity,this can be solved by the following equation:

where PV represents the present value,so that:

Where:

p represents the put price,

c is the call price,

K is the strike price of the put option,

D is the dividend,

S0 is the current stock price.

T is the time to maturity of the option,and

t is the time to the next dividend distribution.

Calculating PV(K),the present value of the strike price,results in a value of or 24.38,while PV(D)is equal to or 0.99.Hence p=3+24.38+0.99-24=USD 4.37.

Q-3.Consider the following bearish option strategy of buying one at-the-money put with a strike price of$43 for$6,selling two puts with a strike price of$37 for$4 each and buying one put with a strike price of$32 for$1.If the stock price plummets to$19 at expiration,calculate the net profit/loss per share of the strategy.

A.-2.00 per share

B.Zero–no profit or loss

C.1.00 per share

D.2.00 per share

Solution:D

The easiest thing to do is to find the net profit or loss for each position and then add them together,recognizing whether a position is short or long.

For 1 long$43 strike put position:[1×(43–19)]–6=18

For 2 short$37 strike puts position:-[2×(37–19)]+(2×4)=-28

For 1 long$32 strike put position:[1×(32–19)]–1=12

The sum of these profit/loss numbers is a$2 gain

Q-4.Which option combination most closely simulates the economics of a short position in a futures contract?

A.Payoff of a long call plus a short put

B.Profit of a long call plus a short put

C.Payoff of a long put plus short call

D.Profit of long put plus short call

Solution:C

Payoff of the long put=Max[0,K–S(t)]and payoff of short call=-Max[0,S(t)–K]=Min[K–S(t)],such that the combination payoff=K–S(t)

》》在线领取整套期权与风险模型真题