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期权期货与其他衍生产品第九版课后习题与答案Chapter

CHAPTER 29

Interest Rate Derivatives: The Standard Market Models

Practice Questions

Problem 29.1.

A company caps three-month LIBOR at 10% per annum. The principal amount is $20 million. On a reset date, three-month LIBOR is 12% per annum. What payment would this lead to under the cap? When would the payment be made?

An amount

20000000002025100000$$,,?.?.=,

would be paid out 3 months later.

Problem 29.2.

Explain why a swap option can be regarded as a type of bond option.

A swap option (or swaption) is an option to enter into an interest rate swap at a certain time in the future with a certain fixed rate being used. An interest rate swap can be regarded as the exchange of a fixed-rate bond for a floating-rate bond. A swaption is therefore the option to exchange a fixed-rate bond for a floating-rate bond. The floating-rate bond will be worth its face value at the beginning of the life of the swap. The swaption is therefore an option on a fixed-rate bond with the strike price equal to the face value of the bond.

Problem 29.3.

Use the Black’s model to value a one -year European put option on a 10-year bond. Assume that the current value of the bond is $125, the strike price is $110, the one-year risk-free interest rate is 10% per annum, the bond’s forward price volatility is 8% per annum, and the present value of the coupons to be paid during the life of the option is $10.

In this case, 0110(12510)12709F e .?=-=., 110K =, 011(0)P T e -.?,=, 008B σ=., and 10T =.. 2121ln(12709110)(0082)18456008

00817656

d d d ./+./==..=-.=. From equation (29.2) th

e value o

f the put option is

011011110(17656)12709(18456)012e N e N -.?-.?-.-.-.=.

or $0.12.

Problem 29.4.

Explain carefully how you would use (a) spot volatilities and (b) flat volatilities to value a five-year cap.

When spot volatilities are used to value a cap, a different volatility is used to value each

caplet. When flat volatilities are used, the same volatility is used to value each caplet within a given cap. Spot volatilities are a function of the maturity of the caplet. Flat volatilities are a

function of the maturity of the cap.

Problem 29.5.

Calculate the price of an option that caps the three-m onth rate, starting in 15 months’ time, at 13% (quoted with quarterly compounding) on a principal amount of $1,000. The forward interest rate for the period in question is 12% per annum (quoted with quarterly

compounding), the 18-month risk-free interest rate (continuously compounded) is 11.5% per annum, and the volatility of the forward rate is 12% per annum.

In this case 1000L =, 025k δ=., 012k F =., 013K R =., 0115r =., 012k σ=., 125k t =., 1(0)08416k P t +,=..

250k L δ=

2120529505295006637

d d ==-.=-.-.=-. Th

e value o

f the option is

25008416[012(05295)013(06637)]N N ?.?.-.-.-.

059=. or $0.59.

Problem 29.6.

A bank uses Black’s model to price European bond options. Suppose that an implied price volatility for a 5-year option on a bond maturing in 10 years is used to price a 9-year option on the bond. Would you expect the resultant price to be too high or too low? Explain.

The implied volatility measures the standard deviation of the logarithm of the bond price at the maturity of the option divided by the square root of the time to maturity. In the case of a five year option on a ten year bond, the bond has five years left at option maturity. In the case of a nine year option on a ten year bond it has one year left. The standard deviation of a one year bond price observed in nine years can be normally be expected to be considerably less than that of a five year bond price observed in five years. (See Figure 29.1.) We would therefore expect the price to be too high.

Problem 29.7.

Calculate the value of a four-year European call option on bond that will mature five years from today using Black’s model. The five -year cash bond price is $105, the cash price of a four-year bond with the same coupon is $102, the strike price is $100, the four-year risk-free interest rate is 10% per annum with continuous compounding, and the volatility for the bond price in four years is 2% per annum.

The present value of the principal in the four year bond is 40110067032e -?.=.. The present value of the coupons is, therefore, 1026703234968-.=.. This means that the forward price of the five-year bond is

401(10534968)104475e ?.-.=. The parameters in Black’s model are therefore 104475B F =., 100K =, 01r =., 4T =,

and 002B =.σ.

212111144010744

d d d ==.=-.=. Th

e price o

f the European call is

014[104475(11144)100(10744)]319e N N -.?..-.=.

or $3.19.

Problem 29.8.

If the yield volatility for a five-year put option on a bond maturing in 10 years time is

specified as 22%, how should the option be valued? Assume that, based on today’s interest rates the modified duration of the bond at the maturity of the option will be 4.2 years and the forward yield on the bond is 7%.

The option should be valued using Black’s model in equation (29.2) with the bond price volatility being

4200702200647.?.?.=. or 6.47%.

Problem 29.9.

What other instrument is the same as a five-year zero-cost collar where the strike price of the cap equals the strike price of the floor? What does the common strike price equal?

A 5-year zero-cost collar where the strike price of the cap equals the strike price of the floor is the same as an interest rate swap agreement to receive floating and pay a fixed rate equal to the strike price. The common strike price is the swap rate. Note that the swap is actually a forward swap that excludes the first exchange. (See Business Snapshot 29.1)

Problem 29.10.

Derive a put –call parity relationship for European bond options.

There are two way of expressing the put –call parity relationship for bond options. The first is in terms of bond prices:

0RT c I Ke p B -++=+

where c is the price of a European call option, p is the price of the corresponding European put option, I is the present value of the bond coupon payments during the life of the option, K is the strike price, T is the time to maturity, 0B is the bond price, and R

is the risk-free interest rate for a maturity equal to the life of the options. To prove this we can consider two portfolios. The first consists of a European put option plus the bond; the second consists of the European call option, and an amount of cash equal to the present value of the coupons plus the present value of the strike price. Both can be seen to be worth the same at the maturity of the options.

The second way of expressing the put –call parity relationship is

RT RT B c Ke p F e --+=+

where B F is the forward bond price. This can also be proved by considering two portfolios. The first consists of a European put option plus a forward contract on the bond plus the present value of the forward price; the second consists of a European call option plus the

present value of the strike price. Both can be seen to be worth the same at the maturity of the options.

Problem 29.11.

Derive a put–call parity relationship for European swap options.

The put–call parity relationship for European swap options is

c V p

where c is the value of a call option to pay a fixed rate of

s and receive floating, p is

the value of a put option to receive a fixed rate of

s and pay floating, and V is the value

of the forward swap underlying the swap option where

s is received and floating is paid.

This can be proved by considering two portfolios. The first consists of the put option; the second consists of the call option and the swap. Suppose that the actual swap rate at the

s. The call will be exercised and the put will not be maturity of the options is greater than

exercised. Both portfolios are then worth zero. Suppose next that the actual swap rate at the

s. The put option is exercised and the call option is not maturity of the options is less than

s is received and floating is paid. exercised. Both portfolios are equivalent to a swap where

In all states of the world the two portfolios are worth the same at time T. They must therefore be worth the same today. This proves the result.

Problem 29.12.

Explain why there is an arbitrage opportunity if the implied Black (flat) volatility of a cap is different from that of a floor. Do the broker quotes in Table 29.1 present an arbitrage opportunity?

Suppose that the cap and floor have the same strike price and the same time to maturity. The following put–call parity relationship must hold:

cap swap floor

where the swap is an agreement to receive the cap rate and pay floating over the whole life of the cap/floor. If the implied Black volatilities for the cap equal those for the floor, the Black formulas show that this relationship holds. In other circumstances it does not hold and there is an arbitrage opportunity. The broker quotes in Table 29.1 do not present an arbitrage opportunity because the cap offer is always higher than the floor bid and the floor offer is always higher than the cap bid.

Problem 29.13.

When a bond’s price is lognormal can the bond’s yield be negative? Explain your answer.

Yes. If a zero-coupon bond price at some future time is lognormal, there is some chance that the price will be above par. This in turn implies that the yield to maturity on the bond is negative.

Problem 29.14.

What is the value of a European swap option that gives the holder the right to enter into a

3-year annual-pay swap in four years where a fixed rate of 5% is paid and LIBOR is received? The swap principal is $10 million. Assume that the LIBOR/swap yield curve is used for discounting and is flat at 5% per annum with annual compounding and the volatility of the swap rate is 20%. Compare your answer to that given by DerivaGem.Now suppose that all

swap rates are 5% and all OIS rates are 4.7%. Use DerivaGem to calculate the LIBOR zero curve and the swap option value?

In equation (29.10), 10000000L =,,, 005K s =., 0005s =., 10202d =.=., 2.02-=d , and 56711122404105105105

A =++=.... The value of the swap option (in millions of dollars) is

1022404[005(02)005(02)]0178N N ?...-.-.=.

This is the same as the answer given by DerivaGem. (For the purposes of using the

DerivaGem software, note that the interest rate is 4.879% with continuous compounding for all maturities.)

When OIS discounting is used the LIBOR zero curve is unaffected because LIBOR swap rates are the same for all maturities. (This can be verified with the Zero Curve worksheet in DerivaGem). The only difference is that

2790.2047

.11047.11047.11765=++=A

so that the value is changed to 0.181. This is also the value given by DerivaGem. (Note that the OIS rate is 4.593% with annual compounding.)

Problem 29.15.

Suppose that the yield, R , on a zero-coupon bond follows the process

dR dt dz μσ=+

where μ and σ are functions of R and t , and dz is a Wiener process. Use Ito’s lemma to show that the volatility of the zero-coupon bond price declines to zero as it approaches maturity.

The price of the bond at time t is ()R T t e -- where T is the time when the bond matures. Using It?’s lemma the volatility of the bond price is ()()()R T t R T t e T t e R

σσ----?=--? This tends to zero as t approaches T .

Problem 29.16.

Carry out a manual calculation to verify the option prices in Example 29.2.

The cash price of the bond is

005050005100005100051044410012282e e 卐e -.?.-.?.-.?-.?++++=.

As there is no accrued interest this is also the quoted price of the bond. The interest paid during the life of the option has a present value of

00505005100515005244441504e e e e -.?.-.?-.?.-.?+++=.

The forward price of the bond is therefore

005225(122821504)12061e .?..-.=. The yield with semiannual compounding is 5.0630%.

The duration of the bond at option maturity is 005025005775005775

005025005075005775005775

02547754775100444100e 卐e e e 卐e -.?.-.?.-.?.-.?.-.?.-.?.-.?..?++.?+.?++++ or 5.994. The modified duration is 5.994/1.025315=5.846. The bond price volatility is therefore 584600506300200592.?.?.=.. We can therefore value the bond option using Black’s model with 12061B F =., 005225(0225)08936P e -.?.,.==., 592B %=.σ, and 225T =.. When the strike price is the cash price 115K = and the value of the option is 1.74. When the strike price is the quoted price 117K = and the value of the option is 2.36. This is in agreement with DerivaGem.

Problem 29.17.

Suppose that the 1-year, 2-year, 3-year, 4-year and 5-year LIBOR-for-fixed swap rates for swaps with semiannual payments are 6%, 6.4%, 6.7%, 6.9%, and 7%. The price of a 5-year semiannual cap with a principal of $100 at a cap rate of 8% is $3. Use DerivaGem (the zero rate and Cap_and_swap_opt worksheets) to determine

(a) The 5-year flat volatility for caps and floors with LIBOR discounting

(b) The floor rate in a zero-cost 5-year collar when the cap rate is 8% and LIBOR discounting is used

(a) First we calculate the LIBOR zero curve using the zero curve worksheet of DerivaGem.

The 1-, 2-, 3-, 4-, and 5_year zero rates with continuous compounding are 5.9118%,

6.3140%, 6.6213%, 6.8297%, and 6.9328%, respectively. We then transfer these to the choose the Caps and Swap Options worksheet and choose Cap/Floor as the Underlying Type. We enter Semiannual for the Settlement Frequency, 100 for the Principal, 0 for the Start (Years), 5 for the End (Years), 8% for the Cap/Floor Rate, and $3 for the Price. We select Black-European as the Pricing Model and choose the Cap button. We check the Imply Volatility box and Calculate. The implied volatility is 25.4%.

(b) We then uncheck Implied Volatility, select Floor, check Imply Breakeven Rate. The

floor rate that is calculated is 6.71%. This is the floor rate for which the floor is worth $3.A collar when the floor rate is 6.61% and the cap rate is 8% has zero cost.

maturities are 5.9118%, 6.3117%, 6.6166%, 6.8227%, and 6.9249%. The OIS zero rates are 4.9385%, 5.3404%, 5.6468%, 5.8539%, and 5.9566%, respectively. When these are transferred to the cap and swaption worksheet and the Use OIS Discounting box is checked, the answer to a) becomes 24.81%% and the answer to b) becomes 6.60%.

Problem 29.18.

Show that 12V f V += where 1V is the value of a swaption to pay a fixed rate of K s and receive LIBOR between times 1T and 2T , f is the value of a forward swap to receive a fixed rate of K s and pay LIBOR between times 1T and 2T , and 2V is the value of a swap option to receive a fixed rate of K s between times 1T and 2T . Deduce that 12V V = when K s equals the current forward swap rate.

We prove this result by considering two portfolios. The first consists of the swap option to

receive K s ; the second consists of the swap option to pay K s and the forward swap.

Suppose that the actual swap rate at the maturity of the options is greater than K s . The swap

option to pay K s will be exercised and the swap option to receive K s will not be exercised.

Both portfolios are then worth zero since the swap option to pay K s is neutralized by the

forward swap. Suppose next that the actual swap rate at the maturity of the options is less than K s . The swap option to receive K s is exercised and the swap option to pay K s is not exercised. Both portfolios are then equivalent to a swap where K s is received and floating is

paid. In all states of the world the two portfolios are worth the same at time 1T . They must

therefore be worth the same today. This proves the result. When K s equals the current

forward swap rate 0f = and 12V V =. A swap option to pay fixed is therefore worth the

same as a similar swap option to receive fixed when the fixed rate in the swap option is the forward swap rate.

Problem 29.19.

Suppose that LIBOR zero rates are as in Problem 29.17. Use DerivaGem to determine the value of an option to pay a fixed rate of 6% and receive LIBOR on a five-year swap starting in one year. Assume that the principal is $100 million, payments are exchanged semiannually, and the swap rate volatility is 21%. Use LIBOR discounting.

We choose the Caps and Swap Options worksheet of DerivaGem and choose Swap Option as the Underlying Type. We enter 100 as the Principal, 1 as the Start (Years), 6 as the End (Years), 6% as the Swap Rate, and Semiannual as the Settlement Frequency. We choose Black-European as the pricing model, enter 21% as the Volatility and check the Pay Fixed button. We do not check the Imply Breakeven Rate and Imply Volatility boxes. The value of the swap option is 5.63.

Problem 29.20.

Describe how you would (a) calculate cap flat volatilities from cap spot volatilities and (b) calculate cap spot volatilities from cap flat volatilities.

(a) To calculate flat volatilities from spot volatilities we choose a strike rate and use the spot volatilities to calculate caplet prices. We then sum the caplet prices to obtain cap prices and imply flat volatilities from Black’s model. The answe r is slightly

dependent on the strike price chosen. This procedure ignores any volatility smile in cap pricing.

(b) To calculate spot volatilities from flat volatilities the first step is usually to interpolate between the flat volatilities so that we have a flat volatility for each caplet payment date. We choose a strike price and use the flat volatilities to calculate cap prices. By subtracting successive cap prices we obtain caplet prices from which we can imply spot volatilities. The answer is slightly dependent on the strike price chosen. This

procedure also ignores any volatility smile in caplet pricing.

Further Questions

Problem 29.21.

Consider an eight-month European put option on a Treasury bond that currently has 14.25 years to maturity. The current cash bond price is $910, the exercise price is $900, and the volatility for the bond price is 10% per annum. A coupon of $35 will be paid by the bond in three months. The risk-free interest rate is 8% for all maturities up to one year. Use Black’s model to determine the price of the option. Consider both the case where the strike price corresponds to the cash price of the bond and the case where it corresponds to the quoted price.

The present value of the coupon payment is

008025353431e -.?.=.

Equation (29.2) can therefore be used with 008812(9103431)92366B F e .?/=-.=., 008r =., 010B σ=. and 06667T =.. When the strike price is a cash price, 900K = and

12103587002770

d d d ==.=-.=.

The option price is therefore

00806667900(02770)87569(03587)1834e N N -.?.-.-.-.=.

or $18.34.

When the strike price is a quoted price 5 months of accrued interest must be added to 900 to get the cash strike price. The cash strike price is 900350833392917+?.=.. In this case

12100319001136

d d d ==-.=-.=-.

and the option price is

0080666792917(01136)87569(00319)3122e N N -.?...-..=.

or $31.22.

Problem 29.22.

Calculate the price of a cap on the 90-day LIBOR rate in nine months’ time when the principal amount is $1,000. Use Black’s model with LIBOR discounting and the following information:

(a) The quoted nine-month Eurodollar futures price = 92. (Ignore differences between

futures and forward rates.)

(b) The interest-rate volatility implied by a nine-month Eurodollar option = 15% per

annum.

per annum.

(d) The cap rate = 8% per annum. (Assume an actual/360 day count.)

The quoted futures price corresponds to a forward rate of 8% per annum with quarterly compounding and actual/360. The parameters for Black’s model are therefore: 008k F =., 008K =., 0075R =., 015k σ=., 075k t =., and 007511(0)09277k P t e -.?+,==.

21220065000650d d ==.==-. and the call price, c , is given by

[]025100009277008(00650)008(00650)096c N N =.?,?...-.-..=.

Problem 29.23.

Suppose that the LIBOR yield curve is flat at 8% with annual compounding. A swaption gives the holder the right to receive 7.6% in a five-year swap starting in four years. Payments are made annually. The volatility of the forward swap rate is 25% per annum and the principal is $1 million. Use Black’s model to price the swaption with LIBOR discounting. Compare your answer to that given by DerivaGem.

The payoff from the swaption is a series of five cash flows equal to max[00760]T s .-, in millions of dollars where T s is the five-year swap rate in four years. The value of an annuity that provides $1 per year at the end of years 5, 6, 7, 8, and 9 is 95129348108

i i ==..∑ The value of the swaption in millions of dollars is therefore

2129348[0076()008()]N d N d ..--.-

where

2103526d ==. and

2201474d ==-. The value of the swaption is

29348[0076(01474)008(03526)]003955N N ...-.-.=.

or $39,550. This is the same answer as that given by DerivaGem. Note that for the purposes of using DerivaGem the zero rate is 7.696% continuously compounded for all maturities.

Problem 29.24.

Use the DerivaGem software to value a five-year collar that guarantees that the maximum and minimum interest rates on a LIBOR-based loan (with quarterly resets) are 7% and 5% respectively. The LIBOR and OIS zero curves are currently flat at 6% and 5.8% respectively (with continuous compounding). Use a flat volatility of 20%. Assume that the principal is $100. Use OIS discounting

We use the Caps and Swap Options worksheet of DerivaGem. Set the LIBOR zero curve as 6% with continuous compounding. ( It is only necessary to enter 6% for one maturity.) . Set the OIS zero curve as 5.8% with continuous compounding. ( It is only necessary to enter

5.8% for one maturity.) To value the cap we select Cap/Floor as the Underlying Type, enter Quarterly for the Settlement Frequency, 100 for the Principal, 0 for the Start (Years), 5 for the End (Years), 7% for the Cap/Floor Rate, and 20% for the Volatility. We select

Black-European as the Pricing Model and choose the Cap button. We do not check the Imply

Breakeven Rate and Imply Volatility boxes. We do check the Use OIS Discounting button. The value of the cap is 1.576. To value the floor we change the Cap/Floor Rate to 5% and select the Floor button rather than the Cap button. The value is 1.080. The collar is a long position in the cap and a short position in the floor. The value of the collar is therefore

1.576 ─ 1.080 = 0.496

Problem 29.25.

Use the DerivaGem software to value a European swap option that gives you the right in two years to enter into a 5-year swap in which you pay a fixed rate of 6% and receive floating. Cash flows are exchanged semiannually on the swap. The 1-year, 2-year, 5-year, and 10-year LIBOR-for-fixed swap rate where payments are exchanged semiannually are 5%, 6%, 6.5%, and 7%, respectively. Assume a principal of $100 and a volatility of 15% per annum. (a) Use LIBOR discounting (b) Use OIS discounting assuming that OIS swap rates are 80 basis points below LIBOR swap rates (c) Use the incorrect approach where OIS discounting is applied to swap rates calculate from LIBOR discounting. What is the error from using the incorrect approach?

We first use the zero rates worksheet to calculate the LIBOR zero curve with LIBOR discounting. We then calculate the LIBOR and OIS zero curve with OIS discounting.

(a)The LIBOR zero rates are transferred to the cap and swap option worksheet. The

value of the swaption is 4.602

(b)The LIBOR and OIS zero rates are transferred to the cap and swap option worksheet.

The value of the swaption is 4.736

(c)The LIBOR zero curve from (a) and the OIS zero curve from (b) are transferred to

the cap and swap option worksheet. The value of the swaption is 4.783. The error

from using the incorrect approach is 4.783?4.736 = 0.047 or 4.7 basis points.

期货与期权习题与参考答案

期货学补充习题与参考答案 ▲1．请解释期货多头与期货空头的区别。远期多头指交易者协定将来以某一确定价格购入某种资产；远期空头指交易者协定将来以某一确定价格售出某种资产。 2．请详细解释(a)对冲，(b)投机和(c)套利之间的区别。答：套期保值指交易者采取一定的措施补偿资产的风险暴露；投机不对风险暴露进行补偿，是一种“赌博行为”；套利是采取两种或更多方式锁定利润。 ▲3．一位投资者出售了一个棉花期货合约，期货价格为每磅50美分，每个合约交割数量为5万磅。请问期货合约到期时棉花价格分别为(a)每磅48．20美分；（b)每磅51．30美分时，这位投资者的收益或损失为多少? 答：(a)合约到期时棉花价格为每磅$0.4820时，交易者收入：（$0.5000-$0.4820）×50，000＝$900; (b)合约到期时棉花价格为每磅$0.5130时，交易者损失:($0.5130-$0.5000) ×50，000=$650 ▲4.请解释为什么期货合约既可用来投机又可用来对冲。答：如果投资者预期价格将会上涨，可以通过远期多头来降低风险暴露，反之，预期价格下跌，通过远期空头化解风险。如果投资者资产无潜在的风险暴露，远期合约交易就成为投机行为。 ▲5．一个养猪的农民想在3个月后卖出9万磅的生猪。在芝加哥商品交易所（CME)交易的生猪期货合约规定的交割数量为每张合约3万磅。该农民如何利用期货合约进行对冲，从该农民的角度出发，对冲的好处和坏处分别是什么? 答：农场主卖出三份三个月期的期货合约来套期保值。如果活猪的价格下跌，期货市场上的收益即可以弥补现货市场的损失；如果活猪的价格上涨，期货市场上的损失就会抵消其现货市场的盈利。套期保值的优点在于可以我成本的将风险降低为零，缺点在于当价格朝着利于投资者方向变动时，他将不能获取收益。 ▲6．现在为1997年7月，某采矿公司新近发现一个小存储量的金矿。开发矿井需要6个月。然后黄金提炼可以持续一年左右。纽约商品交易所设有黄金的期货

期货期权总结习题

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1、期权按照买方的权利性质划分，分为（B） A.实值期权、平值期权和虚值期权 B.看涨期权、看跌期权 C.期货期权、现货期权 D.美式期权、欧式期权 2、下列关于白糖、豆粕期权合约最后交易日表述错误的是（C） A.白糖期权合约最后交易日是标的期货合约交割月前二个月的倒数第5个交易日 B.与标的期货合约的最后交易日不同 C.期权合约最后交易日是标的期货合约交割月前的第10个交易日 D.豆粕期权合约最后交易日是标的期货合约交割月前一个月的第5个交易日更多信息关注微公众号海航龙三 3、假设豆粕期权限仓15000手，某客户目前持仓有且仅有10000手M-1707-C-2700 期权合约买持仓，下列对于2017年7月豆粕期权合约的开仓行为，不会超过持仓限额的是（A） A买入2000手M-1707-C-2600，同时卖出3001手M-1707-C-2700 B卖出5001手M-1707-P-2800 C买入5001手M-1707-C-2700 D买入2000手M-1707-C-2700，同时卖出3001手M-1707-P-2900 4、一个离到期日还有90天的M1305-P-3500期权，当前豆粕期货价格为3513元/吨，则该期权的Delta值最接近于（A） A.-0.5 B.-1 C.1 D.0.5

5、关于大商所的期权行权，以下说法错误的是（B） A.期权买方可以申请对其同一交易编码下行权后的双向期货持仓进行对冲平仓，对冲数量不超过行权获得的期货持仓量 B.若虚值期权买方希望行权，无需提交行权申请 C.若实值期权买方希望放弃行权，需在规定时间内提交放弃行权申请 D.非期货公司会员和客户可以申请对其同一交易编码下的双向期权持仓进行对冲平仓 6、在标的期货合约保证金标准不变的情况下，下列可能追加保证金的情形是（A） A.卖出看涨期权，标的期货合约价格上涨 B.卖出看跌期权，标的期货合约价格上涨 C.买入看涨期权，标的期货合约价格下跌 D.买入看跌期权，标的期货合约价格下跌，更多信息关注微公众号海航龙三 7、某投资者买入开仓SR309C5000合约10手后，于次日卖出平仓该合约4手，该投资者的持仓为（C） A.4手 B.14手 C.6手 D.12手 8、期权投资者适当性管理办法规定，客户应当全面评估自身的经济实力、期权认知能力和（A），审慎决定是否参与期权交易。 A.风险控制与承受能力 B.期货认知能力 C.交易操作能力 D.价格趋势判断能力 9、期权投资者适当性管理办法对期权投资者的要求不包括(D)

金融工程期末考题

名词解释：金融工程：包括创新型金融工程与金融手段的设计、开发与实施，以及对金融问题给予创造性的解决。场外交易：指非上市或上市的证劵，不在交易所内进行交易而在场外市场进行交易的活动。远期合约：合约约定买方和卖方在将来某指定的时刻以指定的价格买入或卖出某种资产。即期合约：是指在今天就买入或卖出资产的合约。期权合约：以金融衍生品作为行权品种的交易合约，指在特定时间内以特定价格买卖一定数量交易品的权利。对冲者：采用衍生品合约减少自身面临的由于市场变化产生的风险。投机者：他对于资产价格的上涨或下跌进行下注。套利者：同时进入两个或多个市场的交易，以锁定一个无风险的收益。基差：商品即期价格与期货价格之间的差别。交叉对冲：采用不同的资产来对冲另一资产所产生的风险暴露。向前滚动对冲：有时需要对冲的期限要比所有能够利用的期货到期日更长，这时对冲者必须对到期的期货进行平仓，同时再进入具有较晚期限的合约，这样就可以将对冲向前滚动很多次。系统风险与非系统风险：系统风险是由于公司外部，不为公司所预计和控制的因素造成的风险。非系统风险是由公司自身内部原因造成证劵价格下降的风险。每日结算：在每个交易日结束时，保证金账户的金额数量将得到调整以反应投资者盈亏的做法。短头寸对冲：对冲者已拥有资产并希望在某时卖出资产。。尾随对冲：为了反映每天的结算而对对冲期货合约的数量进行调整的方式。标准利率互换：在这种互换中，一家公司同意向另一家公司在今后若干年内支付在本金面值上按事先约定的固定利率与本金产生的现金流，作为回报，前者将收入以相同的本金而产生的浮动利率现金流。期权的内涵价值;定义为0与期权立即被行使的价值的最大值。期权（看涨、看跌、美式、欧式）：看涨期权的持有者有权在将来某一特定时间以某一确定价格买入某种资产；看跌期权的持有者有权在将来某一特定时间以某一确定价格卖出某种资产；美式期权是指在到期前的任何时刻，期权持有人均可以行使期权；欧式期权是指期权持有人只能在到期这一特定时刻行使期权。问答题 1、金融期货合约的定义是什么，具有哪些特点？ ①定义：期货合约是在将来某一指定的时刻以约定的价格买入或卖出某种产品的合约。 ②特点：1、期货合约的商品品种、数量、质量、等级、交货时间、交货地点都是确定的，是标准化的，唯一的变量是价格。2、期货合约是在期货交易所组织下成交的，具有法律效力，而价格是在交易所的交易厅里通过公开竞价的方式产生的。 3、期货合约履行由交易所担保，不允许私下交易。 4、合约的规模定义了每一种合约中交割资产的数量。 5、交割地点必须由交易所指定，期货合约通常以交割月份来命名，交易所必须制定交割月份内明确的日期。 6、每天价格变动的份额是由交易所决定的。 7、可以通过对冲、平仓了结履行责任。 2、阐述三类远期定价公式，并解释个字母具体含义。答：Fo为远期价格，So为即期价格，T为期限，r为无风险利率，I为收益的贴现值，q为资产在远期期限内的平均年收益。远期合约在持有期间无中间收益和成本：Fo=SoerT 远期合约在持有期间有中间收益：Fo=（So—I)erT 远期合约的标的资产支付一个已知的收益率：Fo=Soe（r-q)T 3、阐述套期保值的定义、思路，并列决实际期货市场中如何进行套期保值。定义:套期保值是把期货市场当作转移价格风险的产所，利用期货合约作为将来在某现货市场上卖卖商品的价格进行保险的交易活动。思路:确定套期保值品种，确定方向，即期货长头寸或短头寸，在产品完成时以一个理想的固定价格卖出。确定套期保值数量，确定套期保值时间。案例:一家公司为了减少产品生产完成时价格降低的风险，在生产完成之前进入期货短头寸，在产品完成时以一个理想的固定价格卖出。

Detmgpa期货与期权复习题

Time will pierce the surface or youth, will be on the beauty of the ditch dug a shallow groove ; Jane will eat rare!A born beauty, anything to escape his sickle sweep .-- Shakespeare 期货与期权一、名词解释 1.刻度值刻度乘以交易单位所得的积，就是每份金融期货合约的价值因价格变动一个刻度而增减的金额，这一金额叫做刻度值。 2.交易单位交易单位也称合约规模，是指交易所对每一份金融期货合约所规定的交易数量。 3.最小变动价位通常也被称为一个刻度，是指由交易所规定的、在金融期货交易中每一次价格变动的最小幅度。 4.未平仓合约所谓未平仓合约是指交易者在成交后尚未作对冲交易或实物交投的期货合约。 5.当日估计成交量当天的实际成交量尚未算出，因此在行情表上只能报出一个估计的当天成交量。 6.转换系数是指可使中、长期国债期货合约的价格与各种不同息票利率的可用于交割的现货债券价格具有可比性的折算比率，其实质是将面值1美元的可交割债券在其剩余期限内的现金流量，用8%标准息票利率所折成的现值。 7.发票金额所谓发票金额，是指在中、长期国债期货的交割日，由买方向卖方实际交付的金额。 8.最便宜可交割债券所谓“最便宜可交割债券”，一般是指发票金额高于现货价格最大或低于现货价格最小的可交割债券。 9.股价指数期货是指以股票市场的价格指数作为标的物的标准化期货合约的交易。 10.恒生指数期货以恒生指数作为交易品种的期货合同。 11.交叉套期保值交叉套期保值，就是当套期保值者为其在现货市场上将要买进或卖出的现货商品进行套期保值时，若无相对应的该种商品的期货合约可用，就可以选择另一种与该现货商品的种类不同但在价格走势互相影响且大致相同的相关商品的期货合约来做套期保值交易。 12.利率相关性是指一种债券凭证与另一种债务凭证之间在利率变动上的一致性。 13.基差风险基差的不确定性被称为基差风险 14.合约内价差也称商品内价差，也被称为跨月套利，投资者在同一交易所，同时买进和卖出不同交割月的同种金融期货合约。 15.合约间价差所谓合约间价差，也称商品间价差，是指投资者在同一交易所或不同交易所，同时买进和卖出不同种类、但具有某种相关性的金融期货合约的套利活动。16.市场间价差是指投资者在不同交易所同时买进和卖出相同交割月的同种金融期货合约或类似金融期货合约，以赚取价差利润的套利行为。 17.基差收敛这种随着期货合约之到期日的逐渐临近，基差逐渐缩小的现象，叫做基差收敛。 18、理论基差是指金融工具的现货价格与金融期货的理论价格之间的差额。

金融期货与期权练习题和答案

金融期货与期权练习题一、单选题 1.投资者所拥有的今天的100元大于一周后的100元，这意味着（）。 A. 货币是有时间价值的 B.通货紧缩 C.预期利率下降 D.资金需求提高 2.本金100元，投资5年，年利率8%，每月复利一次，则实际年利率为（）。 A.8.3% B.8.24% C.8.5% D.7.24％ 3.假设下一年通货膨胀率为10%，如果一笔贷款要求的实际利率为4%，借款者的名义利率是（） A.15% B.15.4% C.14.4% D.14% 4.某零息债券3年到期，到期时，投资者得到1000元，现在售价为945元，请问该债券到期收益率为（） A.2.5% B.1.9％ C.2.87% D.3% 5.假定其它条件不变，关于利率期货交易说法正确的是（）。 A.当投资者预计市场利率上升时，买入国债期货规避利率上升风险； B.当投资者预计市场利率下跌时，卖出国债期货规避利率下跌风险； C.当投资者预计市场利率上升时，卖出国债期货规避利率上升风险 D.当投资者预计市场利率下跌时，可以卖出短期国债期货买入长期国债期货进行套利 6. 3年零息债券的久期为（） A.2.7 B.2 C.5 D.3 7.期权价格包含时间价值和内涵价值，请问下述哪种情况只包含时间价值，内涵价值为0（） A.看涨期权执行价格>标的物市场价格 B.看跌期权执行价格>标的物市场价格 C.看涨期权执行价格<标的物市场价格 D.以上都不是 8.下列关于衍生品市场的表述，正确的是（）。 A.衍生品都在交易所内交易 B.合理运用衍生品工具都可以达到风险对冲的目的 C.衍生品市场的买方和卖方的风险和收益都是对称的 D.衍生品市场的交易对象都是标准化的合约 9.当前黄金市价为每盎司600美元，一个一年期的远期合约的执行价格为800美元，一个套利者能够以每年10%的利息借助资金（连续复利），假设黄金存储费为0，且黄金不会带来任何利息收入。那么，某套利者下述哪种策略最为可行（）。 A．买黄金现货、同时卖出一年期的远期合约 B．卖黄金现货、同时买入一年期的远期合约 C．买黄金现货、同时买入一年期的远期合约 D．卖黄金现货、同时卖出一年期的远期合约 10.互换交易的表述，不正确的是（）。

期货期末测试题

期货期末测试题一、名词解释 1、结算价 2、交割 3、保证金制度 4、当日无负债结算 5、套期保值 6、期权 7、权利金 8、规避风险功能 9、价格发现功能 10、程序化交易

二、判断题（正确的打“√”，错误的打“╳”，填在空格内。） 1．期货价格分析不可以将基本分析与技术分析结合使用。（） 2．运用技术分析来确定入市时机。（） 3．开立账户实质上是确立投资者与期货公司之间建立的一种法律关系。（） 4．期货公司应当为每一个客户单独开立专门账户，设置交易编码，可以一户多码，但不可以多户一码。（） 5．商品期货通常采取实物交割方式，金融期货主要采用现金交割方式。（） 6．上海期货交易所铝期货合约的每日价格最大波动限制是不超过上一交易日结算价的5%。（） 7．以标的物所有权转移方式进行的交割为实物交割。（） 8．投机者是风险偏好者。（） 9．开盘价是指某一期合约每个交易日开始后的定价。（） 10．同一客户可以在不同期货公司会员处开仓交易。（） 11．中国金融期货交易所的结算会员只能为非结算会员进行结算。（） 12．套期保值者是期货市场存在的前提和基础，投机者、套利者的介入为套期保值者提供了更多的交易机会。（） 13．不同合约的持仓量，有合计持仓限额。（） 14．自然人客户可以委托他人办理开户手续。（） 15．客户在期货公司开户后，期货公司直接向期货交易所申请交易编码。（） 16．可用资金是指结算准备金。（） 17．开仓和持仓是一个意思。（） 18．价格在波动过程中的某一阶段，往往会出现两个或两个以上的最高点和最低点，用一条直线把这些价格最高点连接起来，就形成阻力线，把这些价格最低点连接起来，就形成支撑线。（） 19．蝶式套利是两个跨期套利的互补平衡的组合，可以说是“套利的套利”。（）20．套期保值实质上是以较小的基差风险代替较大的价格风险。（） 21．市场机制不健全是造成期货价格非理性波动最直接、最核心的因素。（） 22．我国期货的成交量都是采取“双边计算”。（） 23．期货行情图主要反映了某一时段某种期货合约的价格和成交量的走势。（） 24．最高价是指开盘后到当天交易结束后的最高成交价格。（） 2

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. The pattern of profits from the strangle is the following: Stock Price Range Payoff from Long Put Payoff from Long Call Total Payoff Total Profits ST ≤65 65- ST 0 65- ST 55 - ST 65 ＜ ST ＜70 0 0 0 -10 ST >70 ST-70 ST-70 ST-80 当 50=- ()()21()()r T t q T t p Xe N d Se N d ----=--- 21ln(/)(/2)()S X r q T t d T t σσ+-+-=- 21d d T t σ=-- 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 ------=-=

期货期权期末考试复习必备

1.1 When a trader enters into a long forward contract, she is agreeing to buy the underlying asset for a certain price at a certain time in the future. When a trader enters into a short forward contract, she is agreeing to sell the underlying asset for a certain price at a certain time in the future. 1.2. A trader is hedging when she has an exposure to the price of an asset and takes a position in a derivative to offset the exposure. In a speculation the trader has no exposure to offset. She is betting on the future movements in the price of the asset. Arbitrage involves taking a position in two or more different markets to lock in a profit. 1.3. In the first case the trader is obligated to buy the asset for $50. (The trader does not have a choice.) In the second case the trader has an option to buy the asset for $50. (The trader does not have to exercise the option.) 1.4. The investor is obligated to sell pounds for 1.4000 when they are worth 1.3900. The gain is (1.4000-1.3900) ×100,000 = $1,000. The investor is obligated to sell pounds for 1.4000 when they are worth 1.4200. The loss is (1.4200-1.4000)×100,000 = $2,000 1.5. You have sold a put option. You have agreed to buy 100 shares for $40 per share if the party on the other side of the contract chooses to exercise the right to sell for this price. The option will be exercised only when the price of stock is below $40. Suppose, for example, that the option is exercised when the price is $30. You have to buy at $40 shares that are worth $30; you lose $10 per share, or $1,000 in total. If the option is exercised when the price is $20, you lose $20 per share, or $2,000 in total. The worst that can happen is that the price of the stock declines to almost zero during the three-month period. This highly unlikely event would cost you $4,000. In return for the possible future losses, you receive the price of the option from the purchaser. 1.6 One strategy would be to buy 200 shares. Another would be to buy 2,000 options. If the share price does well the second strategy will give rise to greater gains. For example, if the share price goes up to $40 you gain [2000($40$30)]$5800$14200 ,?--,=,from the second strategy and only 200($40$29)$2200 ?-=,from the first strategy. However, if the share price does badly, the second strategy gives greater losses. For example, if the share price goes down to $25, the first strategy leads to a loss of 200($29$25)$800 ?-=, whereas the second strategy leads to a loss of the whole $5,800 investment. This example shows that options contain built in leverage. 1.7 The difference between Exchanges and Over-the-Counter Markets is that in an exchange markets buyers and sellers meet in one central location to conduct trades and in an over the counter market buyers and sellers in different location that are ready to buy or sell over the counter to any one who comes up and are willing to pay the price. 1.9 An exchange-traded stock option provides no funds for the company. It is a security sold by one investor to another. The company is not involved. By contrast, a stock when it is first issued is sold by the company to investors and does provide funds for the company. 1.10 If an investor has an exposure to the price of an asset, he or she can hedge with futures contracts. If the investor will gain when the price decreases and lose when the price increases, a long futures position will hedge the risk. If the investor will lose when the price decreases and gain when the price increases, a short futures position will hedge the risk. Thus either a long or a short futures position can be entered into for hedging purposes. If the investor has no exposure to the price of the underlying asset, entering into a futures contract is speculation. If the investor takes a lo ng position, he or she gains when the asset’s price increases and loses when it decreases. If the investor takes a short position, he or she loses when the asset’s price increases and gains when it decreases.

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