［2008］Topic 31: The Science of Term Structure Models相关习题 principles, backward, interest, multiple, possible

Baran

 

AIM 3: Explain how the principles of arbitrage pricing of derivatives on fixed income securities can be extended over multiple periods.

 

1、With respect to interest rate models, backward induction refers to determining:

A) convexity from duration.

B) duration from convexity.

C) one portion of the yield curve from another portion.

D) the current value of a bond based on possible final values of the bond.

vknk0977

北京最专业的特大幅面全开菲林输出公司 最大全开菲林输出尺寸1.50米X3.00米 联系人:张鹏 手机:15801015815 本全开菲林输出公司位于北京市国贸CBD商业区，拥有可输出幅面1.50米X3.00米胶片 的激光照排机两台、扫描精度可高达2400-3600DPI。 重复对位精度可达±10UM。客户遍布北京、河北、浙江、上海、江苏、广东、山东、 福建等全国各地。 我们的服务优势：

        1、硬件设施好：我司采用瑞士先进电子技术，菲林输出网点圆实，平网均匀，渐变平滑， 输出效果可与网屏5055相媲美，输出幅面特大。

        2、技术积累深：公司技术员从业长达四年，在特大幅面输出上有着深厚功底，能处理QUARK EXPRESS 等国内广告业十分陌生的软件。 在胶印上，由于我们成功的解决了大包装用小菲林拼接有线条、尺寸有一定的误差的难题，省却 了手工拼接菲林这样费时易出错的工作，也省却了给最终客户就线条问题解释半天的麻烦事情， 保持最终用于晒版的菲林非常干净，将使贵公司的印刷质量和效率进一步提高，从而大大加强贵 公司在业界的竞争力。我们能根据包装印刷的特点，熟练把握专色、四色等印刷要求，特别是一 些重要部位如叠印、镂空、压印等处理，通过与贵公司设计师沟通，确保优质菲林的输出。 在丝印上，传统彩色丝网印刷的分色网版制作，尤其是遇到超大型网印时，无非是采用手工菲林 拼版，放大菲林或投晒网版。手工拼接菲林，难以保证不露拼接痕迹，并且尺寸有一定误差，并 且易出差错。放大菲林及投晒网版，由于受像距、镜头球面等客观因素的制约，易造成网点大小 不匀，边缘网点不全等，使网版质量难以控制,给丝网印刷造成很多麻烦。我们通过大量试验， 不仅给丝印公司解决了拼版有细线，放大时候网点大小不匀等问题，省却了计算像距、手工刮网 点的麻烦事情，而且还通过多次与丝印公司沟通，成功地在菲林输出之前就解决了丝印龟纹现象， 将使贵公司的印刷质量和效率进一步提高。

        3、公司自备发电机，电力紧张时也能正常工作，从而保证生产运行；24小时不间断营业， 每个班次都配专业出片师、检查人员，确保胶片质量。

        联系人:张鹏 手机:15801015815

Baran

 

2、With respect to bond investing, reinvestment risk is a very important component of what other type of risk?

A) Default risk.

B) Liquidity risk.

C) Call risk.

D) Downgrade risk.

Baran

 

The correct answer is C

Call risk is composed of three components: the unpredictability of the cash flows, the compression of the bond’s price, and the high probability that when the bond is called the investor will be faced with less attractive investment opportunities. This latter risk is reinvestment risk. Reinvestment risk is not a directly related to any of the other choices.

Baran

 

3、If a put feature expires on a bond so that it becomes option-free, then the curve depicting the price and yield relationship of the bond will become:

A) more convex. 

B) a straight line. 

C) less convex. 

D) inversely convex. 

Baran

 

 The correct answer is C

 

When the option expires, the prices at the lower end of the curve will become lower. This will make the curve less convex.

Baran

 

The correct answer is B

 

The option-free bond price tree is as follows:

 100.00

A ==> 99.74

 

99.81  100.00

 100.16 

 100.00

As an example, the price at node A is obtained as follows:

PriceA = (prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2) = (0.5 * (100 + 3) + 0.5 * (100 + 3))/(1 + 0.0653/2) = 99.74. The bond values at the other nodes are obtained in the same way.

The calculation for node 0 or time 0 is

0.5[(99.74 + 3)/(1+ .063/2) + (100.16 + 3)/(1 + .063/2)] =

0.5 (99.60252 + 100.00969) = 99.80611

Baran

 

AIM 7: Explain the impact of embedded options on a fixed-income security’s price.

1、Mortgages are subject to prepayment when interest rates fall. This results in duration extending when interest rates rise, but shortening when interest rates fall. This characteristic is called:

A) positive convexity.

B) negative duration.

C) negative convexity. 

D) reverse duration.

Baran

The correct answer is C

 

An instrument that declines more in value when interest rates rise than it increases when interest rates fall is said to have negative convexity. Mortgage-backed securities have this characteristic because of the mortgagor’s option to prepay.

Baran

 

10、Why is the backward induction methodology used to value a bond rather than a forward induction scheme?

A) The convexity of a bond changes over time.

B) The price of the bond is known at maturity.

C) Future interest rate changes are difficult to forecast.

D) The mathematical properties of a forward difference scheme are not tractable.