各位同学们大家好呀，我们又双叒叕见面了呢，学姐今天也非常的想念远在英国留学的中国留学生们呢，学姐更加关心的是同学们在英国大学中的学习进度与情况，其实由于国内外学习形式差距的原因，很多同学都已经感觉到了学习压力，这种压力其实是由多方面因素造成的，学姐今天就给KCL大学学习金融数学的同学们普及一下基础知识，希望对同学们有所帮助。

KCL大学金融数学主要课程

概率论(15学分)

风险中性估价(15学分)

金融数学项目理学硕士(60学分)

选修课程

金融市场(15学分)

金融统计(15学分)

随机分析(15学分)

不完全市场(15学分)

金融数学C++课程(15学分)

外来衍生品(15学分)

利率和信贷风险(15个信贷)

经济物理学(15学分)

机器学习(15学分)

金融和数据分析优化(15学分)

金融中的数值和计算方法(15学分)

债券的公平市场价值

每当一个企业，就此而言比如美国政府，需要筹集资金时，就会通过出售债券来筹集。A债券是一个承诺证书，声明了协议的条款。通常该公司出售债券给面值每份1000美元学期

购买债券的人支付1000美元购买债券。

债券持有人被承诺两件事：第一，他将在到期日取回他的1000美元，第二，他将每六个月收到一笔固定金额的利息。

随着市场利率的变化，债券价格开始波动。这些债券在市场上以市价买卖公平市场价值。

债券支付的利率是固定的，但是如果市场利率上升，债券的价值就会下降，因为投资在债券上的钱如果投资在其他地方可能会赚得更多。当债券的价值下降时，我们说它的交易价格是打折。

另一方面，如果市场利率下降，债券的价值就会上升，因为债券现在的回报率高于市场利率，我们说它的交易价格是保险费。

金融数学的练习作业题目：

Conditional expectations

1. An urn contains five envelopes: two blue and three red. The blue contain

respectively 50 dollars and 150 dollars,whilst the red contain respectively

100,200 and 500 dollars. We randomly draw an envelope out of the urn.

a) Determine the expected value of the contents of the envelope.

b) Determine the conditional expected value of the contents of an envelope

given that it is blue.

c) Determine the conditional expected value of the contents of an envelope

given that it is red.

We can now regard the conditional expected values of the contents as a random

variable X = X(ω) on the sample space {blue,red}:

X(ω) = E[contents | colour of envelope is ω]

d) What is X(ω) for each of the two values {blue,red} on ω?

e) Compute E[X] by regarding the random variable X(ω). Compare the

answer to the answer in a).

2. Let us consider the following game: A player tosses a coin four times. There

are sixteen possible outcomes: (heads,heads,heads,heads),(heads,heads,

heads,tails) etc. One gets 10 dollars every time heads turns up,whereas tails

does not pay at all. Also,if heads turns up all four times,one gets 100 dollars.

1

Consider the situation after two toss ups: The sample space consists of

four possible cases:

{ω1,ω2,ω3,ω4}

= {(heads,heads),(heads,tails),(tails,heads),(tails,tails)}.

Let X be the random variable “Money won after four toss ups” and determine

the conditional expected value after two toss ups E[X | ω],where ω can take

the four values ω1,. . .,ω4.

Forwards and Futures

Here we assume interest is continuously compounded.

1. A share is valued at present at 80 dollars. In nine months it will give a

dividend of 3 dollars. Determine the forward price for delivery in one year

given that the rate of interest is 5% a year.

2. A share is valued at present at 80 dollars. In nine months it will give a

dividend of 4% of its value at that time. Determine the forward price for

delivery in one year given that the rate of interest is 5% a year.

3. The current forward price of a share to be delivered in one year is 110 dollars.

In four months the share will give a dividend of 2 dollars and in ten months

will give a dividend of 2% of its value at that time. Determine the current

spot price of the share given that the rate of interest is 6% a year.

4. The exchange rate of US dollars is today 8.50 SEK per dollar. The forward

price of a dollar to be delivered in six months is 8.40 SEK. If the Swedish six

month interest rate is 4% a year,determine the American six month interest

rate.

2

5. The forward price of a US dollar the first of August with delivery at the end

of December is 0.94630 Euros. The forward price of a dollar to be delivered

at the end of June next year is 0.95152 Euros. Assuming a flat term structure

for both countries and that the Euro interest rate is 4% a year—what is the

American rate of interest?

6. Determine the forward price of a bond to be delivered in two years. The bond

pays out 2 Euros every 6-months during 4 1

2

years (starting in six months),and

102 Euros after five years. Thus the bond is,as of today,a 5-year 4%-coupon

bond with a coupon dividend every six months with a 100 Euro face value.

The bond is to be delivered in two years immediately after the dividend

has been paid. The present term structure is given by the following rates of

interest (on a yearly basis)

6 months 5.0% 18,24 months 5.6%

12 months 5.4% 30–60 months 5.9%

7. A one-year forward contract of a share which pays no dividend before the

contract matures is written when the share has a price of 40 dollars and the

risk-free interest rate is 10% a year.

a) What is the forward price?

b) If the share is worth 45 dollars six months latter,what is the value of the

original forward contract at this time? If another forward contract is to

be written with the same date of maturity,what should the forward price

be?

Answers: 1) 81.06 2) 80.74 3) 107.67 4) 6.37% 5) 2.90% 6) 94.05 7a)

44.207 7b) 2.949 dollars,47.307 dollars.

上面这些都是学姐为大家辛辛苦苦找到的学习资料呦~同学们认真观看后感觉是否对自己的学习有所提升了呢，如果觉得学姐讲的专业性知识并不是太满意，学姐也不怪各位同学们，毕竟学姐没有学习过这门专业，但是留求艺英国留学生辅导老师可以非常非常专业的呢，同学们如果真的想要解决学习中的作业问题，学姐还是建议同学们直接找老师进行线上一对一的答疑呦~