各位同學(xué)們大家好呀，我們又雙叒叕見面了呢，學(xué)姐今天也非常的想念遠(yuǎn)在英國留學(xué)的中國留學(xué)生們呢，學(xué)姐更加關(guān)心的是同學(xué)們在英國大學(xué)中的學(xué)習(xí)進(jìn)度與情況，其實(shí)由于國內(nèi)外學(xué)習(xí)形式差距的原因，很多同學(xué)都已經(jīng)感覺到了學(xué)習(xí)壓力，這種壓力其實(shí)是由多方面因素造成的，學(xué)姐今天就給KCL大學(xué)學(xué)習(xí)金融數(shù)學(xué)的同學(xué)們普及一下基礎(chǔ)知識(shí)，希望對同學(xué)們有所幫助。

KCL大學(xué)金融數(shù)學(xué)主要課程

概率論(15學(xué)分)

風(fēng)險(xiǎn)中性估價(jià)(15學(xué)分)

金融數(shù)學(xué)項(xiàng)目理學(xué)碩士(60學(xué)分)

選修課程

金融市場(15學(xué)分)

金融統(tǒng)計(jì)(15學(xué)分)

隨機(jī)分析(15學(xué)分)

不完全市場(15學(xué)分)

金融數(shù)學(xué)C++課程(15學(xué)分)

外來衍生品(15學(xué)分)

利率和信貸風(fēng)險(xiǎn)(15個(gè)信貸)

經(jīng)濟(jì)物理學(xué)(15學(xué)分)

機(jī)器學(xué)習(xí)(15學(xué)分)

金融和數(shù)據(jù)分析優(yōu)化(15學(xué)分)

金融中的數(shù)值和計(jì)算方法(15學(xué)分)

債券的公平市場價(jià)值

每當(dāng)一個(gè)企業(yè)，就此而言比如美國政府，需要籌集資金時(shí)，就會(huì)通過出售債券來籌集。A債券是一個(gè)承諾證書，聲明了協(xié)議的條款。通常該公司出售債券給面值每份1000美元學(xué)期

購買債券的人支付1000美元購買債券。

債券持有人被承諾兩件事：第一，他將在到期日取回他的1000美元，第二，他將每六個(gè)月收到一筆固定金額的利息。

隨著市場利率的變化，債券價(jià)格開始波動(dòng)。這些債券在市場上以市價(jià)買賣公平市場價(jià)值。

債券支付的利率是固定的，但是如果市場利率上升，債券的價(jià)值就會(huì)下降，因?yàn)橥顿Y在債券上的錢如果投資在其他地方可能會(huì)賺得更多。當(dāng)債券的價(jià)值下降時(shí)，我們說它的交易價(jià)格是打折。

另一方面，如果市場利率下降，債券的價(jià)值就會(huì)上升，因?yàn)閭F(xiàn)在的回報(bào)率高于市場利率，我們說它的交易價(jià)格是保險(xiǎn)費(fèi)。

金融數(shù)學(xué)的練習(xí)作業(yè)題目：

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.

上面這些都是學(xué)姐為大家辛辛苦苦找到的學(xué)習(xí)資料呦~同學(xué)們認(rèn)真觀看后感覺是否對自己的學(xué)習(xí)有所提升了呢，如果覺得學(xué)姐講的專業(yè)性知識(shí)并不是太滿意，學(xué)姐也不怪各位同學(xué)們，畢竟學(xué)姐沒有學(xué)習(xí)過這門專業(yè)，但是留求藝英國留學(xué)生輔導(dǎo)老師可以非常非常專業(yè)的呢，同學(xué)們?nèi)绻娴南胍鉀Q學(xué)習(xí)中的作業(yè)問題，學(xué)姐還是建議同學(xué)們直接找老師進(jìn)行線上一對一的答疑呦~