left python
Hello, my literature for this "introductory math finance" is very poor and I can't get a good grip on bonds and various tasks related to them (because there's so many interesting formulas and I don't know any of them).
Look at the attachment, that's pretty much the only formula that was introduced to me and I can't understand parts of it and don't know how to use it in various tasks that don't actually need all of this information.
hexed lanceBOT
Hello, my literature for this "introductory math finance" is very poor and I can...
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green pantherBOT
@left python
quasi marlin
what are your questions?
left python
what are your questions?
what exactly are $\lambda$ and $k$?
velvet reefBOT
danilojonic
quasi marlin
missing context, no way for the reader to know what the notation means
left python
I understand the t is the duration for which the bond is active, r is the interest rate and n is the amount of times per year. I understand F is the initial (resale?) value of the bond, R is equal to F (unless resold at a different price) and P is the current value of the bond.
left python
missing context, no way for the reader to know what the notation means
\lambda is yield to maturity and k is the amount of times per year (with quarterly settlement it would mean k = 4).
quasi marlin
**danilojonic**
does that not answer this question, then?
left python
so I don't understand what exactly is yield to maturity. Is it supposed to be something against inflation?
left python
does that not answer this question, then?
I know what they're defined as but don't understand the true meaning of those words
quasi marlin
yield to maturity is roughly speaking the total return you can expect if you buy the stock/bond at its current price
assuming you hold the stock until it "matures"
left python
I know compound interest is calculated as $P\cdot (1+\frac{r}{n})^{n\cdot t}$ where P is the money we start with, r is interest and n is the amount of times that interest occurs in a year. So with that in mind this formula looks exactly the same but lambda is something similar to interest.
velvet reefBOT
danilojonic
quasi marlin
where is this formula taken from
left python
yield to maturity is roughly speaking the total return you can expect if you buy...
so if the bond value is the same in the beginning and the end and someone wants to sell me that bond for a different price, that yield to maturity in the formula will give me back the original worth of the bond?
left python
where is this formula taken from
which one? Original or this one
quasi marlin
Hello, my literature for this "introductory math finance" is very poor and I can...
this one
quasi marlin
the exponents dont make sense to me
this almost looks like something called "zero coupon price"
this is something I would expect
left python
this almost looks like something called "zero coupon price"
that is translated as initial redemption value
and then followed by the sum of all initial values of the coupons
Does it make sense that if some coupons get issued over time then a lesser number of them remains hence the bond loses on its resale value over time?
quasi marlin
nvm, I understand what's going on now
it is zero coupon price
t is the time it takes to mature, correct?
or is it kt?
left python
lets say $F = R = 1000$ and $t = 5$ years. then if we say $r = 0,05$ then $\frac{F\cdot r}$ is the value of a single coupon that gets paid back to you in a year. And now if we decide to sell that bond at $t = 4$, we would've already claimed the 3 initial coupons hence the bond value would decrease I think.
velvet reefBOT
danilojonic
Compile Error! Click the 
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(You may edit your message to recompile.)
left python
t is the time it takes to mature, correct?
correct
left python
or is it kt?
k is the amount of times yield to mature gets calculated during a single year
if it's quarterly, then it gets divided by 4 and time (in years) gets multiplied by 4 because that's the amount of times it would happen in total.
left python
nvm, I understand what's going on now
I have an example I have issue with:
For a bond of $3,000$ with a maturity of $4$ years, it is necessary to pay annual coupons of $2,500$ at the end of each of those $4$ years until maturity. Determine the duration of that bond if the profit until maturity is 15% with half-yearly calculation.
Okay so F = R = $3,000$, $t = 4$, coupon per year ($m = 1$) is $2,500$, profit until maturity is $\lambda = 0,15$ and $k = 2$. I don't understand what "the duration of that bond" means if the maturity is already set at $4$ years.
velvet reefBOT
danilojonic
left python
oh, you think time to mature = duration of bond?
yeah that's what I thought
left python
15% you mean
15% = 0.15 tho?
quasi marlin
you're missing the % sign here, confused me for a second
left python
The formula is $P = \frac{R}{(1+\frac{\lambda}{k})^{kt}} + \frac{F\cdot r}{m}\cdot \frac{1}{(1+\frac{\lambda}{k})^{\frac{k}{n}} - 1}\cdot (1 - (1+\frac{\lambda}{k})^{-kt}$ btw, made a few mistakes earlier
velvet reefBOT
danilojonic
left python
you're missing the % sign here, confused me for a second
check original text, it's there but latex didn't display it for some reason
velvet reefBOT
aL
quasi marlin
you have to write %
left python
ahh I didn't put it under the dollar signs
left python
**danilojonic**
so if I use this formula, I have pretty much everything except $r$ I think
velvet reefBOT
danilojonic
left python
and so I don't understand what that duration means in the context of the formula
quasi marlin
well, cassically, duration is defined as the change in value of a bond for a 1% change in interest rates
left python
I don't have P (current value) but if as it says in the task 2,500 is a coupon yearly, then that means $\frac{F\cdot r}{m} = 2,500$??
velvet reefBOT
danilojonic
left python
well, cassically, duration is defined as the change in value of a bond for a 1% ...
can you give me an example I still can't understand you properly?
quasi marlin
as an example: let's say interest rates decrease by 1% p.a and you have a 10 year bond with a duration of 5, the price is expected to increase by 5%
does that make sense?
quasi marlin
but duration is by definition a measure of price change in the presence of change in interest rates
left python
but duration is by definition a measure of price change in the presence of chang...
So what exactly are they asking for in the above formula?
The price difference between F and P? (F = bond issue price, P = bond current price)
