Value of FRA

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tarving_Banker

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I am having a hard time trying understand the intuition behind the formula for valuing FRA–(1 / (1+ Lg (h - g) ( h - g / 360 ) - 1 + FRA ( 0, h, m) ( m / 360 ) / ( 1 + Lg ( h + m - g ) ( h + m - g / 360 )
Can someone explain to me what does this formula mean and how we arrived at it? Thanks!
 
The first term is a discount factor applied to the notional amount, which is essentially the value of $1 discounted to the time of valuation by the appropriate rate. The appropriate rate corresponds to the time gap between contract settlement and time of valuation, or (h-g). This can also be viewed as the amount needed to invest today at the stated rate to earn enough interest to have the necessary notional amount at contract settlement (assuming you multiply the factor times the notional amount).
The second term discounts the FRA rate back to the time of valuation (g). Since the FRA rate “serves its term” beyond the date of contract settlement, we need to discount back from the end of the FRA rate term to the time of valuation. This is why the longer term rate is in the denominator, based on (h+m-g).
Subtracting the second term from the first term gives the value of the FRA to the long position, given all of the discounting/compounding based on prevailing market rates at time g.
 
There was a great post on this last year. I will search for it.
Hold tight!
 
swaptiongamma Wrote:
——————————————————-
> search for jscott24. He is my Derivatives GOD!
That is exactly what I did. The link is above.
 
I am kinda confused over the valuation of FRAs. It appears that there is a discrepancy between what is covered by Schweser and the official text. Using example 4 of from the text as an example, the market value of the FRA in part c is about 22k. However, that 22k was not discounted to t=20, as shown in Schweser. Any reason for that?
 
For Qtn 1 in page 60 of book 6 cfai text, the value of the long position is -30.44. So why is it that it is the short position paying the long position as mentioned in the solution? i thought it is the othre way round cos the value of the contract to the guy who longed it is -ve?
 
value of the long is negative means short owes the long that money in order to make the value of the future = 0 at initiation. At the initiation of a forward contract, the value should be 0
 
swaptiongamma Wrote:
——————————————————-
> value of the long is negative means short owes the
> long that money in order to make the value of the
> future = 0 at initiation. At the initiation of a
> forward contract, the value should be 0
Makes perfect sense now. Thanks…..you happen to have any idea about my earlier question about FRA valuation? ;)
 
HR - I completely follow the Schweser methodology.
I will dig into the CFAI FRA page you listed and make it Schweser compatible tomm morning. I am hitting bed not.
 
I honestly think the presentation for FRAs in Schweser is a lot easier. Beats memorising a heck load of formulae when a simple time diagram can solve it. But I jsut don’t understand why in Schweser the PV of the savigns is taken while in CFAI it does not tkae the PV of the savigns.
 
HydrogenRainbow
The CFAI text book has a lot of rounding issues in the Forwards chapter - esp. with relation to FRAs.
The actual number I got was -.001132835 using the method that JScott / Schweser used – for the Example 4c. so 22656.7 for the 20 Million notional. Can you please confirm the above number?
 
CPK - I do have a lot of rounding issues. I have not tried figuring out the forumulae in the CFAI text but when I was doing Questions 9 and 10, my answers were different because of rounding…Like the difference in interest rates will be something of the order of 10^-4, but multiply that by 10m, and the difference is huge.
Am kinda worried that this will happen for the exam….I won’t be able to find the answer!!!
 
cpk: using the schweser method the answer i got in 4c was -1.0915*10^-3*20m= -21830, almost 800 different although the difference in rate was something like, 4.1335x10^-5.
 
hydrogen – I do not have the rates with me (since I do not have the text book). Could you post the rates in 4 c both the initial and the later.
r30
r210
r10
r190
Thanks
 
Initially, at t = 0 the 30 day rate was 5.75%, 210 day rate was 6.15%. Then 20 days later, the 10 day rate is 5.45%, 190 day rate is 5.95%
 
r30 = 1 + .0575 * 30/360 = 1.004791667
r120 = 1 + .0615 * 210 / 260 = 1.035875
Initial: (1.035875 / 1.004791667 - 1) * 360/180 = 0.061870205 ==> 6.19%
r10 = 5.45% = 1.001513889
r190 = 5.95% = 1.031402778
New rate: (1.031402778/ 1.001513889) -1 * 360/180 = .059687417 = 5.97% approx
Value to long : [.059687417 * 180/360 - 0.061870205 * 180 / 360]
= -0.001091394
* 20 Million
= -21827.87
Current Value = -21827.87 / (1+.0595 * 190/360) = -21827.87/1.031402778 = -21163.29
they have rounded to -22000 somewhere…
 
swaption: I managed to get my question on the “discrepancy” between schweser and CFAI fixed by attempting to derive the equations in the cfai text. It’s the exact same thing, just that visualising it the way schweser does it makes life so much easier and frees up valuable brain space!! It looks like the reason why the difference I got was so huge because of rounding. The small difference in the interest rates makes a heck load of difference in the final answer when you multiply it by 20m.
 
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