## QUANTS

saichitale1994
Good Student
Posts: 12
Joined: Mon Jun 15, 2015 3:48 am

### Re: QUANTS

A financial institution has agreed to pay 6-month LIBOR and receive 8% per annum (with semi-annual) compounding on a principal of \$100 million. The swap has a remaining life of 1.25 years. The LIBOR rates with continuous compounding for 3-month, 9-month, and 15-month maturities are 9%, 9.5%, and10% respectively. The 6-month LIBOR rate at the last payment date was 9.2% (with semiannual compounding). What is the value o f the swap to the financial institution?
a. -1.854 million dollars Incorrect
b. -4.566 million dollars Incorrect
c. -2.854 million dollars Correct
d. +1.854 million dollars Incorrect
Sol. We can value an interest rate swap either in terms of bond prices or in terms of FRA’s. Let’s use the FRA approach here.
Here the institution receives a fixed cash flow of 4 million (100x0.08x0.5) semi-annually but the cash outflow is floating dependent on the LIBOR. The floating rate of the first outflow i.e. at T=0.25 years from now was the 6-month LIBOR rate at the last payment date i.e 9.2%.
The next outflow which occurs at time 0.75 years from now is dependent on the current LIBOR which can be calculated using the 3-month and 9-month LIBOR rates. i.e
(0.75x9.5-0.25x9)/0.5=9.75% with continuous compounding or 9.99% with semi-annual compounding.
Similarly the next cash outflow occurs at time = 1.25 from now and the floating rate is determined similarly. i.e.
( 1.25x10-0.75x9.5)/0.5 = 10.75% with continuous compounding = 11.044% with semi-annual compounding

I did not get how to find the cash outflow.

saichitale1994
Good Student
Posts: 12
Joined: Mon Jun 15, 2015 3:48 am

### Re: QUANTS

If Y = ln(X) and Y is normally distributed with zero mean and 2.33 standard deviation. What is the expected value of X?
a. 15.10 Correct
b. 3.21 Incorrect
c. 227.90 Incorrect
d. 1 Incorrect

mayankmundhra30
Good Student
Posts: 23
Joined: Sat Jun 25, 2016 8:13 am

### Re: QUANTS

Hi
i have some doubts in the quant part of FRM 1 exam.The doubts are:

1) Could you please explain why multi collinearity result in type 2 error?
2) For two tail F-test why the critical value is given by F Alpha/2 and not simply F alpha?
3) What do you mean by statistical significant?
4) Could you please explain Gauss Markov Theorem and GARCH Model?
5) Is there any relation between Type1 error and Type2 error value?

edupristine
Finance Junkie
Posts: 722
Joined: Wed Apr 09, 2014 6:28 am

### Re: QUANTS

Hi Mayank

4)Gauss Markov Theorem- A Gauss Markov Theorem is proves that if the error terms in a multiple regression have the same variance and are uncorrelated, then the estimators of the parameters in the model produced by least squares estimation are better than any other unbiased linear estimator ( having lower dispersion about the mean). it defined as if people generally have about the same variance in height at each age, then the "ordinary least squares" estimate of the mean (the slope and offset of the average line) would give you the best unbiased estimate of how people's height varies with age on average.

GARCH Model- The generalized autoregressive conditional heteroskedasticity (GARCH) process is an econometric term developed in 1982 by Robert F. Engle, an economist and 2003 winner of the Nobel Memorial Prize for Economics, to describe an approach to estimate volatility in financial markets. There are several forms of GARCH modeling. The GARCH process is often preferred by financial modeling professionals because it provides a more real-world context than other forms when trying to predict the prices and rates of financial instruments.