Risk Latte - FE Problem Set #01
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FE Problem Set #01

Team Latte
Oct 20, 2005

Problem #1

Asset Swap Problem

You are a structured notes trader with SmallBank. An investor who holds a collared FRN (a floating rate note with a cap and a floor) wants to sell it to you. Comparable maturity FRNs of the same issuer are currently trading at LIBOR flat. You know of another counterparty, CrapFund, who would purchase this note on an asset swap basis at LIBOR + 0.20%. The details of the notes are:

 Issuer: BankBig Coupon: LIBOR + 0.125% Coupon Cap: 9.625% Coupon Floor: 5.125% Maturity: 9.5 years

You do a survey of the market and find out that a 9.5 year LIBOR Floor at 5% strike is currently being bid at 415 bp upfront and a 9.5 year LIBOR Cap at strike 9.50% is currently being offered at 500 bp upfront.

What should your bid price to the investor who wants to sell you the note?

Problem #2

(a)  What is the Excel's function for generating a random number between zero and one?

(b)  If you want to generate a sequence of random normal numbers (random numbers drawn from a normal distribution with mean zero and standard deviation of one) by Sobol sequence then what should be the function?

(c)  If you are writing a VBA function to calculate the value of a call option using a simple binomial tree then which of the following Excel library functions you are most likely to use:

=binomdist(),
=bin2dec(),
=negbinomdist()?

(d)  In Excel a linear regression (by ordinary least squares) can be done either using the Data Analysis function in the Tools menu (on too in the Toolbar) or using a library function. Describe both of them.

Questions:

1. What is type of option X that is plotted in chart 1 ?

2. What is the type of option Y that is plotted in chart 2 ?

3. Is vega of option X constant or it varies, and if so, explain the nature of variation of vega of X.

4. If option prices are quoted only until second decimal places (in Dollars and cents) then is it safe to say that vega of option X can be zero at some point in the map?

5. Calculate the vega of option Y.