FE Problem Set #19
Team Latte April 18, 2011
The following is an extract from the Certificate in Financial Engineering (CFE) sample test. Many of these questions will require use of Excel^{TM} spreadsheets and application of numerical techniques.
 A correlation matrix is given by:
The Cholesky matrix of the above correlation matrix is given by:
 Given a function :
Using the Gauss Legendre method (using 2 points) the value of this integral will be close to:
 2.35
 3.54
 5.23
 6.75
 Given a function:
Using a trapezoidal rule the value of the above integral will be close to:
 105
 125
 188
 235
 The nth order Bessel function is given by: The value of the function at and order, is:
 0.1657
 0.3641
 0.7563
 0.9215
 A vector of magnitude 10 along the original, positive x axis is rotated along a 45 degree counterclockwise direction. The new coordinate system will be represented by the column vector:
 A correlation matrix is given by:
The eigenvalues of the above matrix are given by:
 1.25 and 0.75
 0.50 and 1.50
 0.15 and 1.85
 0 and 2
 If is a one dimensional standard Weiner process, then which of the following stochastic differential equations represent a Bessel process of dimension for the variable :
 The difference in interest rate differential between two countries follows a drift less arithmetic Brownian motion (ABM) given by the following stochastic differential equation:
In the above equation, is the random variable (interest rate differential) following the ABM, is the volatility and is a standard Weiner process. If at time, , the interest rate differential is 1% and if the daily volatility of the interest rate differential is 0.50% then the probability that this differential will hit 3.5% at any point during the next one year is:
 46.25%
 65.35%
 75.28%
 82.15%
 The Laplace transform of a function, is defined as:
If, is the maturity of a financial derivative contract and at any point in time, , and are constant parameters, and at the boundary condition is given by then the price of this financial derivative contract, , is a function of the underlying asset, and is governed by the following partial differential equation (PDE):
Using the Laplace transform, as defined above, we can write the above PDE as Ordinary differential equation in as :
 If is an Ito diffusion then the Dynkin Operator is given by:
Answers
 (b)
 (c)
 (c)
 (b)
 (c)
 (a)
 (d)
 (c)
 (b)
 (a)
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