1. What is SHx (the sensitivity of H to small changes in x) when H =...

1. What is S^H_x (the sensitivity of H to small changes in x) when H = −5/x and the nominal value of x = 8?

2. What is S^H_x (the sensitivity of H to small changes in x) when H = x³/(x − 1) and the nominal value of x = 4.1?

Expert Solution

Manojponduru answered 1 year ago

When is duration appropriate for estimating the bond’s sensitivity to changes in interest rates.

1) Define a sequence of polynomials H n (x ) by H 0 (x )=1, H...

1) Define a sequence of polynomials H n (x ) by H 0 (x )=1, H 1 (x )=2 x , and for n>1 by H n+1 (x )=2 x H n (x )−2 n H n−1 (x ) . These polynomials are called Hermite polynomials of degree n. Calculate the first 7 Hermite polynomials of degree less than 7. You can check your results by comparing them to the list of Hermite polynomials on wikipedia (physicist's Hermite polynomials). 2)...

Compute growth function and VC dimension H ={h: R -> {-1, +1} | h(x) = 1D(x)...

Compute growth function and VC dimension H ={h: R -> {-1, +1} | h(x) = 1D(x) where D is a finite set of R}

Given that h(x) = x.sinx . Find the root of the function h(x) = 1, where...

Given that h(x) = x.sinx . Find the root of the function h(x) = 1, where x is between [0, 2] using substitution method.

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

Show that Var(x-a/)=1/h^2 Var(x)

1a. Which of the following does the sensitivity of the bond price to the changes in...

1a. Which of the following does the sensitivity of the bond price to the changes in interest rates depend on? Maturity of the bond Coupon rate Both maturity of the bond and the coupon rate None `1b. Which of the following is correct when the Coupon Rate of a bond is equal to its Yield to Maturity? The price of this bond is equal to its face value. The price of this bond is higher than its face value. The...

Which of the following does the sensitivity of the bond price to the changes in interest...

Which of the following does the sensitivity of the bond price to the changes in interest rates depend on? Maturity of the bond Coupon rate Both maturity of the bond and the coupon rate None Which of the following is correct when the Coupon Rate of a bond is equal to its Yield to Maturity? The price of this bond is equal to its face value. The price of this bond is higher than its face value. The price of...

PART A: Suppose X and Y are independent. Show that H(X|Y) = H(X) . (H represents...

PART A: Suppose X and Y are independent. Show that H(X|Y) = H(X) . (H represents entropy i think) PART B: Suppose X and Y are independent. Show that H(X,Y) = H(X) + H(Y) PART C: Prove that the mutual information is symmetric, i.e., I(X,Y) = I(Y,X) and xi∈X, yi∈Y

Phase changes also involve changes in enthalpy (H). Assume an ideal system: Calculate the total H...

Phase changes also involve changes in enthalpy (H). Assume an ideal system: Calculate the total H to bring m=46.884g of ice at T=0 deg C to steam at T=100 deg C. Show your work. (Hint: Cp values vary based on states of matter and energy is required to execute a phase change.)

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