Assignment Netflix Bonds Case Study Solution
Introduction
In the year 2018, it presents that Netflix launched its largest junk-bond sales in this year and as an analyst, there is a need to analyze the overall situation and condition of the bond pricing and its standpoint of capital structure arbitrage. In this period the process follows by the organization is (CEV) process that helps to measure the risk-neutral and the interest rate follows a stochastic process uncorrelated with the stock.
Looking over the situation and the given data there is a need to compute together the closed-form solution and the finite difference method and to hedge against stock price and interest rate risks. Moreover, examine whether the structural model used in the valuation is justified and whether the bonds are still attractive when considering the cost of hedging jump risk.
Question 1
Cox-Ingersoll-Ross (CIR) Model
To begin, there is a need to select a range of grid points for an r x S grid and evaluate the closed-form solution for the Cox-Ingersoll-Ross zero coupon bond prices, Btn, T, for each date, tn, and r value over the life of the bond. Now, use a time step of Δt = 1/52 (one week). There are various values and data are given, which include that bond has a face value of $100 and assumes a coupon rate of 5.875%. The bond has a maturity date of November 15, 2028, and valuing the bond on November 2, 2018.
Using the parameters given in the problem, help to generate an r x S grid. Let's choose a range of 0.01 to 1.0 for r, with a spacing of 0.01. This gives us a grid of 520 x 10 points. It helps to evaluate the CIR zero coupon bond prices using the closed-form solution given above and store the results in a matrix. The resulting matrix will have 520 rows (one for each week) and 10 columns (one for each maturity). For S, let's choose a range of 0 to 600, with a spacing of 20. In the next step, use the Cox-Ingersoll-Ross model to produce the locked-method result for the bond prices by using the formula:
Btn, T = exp (-Atn-T-rn/2)*P1 (rn) +exp (-Atn-T-rn/2)*P2 (rn)
Where,
Atn-T = (1 - exp (-K*(T - tn)))/K
P1 (rn) = (1 - exp (-K*(T - tn)))/ ((K + rn) (s2/2K) (1 - exp (-K (T - tn))))
P2 (rn) = (1 - exp (-K*(T - tn)))/ (K + rn) * ((K*(exp (-K*(T - tn))) - s2/2K)/ (s2/2K))
After applying the “Cox-Ingersoll-Ross” (CIR) model to the given data. The model is used to calculate bond prices (Btn, T) for different values of the immediate interest rate (r) and the stock price (S) over 10 years (T). The parameters of the model are k (0.7) and r* (0.0345), and tn is a constant value of 31. For each value of r and S, the result presents the corresponding values of Atn - 1, P1(rn), P2(rn), and Btn, T.
Atn - 1 represents the periodic arrangement of interest rates, which is the accumulation of the interest rate over time. P1 (rn) and P2 (rn) represent the current worth of the interest rate over time, and the bond price is calculated using these values. The bond price decreases as the immediate interest rate increases, which is reflected in the negative values of P1(rn) and P2(rn). The calculated bond prices (Btn, T) decrease as the short-term interest rate increases.
Value the Bond Using (Finite Difference Method)
Next, look over the value of the bond using the finite difference method. This method involves discretizing the partial differential equation using the Crank-Nicolson scheme in each direction, and then alternating between the x-direction and y-direction to solve the resulting tridiagonal systems.
This process is unreservedly steady and second-order precise in period and space. Use the alternating direction-implicit algorithm described in Lecture Note 4.2. Using this algorithm, calculate the bond value at each grid point at each time step, and then interpolate to get the bond value at any given r and S................
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