Convertible Bond Exercise

This practical assignment requires students to calculate the price of a convertible bond and the value of its embedded option using a provided Excel file. Students must also calculate the Greeks (Delta, Vega, and Rho) to measure price sensitivity to changes in asset price, volatility, and interest rates, respectively. Additionally, they need to determine the effective duration of the bond. The calculations should be repeated for different asset prices ($15 and $85). The final submission is a two-page memo summarizing the results in tables and discussing the findings.

Convertible Bond Exercise
Due at Final
Download the Convertible Bonds Excel file.
Use the following inputs as the base case:
Find the price of the convertible bond and the value of the embedded option.

The Greeks
The Greeks measure price sensitivity to changes in the inputs. They can be estimated as follows.
Suppose that P(x) is a formula that finds the price of a security for an input value of x, with all of
the other inputs using the given values. Then, the sensitivity to x when x = x 0 can be estimated
as follows:
P ( x0 + Δx ) −P ( x0−Δx )
2 Δx
Delta () measures sensitivity to changes in asset price (x=S). Vega (v) measures sensitivity to
changes in volatility (x=). Rho () measures sensitivity to changes in interest rates (x=rf). Find
the Delta, Vega and Rho for this convertible bond. For your calculations, use the following:
Greek Change in Input
Delta () $0.25
Vega (v) 0.25%
Rho () 0.10%
For the Rho calculations, don’t forget to change both the Risk Free rate and the Yield by the
change in rates.
.
In addition, find the Effective Duration (Deff). This is equal to the percent change in price for a
small change in yield. You can calculate it using the following;
Deff =− ρ
BondPrice
Repeat the process for asset prices equal to $15 and equal to $85.
Write a memo (maximum of two pages, not including cover page, tables and charts) showing
your results (in tables) and discussing your results. Hand in a hard copy in class.