Fixed Income and Derivatives Analysis: Market Scenarios

Financial Market Scenarios: Fixed Income and Derivatives

Sildavia: Term Structure and Yield Curve Construction

In Sildavia's financial market, we assume the existence of a series of zero-coupon bonds and conventional bonds. Each bond type presents specific traits:

• Zero-Coupon Bonds: Defined by spot rates and coupon interest rates.
• Conventional Bonds: Defined by specific characteristics (data assumed to be provided in an accompanying table).

Based on the provided data, the objective is to construct the TSIR (Term Structure of Interest Rates) and the Yield Curve for both kinds of bonds.

Moravia: Calculating Forward Rates

Considering the TSIR shown in Table 1, calculate the corresponding forward rates (r_t).

Furthermore, if the market involves an inverted yield curve situation (as shown in Table 2), deduce the implicit TSIR forward rates for zero-coupon bonds with spot rates under these conditions.

Genovia: Yield Curve and Discount Factors

Assuming the existence of interest rates in the money market, as well as treasury bonds in Genovia's financial market, presenting traits shown in the accompanying table, the task is to construct the Yield Curve and the corresponding discount factors.

Invertia 1: Floating Rate Deposit and Floor Contract Analysis

Invertia has made a floating rate time deposit of €400,000 in a financial institution. This deposit is indexed to the 6-month EURIBOR plus a spread of 0.25%, with semi-annual interest payments.

The company plans to withdraw €100,000 every semester to meet periodic payments. Fearing a drop in rates, but wishing to retain the benefit of a possible rise, Invertia decides to purchase a floor contract activated when the EURIBOR reaches a level of 4.5%.

The market fees, quoted in basis points (b.p.), for the sale of the floor are provided below (in an accompanying table). The company estimates the 6-month EURIBOR rates over the next few years are those indicated in the following table.

Required Calculations for Invertia's Floor Contract:

1. Determine the minimum rate of return that the company will receive for its investment.
2. Calculate the semi-annual interest payments from the investment, both if the floor contract is purchased and if it is not.
3. Compare the APR (Annual Percentage Rate) for the guaranteed investment versus the investment without the floor contract. Based on this data, comment on whether purchasing the floor contract is beneficial.
4. Draw a comparative graph illustrating the investment made with and without the floor contract, indicating the four points corresponding to each semester.

Invertia 2: Constructing an Interest Rate Collar

Instead of buying a floor contract, Invertia decides to construct an interest rate collar. This collar is activated when the EURIBOR falls below 4.5% or exceeds 5.25%.

The market fees used to calculate the premiums are the same as those previously provided for the floor contracts, along with those represented in the following table for the case of cap contracts (annual premiums in b.p.).

Based on these data and Invertia's expectations regarding the evolution of the 6-month EURIBOR (as seen in the previous exercise), estimate the following:

1. Determine the maximum and minimum rate of return if the company implements the collar.
2. Calculate the semi-annual interest payments from the investment, both if the collar is constructed and if it is not.