Bond Value Calculator (BVC) User's Guide

Bond Value Calculator makes it possible to estimate the prices of bullet and callable bonds using the arbitrage-free binomial tree of risk-free short rates model.

Input parameters.

T(i) - time intervals in 6 months increments. (T(1) 1-6 months, T(2) 7-12 months, and so on.)

Spot(i) - observable spot rate (as a percentage) at the end of a time interval T(i).

Payment(i) - coupon and/or principal that will be paid at the end of time interval T(i).

Exercise Price(i) - price at which the call provision of a callable bond will be exercised at the time interval T (i).

Probability(i) - probability (as a percentage) that rates will move up at time interval T(i).

Volatility(i) - volatility (percentage) of rates at a time interval T(i).

1. Entering data

-Enter parameters Spot(i), Volatility(i), and Probability(i) into the main form.

-Click on the "Next" button. The second form will appear.

-Enter parameters Payment(i) and Exercise Price(i) into the second form.

2. Calculation

-Click on the "Calculate" button. The estimated price of the bond will be shown in the message box.

3. Calibration

-The user may calibrate a model by means of changing the calibration parameters, probability(i) or volatility(i)

Example 1 (Bullet Bond)

Estimate the price of a bullet bond with a term of five years, coupons payment of 3% semiannually and the principal -100.

1. There are 10 time intervals (5 years * 2)

2. Probability(i)=50 for I=1,10

3. Volatility(i)=10 for I=1,10

4. Payment(i)=3 for I=1,9 (coupons) and Payment(10)=103 (coupon+principal).

The calculated price of the bond based on these data is 80.037.

Example 2 (Callable Bond)

Estimate the price of a callable bond with a term of five years, coupons payment of 3% semiannually and principal -100. An issuer of the bond may call it back at the time interval T(9) at 90. It is assumed that volatility will be 10% and probability of the rates moving up will be 50% during the whole term; the observable spot rates are the same as in Example 1

1. There are 10 time intervals (5 years * 2)

2. Probability(i)=50 for I=1,10

3. Volatility(i)=10 for I=1,10

4. Payment(i)=3 for I=1,9 (coupons) and Payment(10)=103 (coupon+principal)

5. An issuer of the bond may call it back at the time interval T(9) at 90.

The calculated price of the bond based on these data is 78.798

Example 3 (Calibration)

The observable price of a bullet bond with a term of five years, coupons payment of 3% semiannually and principal -100 is 80.309.

It is assumed that volatility will be 10% and probability of the rates moving up will be 50% during the whole term; the observable spot rates are the same as in Example 1.

It is expected that volatility during intervals T(9) and T(10) will be higher than 10%.

Based on expectation of higher volatility at the time intervals T(9),T(10), the user can change these parameters until the calculated price of the bond is close to the observable price. In this case, the calibrated value of the volatility will be 20%.