Numerical Valuation of Convertible Bonds

The software handles embedded puts and calls (including soft calls) and has limited support for multi-currency structures. The software uses a binomial lattice with the stock price as the only state variable. This means that all call and put features are regarded as options only on the stock price, and values that may attach to these because of the volatility of interest rates, exchange rates or the credit spread are ignored. The software does not use the warrant valuation approach which requires the volatility of equity (stocks plus warrants). Instead, it ignores the dilution effect and uses stock price volatility which is more readily available. Cash flows arising out of conversion into equity are discounted at the risk free rate as required by risk neutral valuation. Coupons and redemption cash flows are discounted at the cost of debt. The approach used is that of Tsiveriotis, K. and Fernandes,C. (1998) "Valuing Convertible Bonds with Credit Risk", Journal of Fixed Income, 8(2), 95-102.

This software was designed for educational use and no representation is made that it is suitable for commercial use. No warranty is provided that the software is error free.

Bond Details..

Maturity: Years Days

Annual Coupon Rate(Percent)

Coupon Frequency

Risk Free Rate(Percent)    continuous annual semiannual

Required Yield(Percent)    Continuous Annual Semi Annual

Redemption value per 100 face value

Current bond price
(The current bond price is used only if you want the software to compute the YTM (and OAS) of the bond. Otherwise, you can leave this field blank or leave it at its default value of 100.)

Stock Price and Conversion Details:

Stock Price

Country Discount on Stock Price (Percent)
This is useful when the convertible is issued/traded in one country while the stock is traded in another country. If the markets are segmented, a country discount/premium may exist. If these situations do not obtain, you should leave the field at its default value of 0. You may enter a negative number here to denote a country premium.

Stock Volatility (Percent)

Conversion Price

Known Dividends, if any 

   Amount          Date(time in years)

Expected Continuously Compounded Dividend Yield, if any    Continuous Annual Semi Annual

Maturity of Conversion Option Equals bond maturity Specified below
If maturity differs from bond maturity specify it here

Earliest Conversion Time
For an American option, this should be 0, for a European option this should be the maturity of the conversion option. The terms of the bond may imply a value in between these two.

Call provisions

Number of redemption call options to issuer (including soft calls) if any

For each call option you must specify the time period during which the call can be made, the minimum stock price at which the call can be made (0 if it is a hard call), and the redemption value if the bond is called.

    Min Time    Max Time     Minimum Stock Price      Redemption value
                              (for softcall)

Put options

Number of put options to investor

For each put option you must specify the time period during which the put can be exercised, and the put value either as the yield to put or as the put price.

Put value is specified as 

       Min Time       Max Time        Put value

Multi Currency Bonds

The software has limited support for dual currency bonds and other multi-currency structures. All calculations are done in the base currency which is the currency in which the stock price is specified. The software allows all other currencies to appreciate at constant known rates of appreciation.

To value multi-currency bonds, convert all currencies into the base currency at the current spot rate in the data above and specify the appreciation rates for the various currencies. (Use negative appreciation rates for depreciating currencies).

Give appreciation rates (percent per annum) for: 

Dividends               Coupons      Redemption Value 

Min Stock price      Redemption Value             Put Price 
for soft calls             when called

Specify the Compounding frequency for above rates: Continuous Annual Semi Annual

Partial Valuation

Value bond ignoring put option to Investor:

Value bond ignoring call option to Issuer:

Computational parameters

No of Lattice points
(multiple of coupon periods or numbers of months to maturity is recommended.)

Choose the outputs desired

  1. Input Data
  2. Lattice Parameters
  3. Full Lattice
  4. Option Results
  5. Bond Results, if any
  6. Yield to Maturity (YTM) and Option Adjusted Spread (OAS):
  7. If YTM/OAS Required, specify the following
    • Tolerance for bond price
    • Maximum number of iterations
  8. Estimate of Vega: None Use Forward Difference Use Central Difference
  9. Specify the Compounding frequency for interest rates in the output: Continuous Annual Semi Annual

    
This software was designed for educational use and no representation is made that it is suitable for commercial use. No warranty is provided that the software is error free.

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