Convertible Bond

ORE defines the product as follows:

A convertible bond is a bond, that can be converted to a prespecified number of shares. The shares are usually from the bond issuer, but it is also possible that the shares are from a different issuer (exchangeables). In addition, the share currency can be different from the bond currency in both cases (cross-currency convertibles).

Source: ORE User Guide, Products catalogue, convertiblebond.tex.

ORE describes the call and put rights as follows:

The bond might be callable by the issuer (typically in American style) and / or puttable by the investor (typically in Bermudan style).

Source: ORE User Guide, Products catalogue, convertiblebond.tex.

ORE describes forced conversion as follows:

If a soft call is exercised, the investor has the right to convert the bond into shares instead of accepting the payment from the issuer call ("forced conversion").

Source: ORE User Guide, Products catalogue, convertiblebond.tex.

ORE describes the detachable form as follows:

For a detachable or stripped convertible bond the optionality can be traded separately from the bond. We set the NPV for a detachable convertible bond to the difference of the convertible bond npv and the bond floor npv, where the bond floor denotes the underlying vanilla bond stripped of any optionality.

Source: ORE User Guide, Products catalogue, convertiblebond.tex.

A convertible bond is a bond with a stock option attached. The investor receives coupons and the return of principal, exactly like a bond. The investor can also hand the bond back and receive shares instead. The conversion right is worth more when the share price rises. The bond pays a lower coupon than a plain bond of the same issuer because of that right.

The trade type is ConvertibleBond. The ConvertibleBondData block names the bond and its quantity. SecurityId is typically the ISIN of the underlying bond with the ISIN: prefix. BondNotional is the notional of the underlying bond in its currency. The optional CreditRisk flag decides whether credit risk shows on the product.

The bond terms can come from reference data, or be given explicitly in the trade. ORE states the relationship between the two:

All fields that are not given in the trade XML are filled up with the information from the reference data if available in the reference data. In other words, if reference data is given, the trade xml can still be used to overwrite the information partially, if this seems appropriate.

Source: ORE User Guide, Products catalogue, convertiblebond.tex.

In the explicit form, the block carries five sub-blocks. BondData holds the vanilla part of the bond. CallData and PutData hold the call and put terms; when they are not given, no calls or puts are present. ConversionData holds the conversion terms and must always be given, even when no conversion rights are present; an empty conversion date list expresses that case. DividendProtectionData holds the dividend protection terms. Detachable is a flag, false by default; when it is true, the trade represents the embedded optionality only, that is the difference between the full convertible bond and the bond floor.

The call and put data are lists of exercise rights. Styles holds the exercise styles, American or Bermudan. Bermudan also defines European exercises, namely as a Bermudan exercise with a single exercise date. ScheduleData holds a schedule of exercise dates for Bermudan exercises, or start and end dates for American exercises. Prices holds exercise prices in relative terms: a price of 1.02 means the amount paid on exercise is 1.02 times the current notional of the bond, plus accrued interest when the price type is clean. PriceType gives the flavour in which the prices are quoted. Lists in the sub-nodes can be explicit lists or use the startDate attribute. An explicit value list can be shorter than the list of dates; the last value then applies to the remaining dates.

The trade type supports perpetual schedules. Omitting the EndDate in a schedule makes the schedule perpetual. Only rule based schedules can be perpetual. This applies to the bond leg, the call and put data, the conversion data, the conversion resets and the dividend protection schedule.

The conversion ratio is the number of shares received for one bond, that is for the bond face value. The conversion value, also called the parity, is the ratio times the share price. The number of shares delivered on conversion is the bond notional divided by the conversion ratio; the ratio lives in the underlying bond reference data.

The bond reference data in ORE is typically set up with a face value of one, even when the market quotes the bond at 100 or 100,000. The value of a convertible bond splits into the bond floor and the embedded optionality. The floor is the vanilla bond stripped of any optionality. The optionality is a conversion right, long for the investor, an issuer call, short for the investor, and an investor put, long for the investor.

A hard issuer call pays the call price times the current notional, plus the accruals when they are due. A call price of 1.00 is a call at par; 1.02 is a call at 102 percent. A soft call can only be exercised when the share price on the exercise date is above the conversion price times a trigger. The issuer call always leaves the investor the choice to convert instead, which is the forced conversion.

• The share price of the underlying equity, through the conversion right.
• The volatility of the equity.
• The interest rates, which price the bond floor and discount the cash flows.
• The credit of the issuer and the recovery value on default.
• The FX rate, for cross-currency convertibles.
• The terms of the deal: the conversion ratio, the call and put schedules, the triggers and the dividend protection.

The value moves like a bond at low share prices and like the equity at high share prices. Between the two, the conversion right, the call rights and the credit of the issuer all compete.

As the share price moves, the investor compares the conversion value with the bond floor. When a soft call is in the money, the issuer can force a conversion and end the bond. The conversion ratio can change over time through dividend protection and reset features. When a dividend is paid, the protection can adjust the ratio to compensate the investor. Near maturity the investor decides between redemption and conversion. On a default of the issuer, the claim is bounded by the recovery of the bond and the conversion value.

A convertible bond is hybrid financing. The issuer pays a lower coupon than on a plain bond, because the conversion right is valuable. The investor keeps the downside protection of a bond and gains the upside of the equity. In ORE Studio a customer books convertible bonds to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a convertible bond whose terms are set up in reference data:

<Trade id="ConvertibleBond">
  <TradeType>ConvertibleBond</TradeType>
  <Envelope>...</Envelope>
  <ConvertibleBondData>
    <BondData>
      <SecurityId>ISIN:XS0451905367</SecurityId>
      <BondNotional>1000000.00</BondNotional>
    </BondData>
  </ConvertibleBondData>
</Trade>

Source: ORE User Guide, Products catalogue, convertiblebond.tex, listing Convertible bond set up using reference data. The source also shows the explicit form, in which BondData, CallData, PutData, ConversionData and DividendProtectionData are given with their details and Detachable is set to false.