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Calculating Convertible Bond Parity Across Currency Denominations

Article Quant Q&A · Author: Dzsonibigud
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Summary

Convertible bond parity compares the value of the shares obtainable on conversion with the bond’s face value. When the stock and bond are quoted in different currencies, the share value must first be converted into the bond’s currency using the relevant exchange rate, then divided by face value to express parity as a percentage. The discussion illustrates this with a bond denominated in euros and shares priced in Hungarian forints.

The example estimates parity from a conversion ratio, a historical share price, an exchange rate, and face value, producing a percentage of par. Its accuracy depends on matching the stock and foreign-exchange observations to the same date and using the correct quote convention. A separate answer notes that an unusually high coupon after a call date may make the bond likely to be called, affecting how much detailed valuation is useful. The exchange gives an illustrative calculation, not a general bond-pricing model or a full treatment of call risk.

Key ideas

  • Convertible parity is the conversion value of the shares relative to the bond’s face value.
  • Convert the share price into the bond’s currency before calculating parity.
  • The conversion ratio scales the share value delivered upon conversion.
  • Use contemporaneous stock and exchange-rate observations for a consistent estimate.
  • A high coupon after a call date may influence whether detailed modeling is worthwhile.

Tags

Fixed incomeOptionsForexDerivatives pricing
Full text
# How to calculate conversion parity for convertible bond?


# How to calculate conversion parity for convertible bond?












Can someone explain how can I calculate the parity of this convertible bond?

I know the formula is Current price of common stock x Conversion Ratio, but it doesn't seem to be right in this picture.

## Answer by Brian B (score 2)

https://quant.stackexchange.com/a/21007

That company is probably traded on the Hungarian stock exchange in Hungarian forint. You would have to multiply the stock price by the euro/forint rate to find parity.

Note that in this case, the bond has a huge coupon (Euribor+5.5%) after the "call date", effectively forcing the call and making the bond a 4% maturing in 2016. There's no real point to modeling it any other way.

## Answer by user010010001 (score 1)

https://quant.stackexchange.com/a/21030

The parity in this picture is given as the percentage of the face value. The stock price is given in HUF. I checked the stock price, It reached 16600 in september 2013. The EURHUF that time was something like 299, but we should now the exact time this picture was taken. So we have everything to calculate the parity:

$\text{Parity} = \text{Conv Ratio} \cdot \frac{\text{Stock price}}{\text{EURHUF}}:\text{Face value} =984.8326 \cdot \frac{16635}{299.03} :100000 =54,8 \%$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.