Approaches to Estimating Convertible Bond Delta for Hedging

Summary

The document surveys several ways to estimate a convertible bond’s delta for hedging. A rough option-based approximation treats the conversion price as the strike in a standard Black–Scholes pricer. For a more direct estimate, one reply proposes a symmetric finite difference: revalue the convertible after small upward and downward moves in the underlying stock and divide the price change by twice the stock-price move. Another reply suggests a rolling linear regression of convertible prices on stock prices, using the fitted slope and conversion price to form an approximate delta.

The answers do not provide a worked comparison or a general validation study. They note that callable and putable features complicate valuation, and one contributor warns that standard Black–Scholes hedging assumptions may not hold for convertibles. Commercial models are also mentioned as common practice. The regression method is presented as one practitioner’s approach, so its window choice, stability, and suitability for a particular bond remain unspecified.

Key ideas

• A rough delta approximation can use the conversion price as the strike in a Black–Scholes option calculation.
• A symmetric finite difference estimates delta by repricing the bond after small moves in the stock price.
• A rolling regression can estimate the relationship between convertible bond prices and stock prices.
• Callable and putable features can complicate delta estimation and hedging assumptions.
• The proposed methods are not accompanied by a general empirical comparison.

Tags

# How do I calculate the delta of a convertible bond?


# How do I calculate the delta of a convertible bond?












How can I find the delta of a convertible bond to be used for hedging?

## Answer by Tangurena (score 8)

https://quant.stackexchange.com/a/1054

Well, it takes a little more information than you've provided, but here are links to a pdf and associated excel spreadsheet that should help you answer your question.

## Answer by Brian B (score 5)

https://quant.stackexchange.com/a/1062

Tangurena's answer and links give the right idea. You can get a rough approximation by finding the conversion price $K$ and using that $K$ as the strike in a standard Black-Scholes option pricer.

In practice, most people work with 3rd party models such as the ones built into Bloomberg, Monis, or Kynex.

## Answer by ConvertibleProp (score 0)

https://quant.stackexchange.com/a/16914

To find the delta of a convertible you can apply the basic definition foe the derivative number : lim h->0, P(So+h)-P(So-h)/h, However because a lot of convertible are callable and putable you have to use this formula: P(So+h) - P(So-h) / 2h , with h=0.0001 for instance.

I a not a quant but, the BlackScholes PDE does not work for convertible because the delta hedged portfolio as defined in BS demonstration does not hold for a convertible bond…

## Answer by Rene Chan (score 0)

https://quant.stackexchange.com/a/69018

This is certainly late but in case someone else has the same question, you will need to do a rolling linear regression (StockPx; CBPx) over x days, retrieve the slope. Then multiply that slope to the conversion price. Roughly that is how I do it, and I got to the same result as Bloomberg with their regressed Delta.

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