Callable Bond Price Sensitivity to Hull–White Volatility
Summary
The document frames a callable fixed-rate bond pricing question under the classic Hull–White short-rate model. It specifies a five-year bond with annual coupons, scheduled annual calls at par before maturity, no credit risk, and a euro swap curve as the term structure. The model setup includes stated mean reversion and volatility assumptions, with a particular focus on how changing volatility could affect the clean price.
The central issue is whether reducing volatility could cause a very large price change, including a move from a very low price to one near par, and how such sensitivity might be explained. The document supplies no valuation output, calculation method, or answer, so it does not establish that these price changes occur. Its value is as a clearly parameterized question about callable bond optionality and interest-rate model sensitivity; pricing conventions and tree-grid effects are mentioned as possible sources of smaller differences.
Key ideas
- Callable bond valuation depends on both the short-rate model and the bond’s call schedule.
- The example specifies annual coupons, par redemption, annual call opportunities, and a euro swap curve.
- The author asks whether large clean-price changes could result from changing Hull–White volatility.
- The document poses the pricing question but gives no valuation results or explanation.
Tags
Full text
# Callable bond price sensitivity to Hull-White volatility changes # Callable bond price sensitivity to Hull-White volatility changes I'm using classic Hull-White model for short term interest rate dynamic: $$dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$$ (Notation is quite intuitive, anyway I am using the same as Wikipedia whether any doubt should occur). I would like to have some feedback from users about the price sensitivity to constant volatility of a callable fixed rate bond priced under such model. Let I have a fantasy bond with following features: - termination date $=$ 1,825 days starting from today - coupon payment tenor $=$ annual - face amount $= 100$ - redemption $= 100\%$ - coupon $= 3\%$ of face amount That above is a callable bond whose call schedule says it can be called at $100$ every year at the same date of maturity, hence we have $4$ scheduled call dates (e.g. if maturity were 28-Sep-2020, we would have following call dates: 28-Sep-2016, 28-Sep-2017, 28-Sep-2018, 28-Sep-2019). Hull-White model parameters: - $\alpha=0.03$ - $\sigma=132\%$ For the sake of this example, term structure employed in Hull-White model is a snapshot of (linearly interpolated) current euro swap curve - which I attach here below: ``` LAST_PRICE Tenor -0,135% 0D -0,145% 1W -0,113% 1M -0,040% 3M 0,029% 6M 0,012% 11M 0,025% 1Y 0,029% 18M 0,051% 2Y 0,122% 3Y 0,230% 4Y 0,354% 5Y 0,484% 6Y 0,619% 7Y 0,748% 8Y 0,860% 9Y 0,963% 10Y 1,058% 11Y 1,142% 12Y 1,331% 15Y 1,481% 20Y 1,516% 25Y 1,520% 30Y 1,523% 35Y 1,522% 40Y 1,498% 45Y 1,475% 50Y ``` No credit risk! Regardless of days conventions, day counters and trinomial tree engine grid size - which should account just for small variations in final results - my questions are: - what is the clean price Hull-White model is supposed to return with such parameters (mean reversion, volatility and term structure)? - Is it possible that halving volatility has a huge impact on clean price - about 15 ~ 20 points? - If volatility drops from $132\%$ to, say, $7\%$ does clean price go from very small default-like values (below $10\%$) to "normal" values (around $100\%$)? - If (2) and (3) were correct, how would you qualitatively justify such huge volatility sensitivity of the clean price?
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.