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:
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?