Estimating Hull–White Parameters Without Swaption Data
Summary
The document discusses estimating the volatility and mean-reversion parameters of a Hull–White short-rate model when the market has daily overnight rates and a swap-based zero-coupon curve but no actively traded options. It distinguishes estimation from calibration: without option prices, there is no direct set of nonlinear market quotes to fit the model to.
Suggested approaches include using proxy implied volatilities from related markets or instruments, such as currency, copper, reference-rate historical volatility, and swaption markets, while making correlation assumptions. Another proposal is to simulate relevant state variables and infer risk limits or hedging costs from the resulting profit-and-loss volatility by tenor, then estimate parameters against those values and update them as trades provide new information. Caps and floors are also mentioned as possible nonlinear calibration instruments. These are suggestions rather than a validated procedure; the document gives no empirical comparison, and the suitable proxies depend on the model’s intended use and the relationships assumed between markets.
Key ideas
- Without traded nonlinear products, Hull–White parameters must be estimated from assumptions or proxies rather than fitted directly to option prices.
- Related markets and historical rate volatility can provide proxy volatility inputs, but using them requires correlation assumptions.
- Simulated profit-and-loss volatility and hedging costs can help inform risk limits by tenor.
- Caps and floors can serve as nonlinear calibration instruments when swaptions are unavailable.
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# Workaround for Hull-White short rate model in market without swaptions # Workaround for Hull-White short rate model in market without swaptions Every time I search calibration methods in short-rate models such as Hull-White, I always find information on how to do it with swaptions market data. Yet, I can't find anything about how to do it in markets without swaptions. How can I calibrate Hull-White short rate model in a market without options? It is an overnight interbank rate with daily data and daily zero coupon curve (bootstrapped from swaps). ## Answer by Mercadian (score 1) https://quant.stackexchange.com/a/72162 To me there are some semantics involved here, I'd say you need to take a step back and think about a different adjoining question. More than calibrate your parameters you need to estimate them since you have no points of reference for calibration i.e. no actively traded to Non-Linear / Vol products on this asset. Calibration is simply trying to fit your model to market data by tweaking the parameters until you minimize some target function (like price difference) so that you're sure your model will match as closely as possible the observed market prices.... its a regression (using the term loosely) and your question is basically: how can I do a regression without a could of data points... you can't... but that doesn't mean you can't make educated/assumption driven guesses about your model parameters. What I would do in this case, is I would look for proxy implied vols like: - USD/CLP - Copper - CLP RFR Historical Vols (per tenor ideally) - USD RFR Swaption Rates And try to put together an estimated one based on correlation assumptions. Another way is I would ask myself If I had a swaption position today, what would be my risk limits and how much would it cost me to hedge it? simulate different paths of the relevant state variables and get an idea my PnL Vol, do this for each tenor, that would be your market data. Finish it all off by estimating the model to the above values or a function of them and adjusting for any trades you might do by using the traded vols as new market data. See this question too for some reference: Options when there's no VolSurf - Emerging/Frontier Markets Hope this helps. M ## Answer by Xman (score 0) https://quant.stackexchange.com/a/72156 It all depends on the use case of your model. However, as the model has a volatility and mean reversion parameters, you will need to calibrate on non linear products, not necesserily swaptions but you can also use caps/floors or any type of non linear product...
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