Estimating Option Volatility for an Illiquid Currency Pair
Summary
The document considers pricing options on an illiquid currency pair when only one bank provides option quotes. It asks whether historical realized volatility can support implied volatility estimates, how a market maker might account for a risk premium, and whether an asymmetric forecasting loss could penalize volatility underestimation more heavily. It also raises break-even volatility, inferred from delta-hedged option P&L, as a possible way to study the volatility smile using historical prices.
The response outlines several exploratory routes: forecast volatility and price options by simulation before backing out implied volatilities; consider HAR-RV when suitable intraday data exist or GARCH when they do not; use break-even volatility as another reference; or fit a Gram-Charlier or Edgeworth density and price options from it. It cautions that density fits must remain positive, integrate to one, and reproduce the forward price. These are suggestions, not validated forecasts, and sparse market data limit calibration and evaluation.
Key ideas
- Historical volatility forecasts can be converted into option prices through simulation and then into implied volatilities.
- HAR-RV may require intraday data that an illiquid currency pair lacks, while GARCH is offered as an alternative.
- Break-even volatility from delta-hedged P&L can provide a historical reference for the volatility smile.
- Gram-Charlier or Edgeworth densities require constraints on positivity, normalization, and the forward price.
- Sparse option quotes limit direct inference and validation of implied volatility forecasts.
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# Implied Volatility for illiquid FX currency # Implied Volatility for illiquid FX currency Can anyone help me by providing ideas and references for the following problem ? I'm working on a certain currency pair USD/X where X is not a highly traded currency. I'm supposed to implement a model for forecasting volatility. While this in and of itself is not an easy task per se, the model is supposed to be injected in a BSM to calculate prices for USD/X options. To my understanding, this requires a IV model and not a RV model. The problem with that is the fact that the currency is so illiquid that there is only a single bank that quotes options for it. Is there someway to actually solve this problem ? Or are we supposed to be content with an RV model and add a risk premium to it as market makers ? If it's the latter, how is that risk premium determined and should one go about creating an RV model with some sort of different loss function that rewards overestimating rather than underestimating (in order to be profitable as Market Makers) ? EDIT : I have been reading about Break-Even Volatility (BEV). This is the volatility found by setting the P&L of a delta-hedged option to zero (numerically). This method only uses historical prices and outputs, at the very least, a skewed volatility as a function of moneyness. Given this, could one extrapolate future IV ? Or should this only serve as a reference for the form of the volatility smile ? ## Answer by Frido (score 1) https://quant.stackexchange.com/a/81952 Some suggestions below. I am assuming though that you have some price history at least. - Forecast the volatility, subsequently use your forecast volatility in a MC sim to value options with various strikes. Once you have the prices of these options, you can backout the IVs. One such vol forecast is HAR-RV. The reference for this are the papers by Corsi. EDIT: I just realised since the currency is illiquid you probably won't have sufficient intraday data for HAR-RV, in which case you can try Garch for example. - Break-even volatilities: yes, I think that is another good avenue to explore. Especially with increased computation power this should be more feasible now. The reference for this is the Bloomberg presentation by Dupire and Verma. - Fit a Gram-Charlier/Edgeworth density to historical distribution for various times to maturities. Price options using these GC densities (you have to make sure though the density integrates to one and is everywhere positive and reproduces the forward price), subsequently back-out the IVs, potentially add a pad. Reference for GC/Edgeworth applied to option pricing is Jarrow and Rudd and papers that cite them.
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