Hello,I am interested in calibration of the Hull, Nelken, and White (HNW) model, "Merton's MOdel, Credit Risk, and Volatility Skews", 2004 for evaluatingcredit spreads. Given that one use of option pricing models, such as NIG, IG, VG,Meixner, etc, based on non-normal distributions is for using in determining implied volatility in the Merton model, I am looking for commentswrt to the following idea. The general idea is to use this techniqueto evaluate spreads for issuers without equity options. I will use NIGbelow as example: 1. Characterize the NIG parameters for equity process 2. Determine NIG call option prices for variety of strikes, maturities 3. Determine the associated implied volatilities for the BS model 4. Determine the implied leverage and asset volatility in the HNW model. 5. Determine implied spread by HNW model.I am concerned I am missing something fundamental, or assumingsomething unreasonable. I have yet to do the last steps, and washoping for some feedback prior to spending more time here. Also, if anyone can recommend any additional references or work onthe HNW model, it would be appreciated. Regards,--Dan

How are you going to define and model the default event?Intrinsically Hull, Nelken, and White (HNW) model rests on the Merton's model where the default occurs when the firm's asset value process (which is a geometric Brownian motion in this case) hits a deterministic default barrier. In the case of a geometric Brownian motion, solutions for survival probability and values of call options are available in closed-form and they can be used to back out firm's value and volatility from options data. In the case of NIG, the first-time density is not known in closed-form (as far as I know). So my question is how you are going to resolve this issue? I assume you want the default event happen at any time on (t,T], not just at final time T.Overall, this sounds good, but it might be too involved. The objective of HNW is to imply spreads from available market prices, not historical data. If you don't have available market prices, try to use historical data to directly estimate your model without making such a route.

Hi,The default model reverts back to the Merton model as you say. HNW (as is my understandingto this point) is a framework for calibrating the Merton model from implied volatility, instead of directly from balance sheet data. i.e., HNW just calibrates the Merton model from another source.In the example I outlined, I only propose to characterize the equity process with a NIG distribution,then determine theoretical call prices from that characterization which will generate the impliedvolatility which is then used to characterize the HNW model. So my concern is primarily in goingfrom steps 1,2,3 to 4 in what I outlines.Another thread on capital structure arbitrage discusses the HNW model a bit with respect to findingthe asset volatility and leverage, but not this aspect. Actually, in that thread it wasn't clear therewas a good solution to the original question regarding this aspect of the calibration either.Anyway, reference to the paper is here: http://www.rotman.utoronto.ca/~hull/Dow ... lications/ MertonsModelandVolatilitySkews.pdf Regards,--Dan

I know of that paper.Note that they assume that both the firm's asset value and the stock price follow a geometric Brownian motion, which allows them to derive explicit relationships between asset and equity values as well as between their volatilities. Can you make such a connection in NIG model?

the stock price distributions i am dealing with are far from meeting lognormal returns assumptions. there is no equity options market either. what i wouldlike to do is only use the NIG model (characterized to the stock process) forgenerating realistic equity option prices. From these generated option prices, i would like to go back into the B&S world - and calibrate via the Hull, Nelken, White methodology.regards,--dan

what do you intend to do with these spreads?have you actually looked at the performance of this model - where there is vol trading? its not great...

I would like to see if there is any discrepancies in the barrier extractedfrom option (market) prices and balance sheet data. I am dealing with stock markets without associated equity options markets.My understanding was the hyperbolic models (such as NIG, VG, etc.)provide better estimates of option prices than the BS model. They definately provide better distributional fits (at the expense of additionalparameters). Hence, baring some not too far-fetching assumptions,I was hoping this route would enable me to generate realistic optionprices from stock market returns data. I haven't come across empirical studies of of these models - other thanthe proponents of these models.