Hi Everyone, Could anyone shed some light on is there any way to construct a volatility surface for a illiquid stock where no option prices can be observed from the market? Can a relative sensible volatility smile be estimated from historical data? In practice if you are a market maker and requested by your client to trade such an option, how do you determine the price for such an option and hedge the risk?Many thanks in advance!

the information content of the option-implied volatility may be limited, even though it is calculated by model-free method.But I am wondering why should we assume there exists a volatility smile?If the price process is not governed by BS, it may not be a smile, say 'cry'.

QuoteOriginally posted by: stoneylHi Everyone, Could anyone shed some light on is there any way to construct a volatility surface for a illiquid stock where no option prices can be observed from the market? Can a relative sensible volatility smile be estimated from historical data? In practice if you are a market maker and requested by your client to trade such an option, how do you determine the price for such an option and hedge the risk?Many thanks in advance!I haven't tried this suggestion, but it might be an interesting exercise to explore. Pick some optionable stock XYZ and let's try to estimate option values over 1 month maturityby the following. Run a simple index regression (*) R(ti) = beta RM(ti) + eps(ti),where RM(ti) are the SPX (log)-returns measured at 1-month frequency. Assume the same index relation holds under the market pricing distribution Q. Now, you can get the 1-month Q-distribution of RMfrom the options on that with Breeden-Litzenberger. So, make draws from that to simulate RM(1-month) under Q, multiply by beta, and add back in the draws of residuals from the regression. Use that simulated distribution, with a martingale adjustment, to price options on XYZ.If those option prices are any good, then repeat the procedure on your non-optionable stock.A variation could be to do the same regression against optionable stocks in the same industry.For example, see if you can price Ford options by first regressing Ford against GM, Then, switch to the GM Q-distribution.

This is very interesting suggestion Alan. I will definitely give it a try. Thanks a lotBy the way, is the any document/paper discussing this topic?

QuoteOriginally posted by: stoneylThis is very interesting suggestion Alan. I will definitely give it a try. Thanks a lotBy the way, is the any document/paper discussing this topic? This paper by Peter Carr et al may be relevant.

QuoteOriginally posted by: EBalQuoteOriginally posted by: stoneylThis is very interesting suggestion Alan. I will definitely give it a try. Thanks a lotBy the way, is the any document/paper discussing this topic? This paper by Peter Carr et al may be relevant.Great reference. I was just posting extemporaneously, but it shows that if you ever have an idea in finance -- youshould always check that Peter Carr and co-authors haven't already developed it!A little googoling of who cites that one, turns up this: (Chang & Pant), which should also be of interest to the OP.BTW, does anyone see an accessible online copy of the cited Carr & Madan paper that actually has the figures!?

http://www.ederman.com/new/docs/strike_ ... ad.pdfLook at the section referring to the risk neutralised historical distribution.