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I always find myself in the unknown charted territory when it comes to non-Linear Instruments. I come across the scenario, How to value the option using Delta Vol surface?

Example

I have CME traded Soybean option(900 strikes, Underlying traded future (spot) trading at 880 USD-cents/BU) with dec maturity and delta surface from the Bloomberg.

a) I need to plug out implied volatility from the delta surface and Plug back into the same vol into Black-76.Ho should I go about it. Delta greeks need Implied vol. as input. It is chicken and egg story.

b) If for the same option I need to work it out the historical VaR. How should I calibrate my delta surface to calculate the historical VaR.

Your responses on the concern will be appreciated.

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  • $\begingroup$ This question is rather unclear; I cannot tell what it's really asking. $\endgroup$
    – Brian B
    Nov 5, 2015 at 14:23
  • $\begingroup$ Hello Brian, Appreciate reading me question . The value an option Black 76 model requires (K,S,r, Vol, t). All the parameter are available except implied vol. Bloomberg publish the delta vol. surface.My question is how would i know what delta should i use to fetch the Vol from the delta vol. surface because the Delta Greeks also required implied Vol . Can i use the at the money vol to work it out the delta and search the Vol from the delta vol. surface. $\endgroup$ Nov 6, 2015 at 14:40

1 Answer 1

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1 ) Since you look at commodities, these are options on futures. Hence modelled with Black76 - greeks are here at the end.

If options are quoted in price, one can solve for IVOL. Likewise, if IVOL is quoted in delta, one can solve for strike. That way, you get the IVOL that corresponds to a certain strike and you simpy plug it into the Black formula as shown here. There should be a few ways to use BBG to do this for you. This answer should be one of them.

2 ) Historical VaR just needs a time series of prices. Since it's listed options, you could simply use the listed prices. If its very illiquid, and hence you rely on theoretical pricing, you use the approach in 1 ) to compute daily prices. Bloomberg's API allows you to store options and retrieve daily MtM by simply specifying the dates - no need to compute this yourself. Also, MARS could compute (historical) VaR for entire portfolios.

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