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Using a Delta Volatility Surface to Price Options and Estimate VaR

Article Quant Q&A · Author: user1131338
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Summary

The document explains how to use a volatility surface quoted by delta to price an option on a futures contract. For a given option strike, first find the implied volatility associated with that strike: when the surface is quoted by delta, solve for the strike corresponding to each quoted delta and its volatility. Then use the matching volatility as an input to the Black-76 pricing model, which is designed for options on futures.

For historical VaR, the answer recommends building a time series of option prices. Listed market prices can be used directly; for illiquid options that require theoretical marks, calculate daily prices using the surface-to-strike approach. The guidance is brief and does not specify a VaR confidence level, horizon, or calibration procedure, so those choices remain part of the researcher’s implementation.

Key ideas

  • Options on futures can be priced with Black-76.
  • A delta-quoted volatility surface must be mapped to the option’s strike to obtain its implied volatility.
  • Use the implied volatility associated with the target strike as the pricing input.
  • Historical VaR requires a time series of option values, using market prices or theoretical marks when trading is illiquid.

Tags

OptionsFuturesCommoditiesDerivatives pricingRisk management
Full text
# Delta Volatility Surface Usage to value the option


# Delta Volatility Surface Usage to value the option












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.

## Answer by AKdemy (score 1)

https://quant.stackexchange.com/a/73334

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.