Estimating the Price of an Option at an Unlisted Strike

Summary

When an option is unavailable at a desired strike, the response suggests estimating its theoretical price with an option pricing model such as Black–Scholes–Merton. The model requires an implied volatility assumption; with that input and the custom strike, a user can estimate the option price and its Greeks. If nearby strikes are quoted, their implied volatilities can help guide an estimate for the missing strike.

The interpolation is only approximate. Implied volatility often falls between those of nearby strikes, including in parts of a volatility skew, but this pattern is not guaranteed, especially near at-the-money strikes. The response describes a bound on the middle option’s value relative to neighboring options, with a small qualification for interest rates, but does not provide a complete procedure for fitting a volatility surface or account for liquidity and execution costs. Its discussion is limited to plain-vanilla options on assets such as equities or commodity futures. A theoretical estimate does not mean the option can actually be traded at that price.

Key ideas

• A pricing model can estimate the value and Greeks of an option at a strike without a market quote.
• The estimate depends on an assumed implied volatility as well as the strike and other model inputs.
• Volatilities at neighboring strikes can inform an interpolation for a missing strike.
• The interpolated volatility may not lie between nearby quotes, particularly around at-the-money options.
• A modeled price is an estimate and does not guarantee an executable market price.

Tags

# Can you simulate an option position at a strike when that does not exist


# Can you simulate an option position at a strike when that does not exist












Is there any way to simulate buy an option at a pric of x when that price is not available to buy ? If x-3 and x+3 exists, how do I buy it at price x?

## Answer by confused (score 0, accepted)

https://quant.stackexchange.com/a/55977

With option pricing, at least with BSM model, you can observe every input except for implied volatility. So all you need to do is provide an implied volatility into your pricing model and your custom strike price to produce an option price. With that IV assumption, you can produce all the greeks you need according to BSM model.

If X-3 and X+3 are not that far from X (you'll have to use your judgement), you can expect that the IV of X to be in between the other two. IV also tends to be in between the two if X-3 and X+3 are at one end of the skew. Note that in practice, there may be cases where the IV of the middle option is not in between the two outer options, especially when you get close to ATM. However, the amount the IV of the middle option differs from the outer options has a bound (it cannot be so where the middle option is worth less or greater than both the outside options, with negligible adjustment for interest rates). Even if skew exists, you can still back into an approximate option price as long as you can supply an IV figure.

All the above is under the assumption you are talking about plain vanilla options and options on stuff like equity or commodity futures.

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