# [R-SIG-Finance] Extracting implied probabilities

Robert Sams robert at sanctumfi.com
Tue Jul 14 17:12:11 CEST 2009

```I use the simple, model-free approach of letting (P[i] - P[i+1]) /
(X[i+1] - X[i]) be the probability that the price of the underlying is
*at or above* X[i+1] at expiry and P[i] is the premium of call X[i].
Solve for all i's up the strike chain. Basically, we construct call
spreads from consecutive strikes up the call chain and treat each spread
as a binary option struck at the top strike. The probability is the
spread price divided by the strike difference.

Of course, the resolution of the price intervals is limited by the size
of your strike chain. Your case of three doesn't get you very far,
unfortunately.

Note, you can also check which puts have open interest and using
put-call parity you might be able to fill in some gaps with "shadow"
call values.

Robert

> -----Original Message-----
> From: r-sig-finance-bounces at stat.math.ethz.ch
> [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of
> Ravi S. Shankar
> Sent: 14 July 2009 13:57
> To: r-sig-finance at stat.math.ethz.ch
> Subject: [R-SIG-Finance] Extracting implied probabilities
>
> Hi R,
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> I am trying to extract the implied probability from options
> on individual stocks.
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> I have taken the near month (1 month) call options (American)
> and removed strikes with zero volume. But I end with just
> three strikes and all of them OTM.
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> Date
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> Expiry
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> Strike.Price
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> Settle.Price
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> Spot
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> 29-Dec-06
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> 25-Jan-2007
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> 900
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> 27.75
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> 891.5
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> 29-Dec-06
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> 25-Jan-2007
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> 940
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> 12.5
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> 891.5
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> 29-Dec-06
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> 25-Jan-2007
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> 920
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> 19.75
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> 891.5
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> I will compute the implied volatility and delta using the
> fOptions package. I intend to use the splines package to
> interpolate in the implied volatility-delta space. My
> question is are just 3 strikes sufficient to interpolate and
> extract a meaningful implied probability?
> Any pointers or paper that deals with extracting implied
> probability from thin options markets would be helpful.
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> Thank you,
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> Regards,
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> Ravi Shankar S
>
> This e-mail may contain confidential and/or privileged
> i...{{dropped:13}}
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```