### Decomposing Option Price for Imperfections – Smile, Skew, “Abnormal” Distribution

Currently, it is very rare to see options trading at the Black Scholes price. The reason for this can be classified as:

* Market anticipation of future volatility

* Volatility of volatility effects (which results in the volatility skew or smile), and

“Imperfections” of actual returns distribution

All these are fitted into the fitting parameter which is volatility.

In identifying underpriced options, the above effects should be removed from the implied volatility and residual volatility should be compared with the historic volatility. When doing this, things to consider is that the effects of vvol is not present for ATM options, thus, theirs price reflects more of anticipatory and adjustments for the distributions imperfections.

Imperfections in the distribution results in the distribution’s moments diverting from the normal distribution. These can be modeled using moment fitting techniques where one option is decomposed into a basket of BSOPM options at different vols. The de composition can take the following form:

* Fit a kernel to the distribution and get the basket for the imperfection effects plus the normal BSOPM effects

* Subtract the BSOPM priced option to get a zero weight basket which has the pure imperfection effects

* From the observed price of an ATM option subtract the above to get the price component of the anticipator vol. effects

* The deference between the ATM and options at the other strike with the same term is the risk of volatility effect

NB: in a basket all the option parameters should reflect the modeled option except for the implied volatility which is the fitting parameter.

Best regards, Suminda Sirinath Salpitikorala Dharmasena

* Market anticipation of future volatility

* Volatility of volatility effects (which results in the volatility skew or smile), and

“Imperfections” of actual returns distribution

All these are fitted into the fitting parameter which is volatility.

In identifying underpriced options, the above effects should be removed from the implied volatility and residual volatility should be compared with the historic volatility. When doing this, things to consider is that the effects of vvol is not present for ATM options, thus, theirs price reflects more of anticipatory and adjustments for the distributions imperfections.

Imperfections in the distribution results in the distribution’s moments diverting from the normal distribution. These can be modeled using moment fitting techniques where one option is decomposed into a basket of BSOPM options at different vols. The de composition can take the following form:

* Fit a kernel to the distribution and get the basket for the imperfection effects plus the normal BSOPM effects

* Subtract the BSOPM priced option to get a zero weight basket which has the pure imperfection effects

* From the observed price of an ATM option subtract the above to get the price component of the anticipator vol. effects

* The deference between the ATM and options at the other strike with the same term is the risk of volatility effect

NB: in a basket all the option parameters should reflect the modeled option except for the implied volatility which is the fitting parameter.

Best regards, Suminda Sirinath Salpitikorala Dharmasena

Labels: Derivatives, Options, Pricing

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