0
$\begingroup$

Having studied the basic premises behind option pricing, I thought it would be interesting to look at some real-world options data. I found the following quotes for options on APPL:

https://finance.yahoo.com/quote/AAPL/options?date=1610668800

However, I was surprised to see that the implied volatility for these options varies quite signigicantly, despite having the same underlying and maturity.

Why is this?

$\endgroup$
  • $\begingroup$ Mathematically, because the prices change, both of the options themselves and underlying $\endgroup$ – nimbus3000 Oct 9 at 9:49
  • $\begingroup$ And economically? Wouldn't greater demand for the (call) options with lower implied volatility and lesser demand for those with higher implied volatility push the implied volatility into equilibrium? $\endgroup$ – M Smith Oct 9 at 10:04
  • 1
    $\begingroup$ This effect (that the vols differ) is called "the volatility smile" and it shows that the Black Scholes model is not quite right, its assumptions don't correspond to reality (if it was the volatility would be flat across strikes and maturities). It is not a temporary effect but a stable phenomenon, well studied and well known by now. $\endgroup$ – noob2 Oct 9 at 12:08
1
$\begingroup$

Bear in mind that the IV you see quoted is Black Scholes IV. The only takeaway can be that the BS model is not the correct model to ACCURATELY price options. Differing IVs are the "fudge" to get better pricing and that option quoting (at the market maker level) really occurs through IV and is just expressed as price. When you look at the assumptions in the BS model, they are AT LEAST the shortcoming of the model (no commissions, continuous price movements, returns are gaussian...) and are return even gaussian? Some research points to that some asset returns are, some returns are more fractal.

| improve this answer | |
$\endgroup$
  • $\begingroup$ The Misbehavior of Markets: A Fractal View of Financial Turbulence by Mandelbrot is a worthy read on the "fractology" of markets. $\endgroup$ – Bikenfly Oct 9 at 12:00
1
$\begingroup$

In short, because 1) the assumption of lognormal returns does not hold in real life--the markets have more skewness and kurtosis and 2) writers of protection want to be compensated more for writing insurance on low probability but high cost events.

| improve this answer | |
$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.