Puts and Calls on a Volatility Surface

How puts and calls relate on a volatility surface

A question we sometimes receive from new options traders is, “Why can’t I see puts and calls on a volatility surface?”

The short answer to this question is: You can! In this short blog, we break down why.

The Volbox options implied volatility surface integrates data from both calls and puts.

For each option strike and expiration, there is a corresponding put and call pair.

Their prices are governed by a fundamental principle in finance called put-call parity, which is sometimes expressed mathematically thus:

C - P = S - PV(x)

Here, C is the call price, P is the put price, S is the current stock price, and PV(x) is the present value of the option strike price.

This principle states that a portfolio comprising a long call option and a short put option is equivalent to a forward contract with the same strike price and expiration.

A key implication of put-call parity is that, in an ideal market, a put and a call with the same strike and expiration will share the same implied volatility (IV).

In other words, each “point” on a volatility smile represents an IV estimate for both the put and call with that same strike and expiration.

By convention, however, IV surfaces typically display the IV for out-of-the-money (OTM) calls and puts.

This approach is standard across the industry, as OTM options offer sharper insights due to higher liquidity and narrower bid-ask spreads, resulting in a more reliable fitted curve.

The image above from Investopedia depicts how IV smiles and surfaces are made (in general).

Note: A common misconception is that IV surfaces can be constructed by simply “joining” the IV estimates for puts and calls.

This not quite the case, however, and the resulting “surface” is usually disjoint and unhelpful.

Proper IV surface calibration requires some mathematical intervention and financial expertise.

And this is where Volbox shines!

Our product is a seamless volatility surface that is comparable to what professional options traders use.

Join us today for free at Volbox.com!