Implied Volatility

[vijayaraghavan sundararajan]

Hello David,

Can you please explain why the Implied volatility of calls is different from puts in real markets. As per Hull, the IV of call and puts have to be same. But when I look into actual markets, the data is otherwise. I tried to google around, but could not find a convincing answer.

Appreciate your help on this.

Many Thanks,
Raghavan.

 

[David Harper CFA FRM]

Hi @raghavan.analyst

Did you see this @ http://wilmott.com/messageview.cfm?catid=8&threadid=79623&FTVAR_MSGDBTABLE=&STARTPAGE=1

My summary take is that no-arbitrage is the key assumption when Hull says "In the absence of arbitrage opportunities, put-call parity also holds ... " (Chapter 19) which sets up the necessary equality between put and call implied volatility. In other words, inequality of implied vols implies an arbitrage opportunity. But put-call parity applies to European options such that the arbitrage is not instantaneous, so it doesn't surprise me that technical factors would introduce noise into the equality. In particular: liquidity and simple temporary supply/demand imbalances. For example, puts on an equity might become temporarily highly demanded (tightly supplied) pushing up their implied volatility into technically arbitrage opportunity. We shouldn't be surprised by temporary inequalities (they simply create arbitrage opportunities) and we certainly shouldn't be surprised by small inequalities (e.g., there are transaction costs); I think the surprise would be persistent and large inequalities. But my point is simply that there is a qualifier (no-arbitrage conditions) which are not always realistic. I hope that helps.

 

[vijayaraghavan sundararajan]

Thanks for your reply David.

 

[Kaiser]

Mainly driven by demand/supply and the "insurance" effect. Naturally, investors buy protection on the downside to protect their assets in case of any bad events, hence pushing the price of PUTs higher than those of CALLs. In the real world, the volatility curve is not flat (as it is assumed under Black-Scholes) but rather like a smile. For example, a smile with a higher convexity on the downside reflects the fact that out-of-money PUTs are more expensive that out-of-the money CALLs.