# Realized volatility forecast vs Implied volatility

I have forecasts of realized volatility, as well as implied volatility for individual traded options of the S&P500.

I want to simulate a simple trading strategy; that is, buy signal=1 if forecasted realized volatility is greater than current implied volatility. However, the literature documents that implied volatility is usually higher than realized volatility.

Are there any better approach for this simulation?

• What implied volatility are you talking about? – will Nov 8 '18 at 21:29
• Implied volatility for 30 days to expiry options obtained from WRDS. I have deannualized it, but it still appears a notch higher than realized volatility – Bryan Lwy Nov 9 '18 at 2:00
• What strike are the options? Is there skew? – will Nov 11 '18 at 19:42

On average the implied volatility is higher than realized volatility because you can easily imagine that dealers will ask customers to pay a premium to write them options and risk manage them

you can have a look at this paper for instance

PIMCO-The Volatility Risk Premium

Now you can investigate how realized volatility can be a signal for trading implied vol but the condition will certainly not be "buy when realized > implied" because the 2 quantities are not directly comparable. You need to establish some statistical relationship first.

And to finish here is a little exercise to test your thinking about realized vs implied vol and hopefully help you design properly your strategy: suppose you are long a call option which you purchased at some implied vol level $$\sigma_0$$ and which you are delta-hedging. Now imagine that i grant you that "on average" over a period of time the stock realized volatility $$\sigma_r$$ will be higher than $$\sigma_0$$. In other words i tell you that in expectation $$E[\sigma_r] > \sigma_0$$

Would you be certain to make money even in this situation ?

• I would think yes since forecasted volatility is higher than implied, when it really should be lower on average? (That is if your forecasts make sense) – Bryan Lwy Nov 11 '18 at 16:49
• @Bryan Lwy actually the answer is no. It would depend on the path the underlying asset takes since when delta-hedged you accumulate the realised vs implied vol discrepancy via the Gamma. You can get "hammered at the strike" as some put it. See an example here: trade2win.com/boards/attachments/f112/… pp.12-13 – Quantuple Nov 12 '18 at 12:05
• ^^ correct. Indeed an intuitive (and mathematically correct) way of thinking about it is that the pnl of a delta-hedged portfolio is the gamma-weighed average of the difference between realized and implied vols. The simple average of the difference can be positive and you still lose money if the gamma is small (out-the-money) when realized vol is high but big when realized vol is small. – Ezy Nov 12 '18 at 13:54