I am analyzing the volatility of financial stock returns and let's say I have a pretty good model to forecast tomorrows volatility of the stock returns. So let's say for simplicity reasons I have a GARCH(1,1). With this model I forecasted the volatility tomorrow and I now want to trade on it. The volatility tells me how much the stock returns and therefore the stock itself will "change"/fluctuate. If I have the volatility and if I am pretty sure about the probability of my correctness, how should I trade this? Should I e.g. invest in a straddle? And if yes, how should I determine the optimal options/ options conditions I should use?

EDIT: So my basic question is: I have the value for the volatility forecast and I know that there are certain option-combinations to trade on high and low volatility, but how can I connect these strategies to my forecasted value, to my real value I calculated?

• @quantycuenta Well I was thinking abou profiting from the volatility directly, so no arbitrage in terms of implied vs. historical. Let's assume my model is perfect and I know from looking at historical volatility the volatility of tomorrow. I am analyzing the returns. So from knowing the volatility of the returns tomorrow: How can I benefit from this? Should I and if yes how should I set up things like straddle/strangle and so on to profit from the fact that I know somehow the range where the investment will lie tomorrow. Let's say for simplicity I am 100% sure. Also interesting would be, what – Jen Bohold Dec 23 '13 at 9:07
• if I am 95% sure. So I am using a confidence interval for my forecasted volatility and not only one single value, which is unlikely to happen. So what if I know the range of tomorrows volatility with a 95% probability. – Jen Bohold Dec 23 '13 at 9:08
• @quantycuenta Thanks for commenting on both of my questions :-) Actually I am talking about the actual/historical volatility. So I am not looking at the implied volatility. All I do is analyzing the historical volatility and lets say I have a perfect model to forecast the volatility of tomorrow. So I am wondering how I can trade on this? So from looking at historical stock returns I can forecast the volatility of tomorrow, what should I trade/do to benefit from this knowledge? – Jen Bohold Dec 23 '13 at 12:39
• Then you should trade the gamma of the underlying options, simple as that, though I highly doubt that you have a reliable point forecast of future realized volatility. But hypothetically speaking if you had then you could profit by buying or selling gamma. – Matthias Wolf Dec 23 '13 at 15:36

One thing that is missing from this discussion - only buy the straddle if your forecast for future realized volatility is higher than the implied volatility for which the straddles are currently selling. Nonetheless, having a one-day-ahead forecast isn't much good without knowing at least the expected path of implied volatility priced into options, for the implied volatility is not a constant.

When buying or selling your straddle, you'll want to make sure that it is delta-neutral. That is how you pick the strike, or time the purchases.

As for what other instruments work better, there are broker-quoted "variance swaps", which are linear derivatives on the future realized variance. It might also be worthwhile to look into listed ETPs on various volatility indexes like the VIX, or VIX futures themselves if you are comfortable with them. There are numerous subtleties to VIX index pricing, and all the related indices.

Since you are talking about using volatility of stocks you could just use the straddle strategy both on long or short.

If you are 100% certain (we know this is not possible, but let´s take this as an assumption just for the sake of theory matter) of the volatily you can go two ways:

High Volatility: You will be long on a straddle, this means you would buy a call and a put option with similar prices to take advantage of any direction

Low Volatility: You can be short on a straddle, this means you would sell both call an put option with really similar prices and earn the premium of the options.

• Vonlanten C. Lopez Thanks for your answer! This was what I was aiming at, but could you give me more details? It is clear that I have to buy options where the underlying is my stock, but what other "condition"? So at which strike price etc. ? Is it possible to to this at a daily basis and generate a profit? Or are the transaction costs of the brokers to high? What if I have a range in which the volatility will be tomorrow with e.g. a 95% confidence interval? In general: Is there also an alternative with other investments than options? Thanks a lot for sharing your wisdom. – Jen Bohold Dec 23 '13 at 16:02
• One additional question: I have to define high and low. So what is high and what low. I have to know which volatility is needed so that my long straddle works and I have to know the low volatility it needs that my short straddle is working right? So I have to somehow connect my calculated value to the trades I will be doing based on this. So I am somehow searching for a mathematical connection between volatility and the value of my straddle? – Jen Bohold Dec 23 '13 at 16:04
• Let me try to answer some of your questions: "What are the conditions to buy?" Well, here is the secret, you have to develop a model to try to find the right moment, it will be based on futures market and also on other options that are already in place.; "Is it possible to do this on a daily basis?" Yes, but only if you are a bank, otherwise the costs are too high; "What if im 95% of tomorrows volatility?" You can do nothing with that, at this time the volatility surface is at a high point, you should know the volatility at least 3 weeks before. So, it's not a simple task. – Gabriel Vonlanten C. Lopes Dec 31 '13 at 14:51
• "Are other alternatives other than options for this?" Well, there are some Swoptions that can act as a straddle, but this is a much more complicated thing, and only available at OTC between big banks. You can only use Options for straddle, because if you use any other derivative (a future or a forward) you will basically hedger both investments. You need an option becase they will only be exercised when ATM (and of course, just one of the 2 options will be ATM) – Gabriel Vonlanten C. Lopes Dec 31 '13 at 14:53
• Yes, I agree with this answer. In addition, once you have put on a straddle (long or short) you should compute the Delta every day. It will start close to zero, but may become positive or negative as time goes on. You should trade in the underlying to bring the delta of the overall position back to zero. In this way you have a "pure play" on volatility. This is called a "delta neutralized straddle" and is a standard way to trade a volatility view. – Alex C Sep 28 '15 at 2:08

Don't forget about liquidity holes and transaction costs. You can use more complicated structures, to trade volatility; however, they all come with their own issues. You do need to focus on all the costs and calculate your edge against your forecast and both the entry and exit for the straddles plus possible other risk factors. Focus on ATM straddles to begin with.