# lead lag relationship among futures, options and stock prices

I have the data of past 10 years of NIFTY (the National Stock Exchange of India) stock, futures and options and I want to show the lead-lag relationship (which reacts first, futures, options or stocks) among the three using cointegration test, VECM model and granger's causalty.

The issue is that I don't know how to use the options data because it has both call and put out of the money in the money, and at the money prices on all days for different expiry everyday, but there's multiple data to use for any given day.

I have to perform time-series statistical analysis on the data, so I need to have only one price for one day. Given this issue, how can I perform the tests mentioned above? I am using E-views to perform these tests. I want help to get around the options data.

• Option premiums don't tell you the price of the underlying; they tell you the volatility of the underlying. Jun 13, 2020 at 20:40
• @chrisaycock I have the corresponding underlying price, I wish to find a relationship between the two. Jun 13, 2020 at 20:51

Given that liquidity of NIFTY options decreases rather quickly with moneyness, using the most liquid ATM option is your best bet (i.e. the least bid ask spread). Although, keep it consistent in that you use the same option (i.e. say the one that expiries 3M into the future) for different days. Also, better to use implied volatility as a performance measure instead of the price itself, since that will change depending as the underlying moves.

• Thank you for your answer. I just have a few add-on questions. 1) If I use implied volatility as my performance measure, then I can't apply the models to all three at once, and I'd have to look for other statistical models. 2) If I use ATM options, then also, I'd have two ATM options for the least bid ask spread, one for call and one for put. It would be a huge help if you could help me in this. Jun 17, 2020 at 21:28
• 1. As I don't quite understand your problem statement clearly, i don't see why not. Can you explain? Jun 18, 2020 at 1:54

How about using the ATM option expiring closest to your futures contract delivery date? As in :

• Stock price : price today
• Futures price : price at a future date, usually the nearest expiring contract.
• Option price : price ATM at a comparable future date.
• Could you be kind enough to explain a bit more about the option price? Jun 17, 2020 at 21:33
• You typically have call/put options data at different strike prices and maturity dates. You say you already have spot (stock price) and future prices. So you'd probably interested in comparing the next futures contract (say for delivery in a August) vs an option maturing in August. The ATM option is the one whose strike is the same as the current spot price. If this is the first time you look at financial derivatives, I'd recommend you take a look at the first chapters of Options, Futures and Other Derivatives by John Hull. Jun 18, 2020 at 13:55
• Should I take the premium of call options as one variable and the premium of put options as another? Jun 18, 2020 at 21:17
• They are different assets, so yes, you're probably interested in seeing how both react since they have an opposite relationship. Jun 22, 2020 at 15:04