Using spot prices as the underlying creates a lot of complexities in options pricing and investors generally gets confused with it. Let’s look at a simpler way to option prices i.e. futures as an underlying.
Spot/Cash prices are underlying for Options but should we track that? Using spot prices as the underlying creates a lot of complexities in options pricing and investors generally get confused with it. Let’s look at a simpler way to option prices i.e. futures as an underlying.
The Pricing
Futures are calculated with the following formula: S * e^((r-q) * T) where:
1. S = Spot Price
2. r = Risk-free rate
3. q = Dividend
4. T = Time to maturity
whereas
Options are priced generally using the Black & Scholes formula which takes 6 inputs:
1. Spot Price
2. Risk-free rate
3. Dividend
4. Time to maturity
5. Strike Price
6. Volatility
Notice 4 components that go in the formula of both are common. Let’s try to tweak the maths. If the time to maturity is the same for both Futures and Options (which means evaluating for the same expiry), we can replace the other 3 components i.e.
Spot Price, Risk-free rate & Dividend = Futures Price
Why is Spot as underlying complex?
Why are we doing this? The agenda is to avoid some complexities.
Risk-free rate
The risk-free rate is not a static number and keeps changing all the time if using the spot as an underlying accounting for the risk-free rate on a continuous basis is certainly a difficult task.
Dividends
Even though it may sound simple but adjusting dividends are way too tough. Dividends are not continuous but staggered and clustered most of the times. It affects different expiries for different stocks where dividends are due and it doesn’t end here, even a forecast of what will be declared as a dividend has to be incorporated for the true pricing.
Getting a forecast of the dividend is complex or will need advanced tools for market consensus. If trading in Nifty, for calculating an options price, investors will have to calculate these for each stock and then adjust for weightages of each stock which itself keeps changing.
Using futures can simply eliminate these and the market participants looking for arbitrage will make sure that the pricing is perfect and we can trust the market’s futures prices simply.
The added dimension to VWAP
As we know the expiry’s final settlement price is the last 30 minutes-weighted average price of the spot market. Due to this, many investors/traders get confused with the prices and some option prices may look like an arbitrage or free money (options quoting below intrinsic value).
This may not be correct as the spot prices are moving independent and not according to the VWAP whereas using futures prices are quoting at the calculated VWAP and it’s taken care by the arbitragers if any deviation occurs market arbitragers would jump in and be sure they will jump in before you could do. So, if futures are referenced in the last 30 minutes of expiry, these circumstances and confusions can be avoided.
Futures for Weekly Options
Weekly options of Bank Nifty does not have a futures price with it so how can we use one? The solution to this would be calculating a synthetic future price from the options price itself.
Futures Price = Strike + Call Price – Put Price
The formula holds true for any strike due to the Put-Call Parity but taking ‘At The Money’ options are better due to the liquidity or an average of 3 strikes around ATM can be taken for better accuracy.
