Assuming that all other factors (such as underlying price, strike price, etc.) remain unchanged, I want to see how a spike in VIX would affect the price of the average call option? Assume Vega is almost always positive.
Vega is the option's price sensitivity to the volatility (i.e. IV). In the graph below, vega is shown to be a strictly positive function in volatility, which means that at any point in the graph (i.e. for any value of IV, irrespective of whether the option is OTM, ATM or ITM), the option price:
will increase in value if IV goes up (because Vega is positive)
will decrease in value if IV goes down (because Vega is positive: i.e. higher IV is "good" for option price, lower IV is "bad for option price)
Although we notice that as the IV goes up, Vega has diminishing returns.
It's simple in the end: Vega is strictly positive in Vol => higher Vol therefore always means higher option price => higher VIX means higher Vol => higher Vol (IV) means higher option price (you can argue either because Vega is strictly positive in IV, or simply because Option Price is scaled IV anyway).
- all options have 1-year expiry, rates are set to 0.01 and spot is 100. The ITM call has strike 80, the ATM call has strike 100 and the OTM call has strike 120.
VIX almost always only spikes when SPX goes down as @Jan Stuller also mentions in a comment. Insofar the question is a bit counterfactual. I frequently use twin axis in the charts that follow. The position of the label corresponds to the axes the ticker belongs to.
These are essentially two question in real world scenarios.
1 ) VIX and Vega: VIX up, IVOL up, but Vega is unclear (frequently down)
2 ) VIX and call options price: VIX up, call option down
If you think of VIX and call options vol, these go more or less hand in hand. After all, a generic 1m ATM vol is not very different from VIX (in value, not in how it is computed). Below is a comparison, where the 1m ATM vol comes from a vol surface.
All else equal, higher vol means higher option price. You can find a few charts for vega and volga here. Volga, also called DvegaDvol or vega convexity, measures the rate of change to vega as volatility changes. This question asks about the value of a call option if vol increases (isolated). The question is flawed, as is the accepted answer but the other answers are all correct.
However, the decline in SPX is the most significant driver of option prices. Let's assume we bought the SPX 04/30/20 C3370 option. Simply plotting the price quoted by the primary exchange (Chicago) around the highest value of VIX in 2020 (2020-03-16) demonstrates this nicely.
This also holds for longer tenors. I priced with my in house tool a 1y ATM on 2020-02-24 which cost ~6.53%. On 2020-03-16 (highest VIX), it would have been worth ~0.77%, despite IVOL for the option increasing by ~5.189 percentage points (I am not including screenshots here, but the numbers are reliable).
That shape / direction depends a bit on where your option starts from in terms of moneyness. The link above (for vega and volga) shows that vega is highest for ATM options (volga lowest). Therefore, if you are owning a (deep) ITM call option with low vega, and VIX spikes (equivalent to SPX down), you will get closer to ATM (or even OTM). The closer you are to ATM, the higher it will become.
Below is a chart similar to @Jan Stuller that shows vega as a function of vol and also adds the call option price (this is in isolation, meaning all else equal). The relationship is clear here but not what usually will happen to Vega and prices.