# Relationship between gamma and vega

### options - Link between Vega and Gamma - Quantitative Finance Stack Exchange

Gamma has to do with realized volatility — moves in the underlying asset. Is there a difference between a trader and a stock trader? A volatility trader would be profiting from a rise in VEGA through primarily delta neutral positions on long . You can see when implied volatility is low, the gamma risk is much higher for the at-the-money strikes. relationship between gamma and vega. We looks at formula, calculations, relationships and plots. that we see a difference emerging in the relationship between Vega and Gamma.

This concept is probably best explained visually. The variation in gamma across the strikes is much smoother when volatility is high. Therefore, you can assume that the gamma risk of at-the-money options is much higher when volatility is low.

Here is the same data represented graphically. You can see when implied volatility is low, the gamma risk is much higher for the at-the-money strikes. However, every option combination strategy will also have a gamma exposure. Trades that require you to be a net seller of options, such as iron condors, will have negative gamma, and strategies where you are a net buyer of options will have positive gamma.

Below are some of the main options strategies and their gamma exposure: The weekly condor has a -4 gamma which is twice as high as the monthly condor at Clearly, the weekly condor has a much higher gamma risk.

This is part of the reason why I do not like to trade weekly condors. A small move in the underlying can have a major impact on your position.

Comparing a weekly and monthly 10 point butterfly, we have an interesting situation, with both trades basically having zero gamma at initiation. This is due to the fact that the short strikes were exactly at-the-money with RUT trading at at the time. In any case, we see that with a The weekly butterfly has a whopping point change in delta!

## Gamma Risk Explained

To calculate the Greeks in option we use the Black-Scholes option pricing model. Delta and Gamma are calculated as: Example — In the example below, we have used the determinants of the BS model to compute the Greeks in options.

At an underlying price of If we were to increase the price of the underlying by Rs. As can be observed, the Delta of the call option in the first table was 0.

### Vega, Volga & Vanna. The option volatility Greeks

Hence, given the definition of delta, we can expect the price of the call option to increase approximately by this value when the price of the underlying increases by Rs.

The new price of the call option is The third Greek, Theta has different formulas for both call and put options. These are given below: In the first table on the LHS, there are 30 days remaining for the option contract to expire.

We have a negative theta value of He has to be sure about his analysis in order to profit from trade as time decay will affect this position. This impact of time decay is evident in the table on the RHS where the time left to expiry is now 21 days with other factors remaining the same. This decrease in delta reflects the lower probability the option will end up in-the-money at expiration. How delta changes as expiration approaches Like stock price, time until expiration will affect the probability that options will finish in- or out-of-the-money.

Because probabilities are changing as expiration approaches, delta will react differently to changes in the stock price. If calls are in-the-money just prior to expiration, the delta will approach 1 and the option will move penny-for-penny with the stock. In-the-money puts will approach -1 as expiration nears.

### Greeks (finance) - Wikipedia

If options are out-of-the-money, they will approach 0 more rapidly than they would further out in time and stop reacting altogether to movement in the stock. Again, the delta should be about. Of course it is.

**Delta & Vega's Trade Relationship - Options Trading Concepts**

So delta will increase accordingly, making a dramatic move from. So as expiration approaches, changes in the stock value will cause more dramatic changes in delta, due to increased or decreased probability of finishing in-the-money.

But looking at delta as the probability an option will finish in-the-money is a pretty nifty way to think about it.

As you can see, the price of at-the-money options will change more significantly than the price of in- or out-of-the-money options with the same expiration. Also, the price of near-term at-the-money options will change more significantly than the price of longer-term at-the-money options. So what this talk about gamma boils down to is that the price of near-term at-the-money options will exhibit the most explosive response to price changes in the stock. But if your forecast is wrong, it can come back to bite you by rapidly lowering your delta.

But if your forecast is correct, high gamma is your friend since the value of the option you sold will lose value more rapidly. Theta Time decay, or theta, is enemy number one for the option buyer.

Theta is the amount the price of calls and puts will decrease at least in theory for a one-day change in the time to expiration.