In this workout we're told that you are short 100 at the money one month puts and your long 100 at the money 12 month puts on the same underlying assets, whereas asked to please describe the sensitivities of this position, commenting on the combined either two positions.

Let's look at the similarities between the two put positions. Firstly, the first one there are 100 options.

The second one the same in both of them.

We see they're both at the money and they're both puts that we're looking at.

But the differences, that's where we're going to find more interest.

The first position is a short position, whereas the second is long and the first one we're looking at one month puts, whereas the second month we're looking at 12 month puts.

Okay. Where are the look at the delta gamma, the and Vega? Well let's remind ourselves what delta is.

Delta measures how much the options price changes for a change in the underlying assets price.

Does the option gain value or does it lose value? Well, as both options are at the money, their delta will be around positive or minus 0.5.

For the short one month puts this means a delta of positive 0.5.

For the long 12 month put position, this means a delta of negative 0.5.

The combined delta therefore is close to zero.

Basically they offset with each other, meaning we have a neutral position.

What about gamma? Gamma measures? How much the options delta changes for a change in the underlying assets price.

Gamma is the change in delta.

Well gamma is highest for at the money options with a short time to expiry.

Basically if we are really close to expiry and we're at the money, then anything could happen.

Our option could be worth lots of money and it could be worth absolutely nothing.

A long option Position means we're long gamma and a short option position means we're short gamma.

So we are short gamma on the one the month put and long gamma on the 12 month put as gamma is higher for short dated expires, we are net short gamma and that's our overall position. We are short.

So what about the The measures? How much an options price changes as time passes? It's called time decay.

We are long theater on the short one month at the money put option and we're short the on the 12 month at the money put option.

As with gamma theta is highest in absolute terms for short.

Dated at the money options.

Basically we're really, really close to expiry and because we're at the money, anything could happen.

The option could be valueless or the option could be worth lots of money.

The value of that time decay as those last few seconds pass getting us to expiry, that's worth an awful lot.

So read it again.

As with gamma, the is highest for short dated at the money options, so we are net long theater.

Lastly, vaguer Vaguer measures how much an options price changes for a change in implied volatility.

Volatility coming in the future? Well, Vega is highest for long dated at the money options.

We've got lots and lots of time until we expire. There's lots of potential for volatility there and it's highest for at the money options because again, if we're at the money, the option could be worth lots of money for small price change.

But if the price change goes the other direction, the option will be valueless.

So as we are short, a one month at the money puts, but long a 12 month at the money put, we are therefore net long vaguer.

Next we'll ask what is the p and l or profit and loss impact of the following scenarios.

All else being equal.

The first one is a quick rise in the underlying asset price.

Well what measures the changes in the asset price versus the option price? It's delta. So thinking about delta as you are approximately delta neutral, which we saw earlier at the beginning, the price rise will not generate a significant p and l impact profit and loss impact.

How? It's the difference in the times between those two option positions that is going to make a difference.

However, the delta of the short one month put position will fall faster in absolute terms than the delta of the long 12 month position leading to an overrule short delta position as the market rises.

If this is not addressed, this will lead to a negative p and l impact.

Lastly, a full and overall implied volatility.

Implied volatility is measured by vaguer, so we're currently long vaga.

As you are net long vaga, an overall fall in implied volatility will have a negative p and l impact.