# vega linearity rule for barrier option and Markov/Martingale property

##### Active member
183 0
Hi all

1. the vegas emanating from the barrier part of a barrier option are concave for the seller. The combination barrier vega + vanilla vega will result in a concave vega for the long barrier (long knock in or short knock out) and a convex vega for the short barrier.

2. what's the difference between markov property and martingale property? is markov property referring to the expection of present value based on the nearest past information we have, while martingale property is estimating the expected value at any time in the future based on what we currently have?

many thanks

##### Active member
183 0
Hi all

1. the vegas emanating from the barrier part of a barrier option are concave for the seller. The combination barrier vega + vanilla vega will result in a concave vega for the long barrier (long knock in or short knock out) and a convex vega for the short barrier.

2. what's the difference between markov property and martingale property? is markov property referring to the expection of present value based on the nearest past information we have, while martingale property is estimating the expected value at any time in the future based on what we currently have?

many thanks

##### Active member
183 0
Just looking at your original post and not sure if you're asking for an explanation of both points (1 and 2) or just point 2 (hence my former post). If you're also asking about point 1, what bit of the vega linearity rule don't you understand? Again, I'm not a vol trader, but it's hard to trade FX and not pick up a little about this stuff.

thanks a lot, DowJones

yeah, was asking both 1 and 2. Markov and martingale does look very similar, right?

##### Active member
183 0
Just looking at your original post and not sure if you're asking for an explanation of both points (1 and 2) or just point 2 (hence my former post). If you're also asking about point 1, what bit of the vega linearity rule don't you understand? Again, I'm not a vol trader, but it's hard to trade FX and not pick up a little about this stuff.

I don't understand everything about the vega in the statement 1.

Don't know what the statement mean. The statement comes from the dynamic hedging book.

cheers

##### Active member
183 0
Yeah I know the book Vega is basically the sensitivity of option price to a change in vol of the underlying. Does that clarify?

yeah, , but why the vega linearity rule for barrier options is like that?

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