vega linearity rule for barrier option and Markov/Martingale property

mensatrader

Active member
183 0
Hi all

Can anyone please help explain below 2:

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
 

mensatrader

Active member
183 0
Hi all

Can anyone please help explain below 2:

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

can anyone please help advise, many thanks.
 

DowJones

Experienced member
1,073 391
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?

OK, not my strong spot, but here's my understanding:
Basically Markov states that a stochastic process has no memory. So expectation has no dependence on any previous value information.
Martingale states that the future expectation of a stochastic process is equal to the current value, given all known information about the prior events. So past knowledge can't predict future values.
 

DowJones

Experienced member
1,073 391
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.
 

mensatrader

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?
 

mensatrader

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
 

DowJones

Experienced member
1,073 391
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

Yeah I know the book :) Vega is basically the sensitivity of option price to a change in vol of the underlying. Does that clarify?
 
 
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