how down out and down in call behave like regular call option in section barrier options

FRM
#1

how down out and down in call behave like regular call option in section barrier options

#2

Plain vanilla Call C = Cin + Cout. And then solve required variable such as X via Put - Call Parity. Easy peasy.

#3

Could you please elaborate through example how Down and in call option combined with down and out call option = Standard call option.

Also Up and out call option combined with Up and in call option = Standard call option.

I am unable to relate this.

#4

You do not need to know to elaborate anything. The value of standard option is equal to sum barrier up and down options. You might be given two variables to simply calculate the third variable.

example:

you might be given the value of barrier Call in and out, Cin and Cout. You might be required to calculate the strike, X of standard option. You first calculate the value of standard Call as C = Cin + Cout and you are given the value of stock, S and risk free rate as well as maturity of option.

thus, you simply solve for strike via put - call parity as for regular option once you calculate that regular option value, C as combination of Cin and Cout. Same method you may apply for barrier Puts.

#5

I’d never heard of down and out options and down and in options before seeing this thread. So I read about what they are. Here goes:

A down and in call essentially does not exist until the price of the underlying asset drops below the barrier price. If that happens, it becomes a regular call option.

A down and out call is a regular call option as long as the price of the underlying asset does not drop below the barrier price. If the price of the underlying drops below the barrier price, the down and out call ceases to exist.

So, suppose that you buy a down and in call (Call A) and a down and out call (Call B) with the same everything: strike price, barrier price, and maturity date. Two things can happen between the date that you buy these options and their maturity date:

  1. The price of the underlying asset does not drop below the barrier price. In that case, Call B is a regular call option until maturity and Call A doesn’t exist. You have a regular call option from the date of purchase until maturity.
  2. The price of the underlying asset drops below the barrier price. In that case, we have two time periods:
  3. The time before the price drops below the barrier price. During that time, Call B is a regular call option and Call A doesn’t exist. You have a regular call option from the date of purchase up to that time.
  4. The time at and after the price drops below the barrier price. During that time, Call B doesn’t exist and Call A is a regular call option from that point to maturity. You have a regular call option from that time until maturity.

Putting the last two together, you have a regular call option from the date of purchase until maturity; first it’s Call B, then it’s Call A.

So, under all circumstances, you have a regular call option from the date of purchase until maturity.

#6

Fine S2000 but that’s not how GARP asks the question about those barrier options.

#7

I have no idea how GARP asks questions about barrier options.

I was answering this question:

#8

One call knocks in under condition X (and is not active under condition !X), and one call knocks out under condition X (and is active during condition !X). So, under both condition X and !X, you have one call option.