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Terminal Vs. Immediate Payoff for a Barrier

quotes

quotes

Joined
6/11/10
Messages
189
Points
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Consider two digital barrier options:

One gives off 1 at expiry so long as the underlying spot reaches some level before expiry
The other gives 1 immediately when the underlying spot hits that level

Of course these two options should have separate value.
I assume the first have a textbook solution, but how can we evaluate the second?
 
Values are going to depend on time, prevailing discount rates and on underlying dynamics. Trees can be used to model this and MC.
 
quotes said:
Consider two digital barrier options:

One gives off 1 at expiry so long as the underlying spot reaches some level before expiry
The other gives 1 immediately when the underlying spot hits that level

Of course these two options should have separate value.
I assume the first have a textbook solution, but how can we evaluate the second?
Click to expand...


Okay so you are asking the difference in price between an Instant One Touch and a Pay At Maturity One Touch. The difference is simply just the discount factor difference between maturity and expected time of trigger event given trigger occurs before maturity. If the total maturity is not particularly long dated and/or the forward points of the underlying are relatively flat, the two prices will be roughly equal (though of course the Instant will always have the higher price). Mr Doe is thinking of the difference between a European Digital and a One Touch, which I don't think is what you're asking. Alexei describes one way these products can be valued, but really the most commonly used model in the market, like for most flow exotic products, is PDE methodology which assumes a SV/LV blended process.
 
financeguy said:
Okay so you are asking the difference in price between an Instant One Touch and a Pay At Maturity One Touch. The difference is simply just the discount factor difference between maturity and expected time of trigger event given trigger occurs before maturity. If the total maturity is not particularly long dated and/or the forward points of the underlying are relatively flat, the two prices will be roughly equal (though of course the Instant will always have the higher price). Mr Doe is thinking of the difference between a European Digital and a One Touch, which I don't think is what you're asking. Alexei describes one way these products can be valued, but really the most commonly used model in the market, like for most flow exotic products, is PDE methodology which assumes a SV/LV blended process.
Click to expand...

Thank you for clarifying the post. Yes you got what I mean.
My question is : is there still a probability approach to price the Instant one touch?

I came up with something like forward as the underlying, but the slope barrier for the forward.
Obviously, it complicates the path but simplifies the payoff.
 
No it does not seem correct.
I have to know precisely when the barrier is hit and come up with the present value.
 
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