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Asset or nothing call

T

The AA

Member
Hi,

Can anyone explain why the value for an asset (paying dividends) or nothing call is:

Soe^-(qT)N(d1)

I thought the probability of the asset being higher than the strike price is N(d2) not N(d1), and you then multiply this by the value of the stock at maturity ST.

Also can anyone explain the difference between limit order and market if toucjed order?
 
Hi TheAA -
examstudent mentioned a bit about the asset-or-nothing call in my previous thread (Q&A 4.11). The reason it's N(d1) not N(d2) is that the share price S_T is not fixed if it's above the strike price - so you have to integrate over the whole range of possible values not just look at the probability it's above the strike.

Limit order (sell) - sell at a price which is at least equal to the limit if this is possible, otherwise do nothing.
Market if touched (sell) - once the price touches the limit, then sell at whatever price you can get. If the price never touches the limit, do nothing.

The difference being that if the price reached the limit but fell again immediately, the MIT order would be executed (possibly below the limit price), the limit order might not be.

L
 
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