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# Put-call parity clarification

Video transcript

Voiceover: We've seen that the
payoff diagram at option expiration for owning the stock
plus a put on that stock at some strike price
that this payoff diagram will look exactly the
same as the payoff diagram as owning a call option on that
stock at the same strike price as the put option plus a
bond that's going to be worth the strike price at
the time of expiration. One point of clarification and actually let me just
draw that payoff diagram just so you know what it looks like. So, if this is the underlying
stock price, stock price. And let's just do the payoff diagram when we look at the value of
the portfolio or your holdings. What it looks like is this is
the strike price over here. If the stock is at the stock
price or anything lower you make a fixed value and anything above that you
get some type of upside. So, either if you have
the stock or the put you have this type of a payoff or if you have the call plus the bond. The one point of
clarification I want to make is that you can only say that this
is definitely true for European. For European call options, for European options I
should say in general. European call and put options. Because only in European options
can you know for certain, for sure that the options are
going to be exercised on the ex or they can only be exercised
on the expiration date. If we're dealing with American options either party could either on
the put side or the call side could exercise their options earlier
so it becomes a lot more complicated. Normally when we kind of deal
with the mathematics of options we're dealing with European options. So, even in the example where we
did our put-call parity arbitrage where we're able to make that free $5, the implicit assumption I made is that
we were dealing with European options. That the options could only be
exercised at the expiration date.