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## Finance and capital markets

### Course: Finance and capital markets > Unit 9

Lesson 1: Put and call options- American call options
- Basic shorting
- American put options
- Call option as leverage
- Put vs. short and leverage
- Call payoff diagram
- Put payoff diagram
- Put as insurance
- Put-call parity
- Long straddle
- Put writer payoff diagrams
- Call writer payoff diagram
- Arbitrage basics
- Put-call parity arbitrage I
- Put-call parity arbitrage II
- Put-call parity clarification
- Actual option quotes
- Option expiration and price

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# Put-call parity

The concept of put-call parity is that puts and calls are complementary in pricing, and if they are not, opportunities for arbitrage exist. Explore the concepts of put-call parity in this video. Created by Sal Khan.

## Want to join the conversation?

- The P/L payoff diagram for the Stock + Put seems identical to the payoff diagram for just the Call on its own (i.e. with no Bond) in the previous video. In both cases it is flat at -$10 while the stock price is <$50, $0 when the stock price hits $60 and +ve for all stock prices >$60. Where does the Bond fit in?(12 votes)
- The bond doesn't affect the P/L, it simply affects the value.

If you buy a call without a bond, it's worth $0 at/below $50 (value). You lose $10 (P/L). With the bond, the combination is worth $50 (from the bond) at/below $50 (value). You still lose $10 from the call (P/L). The bond is ALWAYS going to pay $50, unlike the call which fluctuates in value with the stock price, so it doesn't figure into a graph of profit/loss. It's a constant.(3 votes)

- I am still confused about the bond. Would you make a video to explain the purpose of the bond? Maybe it's advantages and definition?(8 votes)
- I think the "bond" acts as an "asset floor" for the buyer of the call. However, I have never seen put/call parity explained in this manner. I found it a bit confusing as well. I think that put/call parity becomes much easier to understand when one is instructed on riskless arbitrage of options using conversions/risk reversals (e.g. netting profits on Buy Call, Sell Put, Sell Stock).(2 votes)

- From my understanding, if we hold a bond, its price may change depending on the prevailing interest rate in the market. So, technically we would not be holding a $50 bond at all time right? If my argument is correct, wouldn't it be better if we simply hold cash of $50?(2 votes)
- The price of the bond itself may change over the period, but the value of the bond at maturity is guaranteed to be $50. Before maturity, the bond price will be the present value of the maturity value, which does depend on interest, but at maturity, the bond price does not depend on interest rates.(6 votes)

- What about buying a call option as insurance when intending to short a stock? Is this done? Is there a downside? For example:

- You borrow a stock (that is worth $50) and sell it at $50 with the intention to short once the stock price drops to $20

- You buy a call option with a strike price of $50

- Instead of going down, the price of the stock rises. But you don't lose money (except for the call option price) because you can still exercise the option to buy the stock back at $50.(3 votes)- Yes, people will sometimes do that. Of course, the downside is that you actually have to pay for the call option.(4 votes)

- Put call parity is a term to describe a call and a put of the same strike and the price of the underlying stock. It is a three way relationship in that there is an equilibrium in the prices of each. And if the prices are not valued accordingly than an arbitrage opportunity occurs and a profit can be locked in synthetically. If a put is offered below fair value relative to the three way relationship then you purchase the put and synthetically sell the same put by buying the stock and selling the call in the same strike. So I'm not sure why the use of a bond in this example of put call parity.(4 votes)
- You are mistaken about what the term means.

Put call parity refers to what sal talks about in this video. You can create a put with a call and a bond and a share of stock, and you can create a call with a put and a bond and a share of stock, and since the bond and the share are the same in either case, there must be a definite relationship between the price of a put and the price of a call.(0 votes)

- can put and calls be used on bonds as well, not just stock?(2 votes)
- Yes there are options on bonds which in case of call you get a right to buy a bond with particular price. There even options on the average temperature during particular month(3 votes)

- Here put call parity is used to reduce the investment risk for the investor . Is it right?(1 vote)
- No. Put call parity is really just an academic way to show how and why put and call prices have to be consistent with one another. If they aren't, then there would be an arbitrage opportunity (risk free way to make profit), and arbitrage opportunities are not supposed to exist for long (in most situations)(2 votes)

- This might be a stupid question, but wouldn't the bond price also go up or down? Surely it wouldn't always be stable. Maybe I'm missing some basic data.(1 vote)
- You are correct but at the expiration the bond issuer will give the holder 50$. The bond is worth 50$ at expiration date because of that.(2 votes)

- Hi there, I'm still a litle bit confused about the bond + call options. Will it gives the same result by shorting the stock and buy the call option? Thank you.(1 vote)
- shouldn't the bond be discounted? because the put call parity formula is S+P = C+K/(1+r)

k being the strike price (bond) in this example(1 vote)- Technically yes, but one could simply assume that the $50 is the present value of the bond at expiration.(1 vote)

## Video transcript

If we want to get the upside
of owning a stock while still mitigating the downside, in
case the stock price goes down, we saw that we could buy a stock
and an appropriate put option. So that when the stock
goes below some price, the put option
starts to have value, and so it mitigates
our downside. And just as a review,
these payoff diagrams are the values of-- or at
least the one on the left, is the value of our holdings
at some future date. And we're defining that
date to be the maturity date of the options
under question. Now, and this one over here
is the profit at that maturity date, and that's why we're
subtracting the actual costs to enter the position on
this one on the right. Now the question I want to
answer in this video is how can we get the same payoff diagram
without buying either stocks or puts? And as a bit of a
clue, think about what happens if we were to
just to buy a call option. Actually let me do it
in that same color. So if you were to just
have a call option, the payoff diagram
would look like this. You would never exercise the
call option at expiration, unless-- and we're
assuming this is at expiration or at maturity. But if the stock
price goes above $50, you would then exercise your
option to buy it at $50. So then it starts to
have value as the stock price goes above $50. If the stock price
goes to $60, you would exercise your
option to buy at $50, and then you could sell at
$60 and you would make $10. So you start to get
some of the upside. So how can we
shift this graph up to get exactly the
same payoff diagram? Well, we could
have a call option, and we could own something
that would essentially shift this entire
graph up by $50. So we could have, essentially,
a $50 bond, or a bond to that is worth-- let
me write it this way. A bond that is worth $50
at option expiration. So if there's some
interest we're getting, we might be able to buy
it for a little bit less. If there's zero interest, then
it's pretty much like cash, we would pay $50 for it. But the payoff diagram for a
bond that will be worth $50 at this date, at maturity,
or at expiration, the payoff diagram for just the bond
would look like this. It would just be
a straight line. It's guaranteed to pay you $50. So if you own the bond and
the call option, below $50, the call option is
worthless, so you're just going to have the
bond over here. And then above $50, you
still have the bond, but now the call option
is worth something. So you have the value of the
bond plus the call option. So at $60, the call option's
worth $10, the bonds worth $50, the combination is worth $60. And so the combination of the
call option plus the bond, you'll see it here
on the left, it's actually going to
have the same payoff diagram as the
stock plus the put. So you have the situation
here that a stock plus an appropriately
priced put or a put with a appropriate
strike price is going to be the same
thing when it comes to payoff, at a future
date, at expiration, as a bond plus a call option. And this right here is
called put call parity. And it shows the
relationship between all of these different securities. And if any of the prices
start to kind of not make this thing hold
true, there might be an arbitrage opportunity. But we'll cover that
in future videos.