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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?
• 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.
• 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?
• 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).
• 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?
• 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.
• 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.
• Yes, people will sometimes do that. Of course, the downside is that you actually have to pay for the call option.
• 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.
• 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.
• can put and calls be used on bonds as well, not just stock?
• 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
• 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)
• 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.