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Option : Price, value, payoff

Dear All:

Coming to the derivatives, I am so confused about these terms: Price , Value , and payoff.

Could you please give an example of each one in terms of Option or Swap.

Thank you so much for your time

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Price and Value are the same thing. Both mean how much money you would pay for the derivative right now. Payoff means what the derivative pays at the maturity date or payment dates.

As an example, take a vanilla call option on some stock.

The Payoff at maturity is max[0, (Final Stock Price - Strike)]. 

The Price, might be, say $5. That’s how much it would cost to buy the option today. 

“The aliens on Mars cloned Hillary Clinton.” - Turd Furgeson

ohai wrote:

Price and Value are the same thing.

Hmm, not sure about this. The book says:

“Some confusion from that terminology may still arise, in that an option could trade in the market for an amount that differs from its value.”

(Institute 84)

Institute, CFA. 2016 CFA Level I Volume 6 Derivatives and Alternative Investments. CFA Institute, 07/2015. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

But then it also says:

“Pricing the option is the same as assigning its value.”

(Institute 84)

Institute, CFA. 2016 CFA Level I Volume 6 Derivatives and Alternative Investments. CFA Institute, 07/2015. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

So not sure.

I believe pricing the option is different than as assigning it’s value, because value at initiation should be 0. The price will be what you pay for it, but the value will change as the swap moves throughout it’s life.

Price and value are most definitely not the same thing.

Price and value are equal if the asset is fairly priced; they are not equal if the asset is either overpriced or underpriced.

The price of a derivative depends on the type of derivative:

  • The price of an option is the premium you pay to purchase it.
  • The price of a futures contract is the agreed price to be paid for the underlying at expiration.
  • The price of a forward contract is the agreed price to be paid for the underlying at expiration.
  • The price of an FRA is the fixed interest rate to be paid on the FRA.
  • The price of a swap is the fixed interest rate to be paid on the swap.
    • A plain vanilla interest rate swap has one price: the fixed rate.
    • A fixed-for-floating currency swap has one price: the fixed rate.
    • A fixed-for-fixed currency swap has two prices: the fixed rates on the two currencies.
    • A floating-for-floating currency swap has no price: there is no fixed rate.
    • A fixed-rate equity swap has one price: the fixed rate.
    • A floating-rate equity swap has no price: there is no fixed rate.

The value of a derivative is the present value of what you will receive less the present value of what you will pay, each discounted at the risk-free rate.

Simplify the complicated side; don't complify the simplicated side.

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More pondering:

“Consider the purchase of a call option at the price c0. The value at expiration, cT, is cT = max(0,ST – X).”

(Institute 123)

Institute, CFA. 2016 CFA Level I Volume 6 Derivatives and Alternative Investments. CFA Institute, 07/2015. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

The book is using little c to mean both price and value! Very confusing.

Anyway, based on what Magician stated:

Currently my interpretation of options is:

If the option is fairly priced, as you pointed out, the price and value will equal. So for a call costing say $5, the underlying must be trading at for example $65 and the exercise price of this option must be $60. Options priced differently to $5 or with strike prices different from what I stated will be mispriced/over(under)valued. I’ve never traded options but I’m assuming that at time t=0, you can buy options with the same strike at different prices and also at the same price with different strikes? This is based on the table in Reading 60 under the heading “2. Option Strategies for Equity Portfolios” As time goes by, we reach cT, at which point we definitely can be observing the value of the option based on the difference between the prevailing underlying’s price and the option’s strike. However, what would the price of this option be at t=T then?

P.S. Would be much clearer if the book didn’t mishmash the two terms. Another example of this happening:

We obtain the profit for the covered call by computing the change in the value of the position, VT – V0. First recognize that V0, the value of the position at the start of the contract, is the initial value of the underlying minus the call premium. We are long the underlying and short the call, so we must subtract the call premium that was received from the sale of the call. The initial investment in the position is what we pay for the underlying less what we receive for the call. Hence, V0 = S0 – c0. The profit is thus

(Institute 130)

Institute, CFA. 2016 CFA Level I Volume 6 Derivatives and Alternative Investments. CFA Institute, 07/2015. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

However at the start of the chapter, it clearly states:

S0, ST = price of the underlying at time 0 and time T

(Institute 120)

Institute, CFA. 2016 CFA Level I Volume 6 Derivatives and Alternative Investments. CFA Institute, 07/2015. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

Atomic_Sheep wrote:
The book is using little c to mean both price and value! Very confusing.

They’re assuming that the option is fairly priced.  It would be nice if they mentioned that somewhere.  (However, in their defense, they probably don’t realize that they’re making that assumption.)

At expiration the option has no time value, so its value is its intrinsic value:

  • Calls: max(ST − X, 0)
  • Puts: max(X − ST, 0)

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

Ah that makes sense!

I love it when I finally make sense.

(It happens so rarely.)

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/