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Covered call / Protective put - VALUE AT EXPIRATION

I might got this completely wrong, but I cannot get one thing out of my head.

VALUE AT EXPIRATION. I got confused with reading 60. Why is the value at expiration sometimes the value of an option, while other times it is the value of the position or (ct/pt and Vt)?

CFA books practice problems at the end of reading 60 got me confused. (I know these questions might sound stupid, it’s just that I cannot get my head around this :) )

What is that that I am not getting?

Thank you!

"Using Wiley for my CFA journey was by far the best option… I was able to pass on my first attempt.”– Moe E., Canada

Further to my message, see  below how CFA books define this:

c0,cT = price of the call option at time 0 and time T

p0,pT = price of the put option at time 0 and time T1

and later…

…The value at expiration, cT, is cT = max(0,ST – X). …

Value…Price?

The value of an option is what it should be worth; the price is what someone actually pays for it in the market.  If it is priced fairly, price = value.  If not, it may be overpriced (price > value) or underpriced (price < value).

As for the value of a covered call or a protective put at expiration, each is the value of the underlying at expiration (of the option) plus the value of the option at expiration.

These are best illustrated with examples. First, the covered call:

Suppose that you have a stock with a current market price of $100/share.  You have a short position in a call option on that stock with a strike price of $120/share.  We’ll compute the value of the covered call for various prices of the underlying stock at expiration.  If the price of the stock at expiration is:

  • $80, then the call is out of the money (the option holder isn’t going to exercise a call option to pay $120 for the stock when he can buy the stock on the market for $80).  The value of the covered call is $80 (stock price) − $0 (call value) = $80.  Note the minus sign on the call value: you’re short the call.
  • $90, the call is still out of the money, so the value of the covered call is $90 (stock price) − $0 (call value) = $90.
  • $100: still out of the money: $100 − $0 = $100.
  • $110: still out of the money: $110 − $0 = $110.
  • $120: now the call option is at the money, but its value is still zero: $120 − $0 = $120.
  • $130: finally, the call option is in the money; the option holder will exercise the option and buy the stock from you at $120.  The call value is $130 (stock price) − $120 (strike price) = $10; you’re short the call, so you will lose that $10.  The value of the covered call is $130 (stock price) − $10 (call value) = $120.
  • $140: now the call is worth $20 (= $140 − $120), so the value of the covered call is $140 − $20 = $120.
  • $150: the call is worth $30; the value of the covered call is $150 − $30 = $120.

Next, the protective put:

Suppose that you have a stock with a current market price of $100/share.  You have a long position in a put option on that stock with a strike price of $80/share.  We’ll compute the value of the protective put for various prices of the underlying stock at expiration.  If the price of the stock at expiration is:

  • $120, then the put is out of the money (you aren’t going to exercise a [ut option to sell the stock for $80 when you can sell the stock on the market for $120).  The value of the protective put is $120 (stock price) + $0 (put value) = $120.  Note the plus sign on the put value: you’re long the put.
  • $110, the put is still out of the money, so the value of the protective put is $110 (stock price) + $0 (put value) = $110.
  • $100: still out of the money: $100 + $0 = $100.
  • $90: still out of the money: $90 + $0 = $90.
  • $80: now the put option is at the money, but its value is still zero: $80 + $0 = $80.
  • $70: finally, the put option is in the money; you will exercise the option and sell the stock at $80.  The put value is $80 (strike price) − $70 (sock price) = $10; you’re long the put, so you will gain that $10.  The value of the protective put is $70 (stock price) + $10 (put value) = $80.
  • $60: now the put is worth $20 (= $80 − $60), so the value of the protective put is $60 + $20 = $80.
  • $50: the put is worth $30; the value of the protective put is $50 + $30 = $80.

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

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I think I will print this to add to my notes, THANK YOU VERY MUCH! (VERY MUCH)

Prego.

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/

S2000magician wrote:

The value of an option is what it should be worth; the price is what someone actually pays for it in the market.  If it is priced fairly, price = value.  If not, it may be overpriced (price > value) or underpriced (price < value).

As for the value of a covered call or a protective put at expiration, each is the value of the underlying at expiration (of the option) plus the value of the option at expiration.

These are best illustrated with examples. First, the covered call:

Suppose that you have a stock with a current market price of $100/share.  You have a short position in a call option on that stock with a strike price of $120/share.  We’ll compute the value of the covered call for various prices of the underlying stock at expiration.  If the price of the stock at expiration is:

  • $80, then the call is out of the money (the option holder isn’t going to exercise a call option to pay $120 for the stock when he can buy the stock on the market for $80).  The value of the covered call is $80 (stock price) − $0 (call value) = $80.  Note the minus sign on the call value: you’re short the call.
  • $90, the call is still out of the money, so the value of the covered call is $90 (stock price) − $0 (call value) = $90.
  • $100: still out of the money: $100 − $0 = $100.
  • $110: still out of the money: $110 − $0 = $110.
  • $120: now the call option is at the money, but its value is still zero: $120 − $0 = $120.
  • $130: finally, the call option is in the money; the option holder will exercise the option and buy the stock from you at $120.  The call value is $130 (stock price) − $120 (strike price) = $10; you’re short the call, so you will lose that $10.  The value of the covered call is $130 (stock price) − $10 (call value) = $120.
  • $140: now the call is worth $20 (= $140 − $120), so the value of the covered call is $140 − $20 = $120.
  • $150: the call is worth $30; the value of the covered call is $150 − $30 = $120.

Next, the protective put:

Suppose that you have a stock with a current market price of $100/share.  You have a long position in a put option on that stock with a strike price of $80/share.  We’ll compute the value of the protective put for various prices of the underlying stock at expiration.  If the price of the stock at expiration is:

  • $120, then the put is out of the money (you aren’t going to exercise a [ut option to sell the stock for $80 when you can sell the stock on the market for $120).  The value of the protective put is $120 (stock price) + $0 (put value) = $120.  Note the plus sign on the put value: you’re long the put.
  • $110, the put is still out of the money, so the value of the protective put is $110 (stock price) + $0 (put value) = $110.
  • $100: still out of the money: $100 + $0 = $100.
  • $90: still out of the money: $90 + $0 = $90.
  • $80: now the put option is at the money, but its value is still zero: $80 + $0 = $80.
  • $70: finally, the put option is in the money; you will exercise the option and sell the stock at $80.  The put value is $80 (strike price) − $70 (sock price) = $10; you’re long the put, so you will gain that $10.  The value of the protective put is $70 (stock price) + $10 (put value) = $80.
  • $60: now the put is worth $20 (= $80 − $60), so the value of the protective put is $60 + $20 = $80.
  • $50: the put is worth $30; the value of the protective put is $50 + $30 = $80.

when calculating the value of either the covered call or the protective put, should not I include the option premium received or paid?

Failure will never overtake me if my determination to succeed is strong enough!

No: sunk cost.

You would, however, include them in calculating the profit.

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/

S2000magician wrote:

No: sunk cost.

You would, however, include them in calculating the profit.

Thanks, very helpful.

Failure will never overtake me if my determination to succeed is strong enough!

You’re quite welcome.

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/