18.1 Options and Option Pricing

Question 1

What is an option

Answer 1

• A contract giving the holder the right to purchase or sell an underlying asset at a fixed agreed price on or prior to a given date
• It is a right not an obligations
• There are two types of options
  o Call options
  o Put options

Question 2

What is a call option

Answer 2

Gives the owner of the option the right to buy an asset at a fixed price on or prior a given date

Question 3

What is a put option

Answer 3

Gives the owner of the option the right to sell an asset at a fixed price on or prior a given date

Question 4

What is the predetermined price

Answer 4

Known as the strike price or the exercise price

Question 5

What is it called if an option is redeemable at a predeterminable date

Answer 5

These are known as European options

Question 6

What is it called if an option is redeemable any time before the predetermined date

Answer 6

These are known as American options

Question 7

What is excising an option

Answer 7

The process of buying or selling the underlying asset using the option contract

Question 8

What is the excise or strike price

Answer 8

This is the fixed agreed price in the option contract, the price on which the holder of the option can buy or sell the underlying asset

Question 9

What is the Expiration date

Answer 9

• The is the maturity date of the option
• Once this date has passed the option is effectively dead

Question 10

What is the difference between American and European options

Answer 10

The difference being when they can be exercised:
* American options exercised any time before maturity
* European at maturity

Question 11

What is being “in the money”

Answer 11

• For a call option this is when the exercise price is below the current market price of the asset
• For a put option it is when the exercise price is above the current market price of the asset
• Note: being in the money does not mean you will be in profit, it just means the option is worth exercising. As the options cost money to buy
  o Of course would not want to exercise the option if it was the inverse as could go to the market and buy the asset at the lower market price that the predetermined price
  o Here we just bear the cost of taking a risk and it not realising a gain

Question 12

What is being “out of the money”

Answer 12

• For a call option this is when the exercise price is above the current market price of the asset
• For a put option it is when the exercise price is below the current market price of the asset

Question 13

What is walking away

Answer 13

The option holder has no obligation to exercise the option, they can ‘walk away’ from the option

Question 14

How do options work for common stock

Answer 14

• Investors regularly trade options on common stocks
• Common stocks often have quotes for options maturing at different dates
• For the different maturity dates there will be a range of exercise prices for which there will be a price for the option

Question 15

What is the relationship between the excise price and the price of the call and put option

Answer 15

• As the exercise price increases the price of a call option decreases
  o Not as attractive to buy the right to buy something at a higher price than it currently trades
• The inverse is true for call options
• Looking at a further horizon it is more expensive
  o More valuable as greater chance for changes to occur
  o Options are a hedge against volatility so more chance for that to occur

Question 16

How is the profit on call options determined

Answer 16

• If the share had no value then you would be at a loss equal to the cost of the option
• When the share price is positive but below the exercise price you would not exercise the option as you could buy it on better terms in the open market
  o Therefore, the level of loss remains equal to cost
• When the share price is greater than the exercise price, and you are in the money, you would get favourable terms on exercising the option but when factoring in the cost it would still be loss making
  o But the loss would be decreasing compared to not calling the option
  o Therefore, would call the option to reduce losses
• Until the share price is equal to the exercise price plus the cost of the option
• Anything further than this is profit
• There is a diagram in notes

Question 17

How do options compare to outright ownership

Answer 17

• If one compares this investment with the outright purchase of the share, then because of the cost of the option, the absolute gain which can be made is smaller.
• However, you have to remember that the initial investment to acquire the option is only going to be a fraction of that to purchase the share

Question 18

Who are the sellers of options

Answer 18

• If you can buy call options therefore someone must be selling them
• The investor who sells a call option must deliver the asset if asked to do so by the call option holder
• The seller of the call option will lose money if the share price ends up greater than the exercise price
• If on expiration date the share price is less than the exercise price that call option will not be exercised, and the seller’s liability is zero
  o All the risk is on the seller of the call option.
  o The seller is paid to take that risk
  o When the option is sold the seller receives a price that the buyer pays.
  o The seller of the call option is speculating with respect to how the market will move
• Can be very high risk if the seller does not already own that share and the stock market moves very positively

Question 19

How do you find the profit on put options

Answer 19

• You only exercise your put option (i.e. exercise your right to sell a share) if the share price is less than the exercise price S < X
• If not you walk away from the option

Question 20

What is the purpose of options

Answer 20

• Options are a means of reducing your risk exposure
• If you own shares in a company but are concerned that the market might fall, bear market, you could
  o Sell the shares
   Transaction costs
   What to then do with the cash
  o Protect your investment by purchasing put options
   The cost of which will depend on the value of the option

Question 21

What are some factors that affect the value of an option

Answer 21

1. The value of a call option will be greater, the greater the value of the underlying share
2. The value of the call option will be greater, the lower the exercise price
3. The purchase of a call option can be regarded as the purchase of a share on deferred terms. By not having to pay the full price now, there is the opportunity cost/saving of investing less initially and so any savings could be invested at the prevailing rate of interest
4. The time to expiry – the longer the period, the greater the value.
   There are at least two reasons for this relationship:
   a. As we have already seen, the lower the exercise price of the call option the greater the value. So, the further away the expiry date, the lower will be the present value of the exercise price
   b. The longer the time to expiry, the greater the chance there is for the share price to rise, since there is the expectation of positive returns on shares
5. The variability of the underlying share – the riskier the security the more valuable is the option. This is because with the greater variability of the share price there is a greater chance that the share will increase in value, than a similar security with a lower standard deviation

Question 22

How can options be valued

Answer 22

• Consider a replicating portfolio
• One that has the same outcomes.
• Then, if we can value that portfolio we can be confident of the option value
  o Via the ‘arbitrage’ principle
  o As you would expect the market to close that gap

Question 23

What is the Black-Scholes valuation model

Answer 23

• All the variables that go into the formulation are relatively straightforward, observable and available, apart from the standard deviation of the underlying share.
• We can estimate the standard deviation of the underlying share using historical data.
• Computer programmes are available to perform these calculations ( option values) at speed which is of vital importance in an ever changing market place

Question 24

What are the assumptions in the Black-Scholes valuation model

Answer 24

The Black-Scholes model does have a number of assumptions.
* The model assumes that no dividends are paid. Clearly there are many companies that do pay dividends so this can be problematic.
* If dividends were paid before expiry of the option this would reduce the price of the share and consequently the value of the option.
* Dividends can be incorporated by adjusting the underlying share price. You can simply deduct the dividend from the share price
* The model assumes European options. Such options cannot be exercised before expiration date. American options are generally priced using another pricing model called the Binomial Option Model.
* The model assumes efficient markets. In other words that the underlying price of the asset reflects all available information
* The model assumes frictionless markets. Friction refers to the presence of transaction costs. The Black-Scholes model was originally developed without consideration for such transaction costs
* Finally the model assumes that asset returns are lognormally distributed.
o It is generally accepted, that stocks have an upward drift. This is partly due to the expectation that most equities will increase in value over the long term and also because a stock price has a price floor of zero.
o The upward bias in the returns of asset prices results in a distribution that is lognormal. A lognormally distributed curve is non-symmetrical and has a positive skew to the upside

Question 25

How does risk relate to general investing

Answer 25

• In most financial environments risk is not looked upon as a good thing, in that you expect to be compensated to bear it.
• Investors investing in high risk securities (high beta) demand a higher return.
• High risk investments are discounted at higher discount rates to achieve positive NPV. Discounting at higher rates reduces present value

Question 26

How does risk relate to investing in options

Answer 26

• With respect to options it the other way round.
• An option written on an asset that is very volatile is worth more than one written on a safe asset.
• This is sometimes easy to forget given that in most financial contexts increases in risk reduces present value