Lecture 8

Question 1

What is an exotic option?

Answer 1

It is an option with a non-standard payoff.

Question 2

What are the main differences with standard options?

Answer 2

(1) Value: may depend on some event happening over the life of the option.
(2) Structure: may embed some extra optionalities.
(3) Expiration dates: may be multiple and random.
(4) Underlying: can be >1.
(5) Usually traded OTC -> thus could be less liquid.

Question 3

Why do exotic options exist?

Answer 3

(1) To meet the clients’ needs.
(2) Cheaper or more effective than standard options.
(3) Taxation.
(4) To solve particular business problems.
(5) Hedging.
(6) Creativity.

Question 4

What makes an option attractive?

Answer 4

Its possibility of fair pricing and hedging the product.
An option is fairly priced when there is a tractable relationship among the Greeks (which may behave differently than under the BS model).

Question 5

Which approach works well in pricing exotics?

Answer 5

Risk-neutral approach.The today option price is just the present value of the expected pay off discounted with the risk-free rate.

Question 6

What is a Gap Option?

Answer 6

A plain vanilla option with a final payoff that has a gap at a given strike price. This gap makes them more expensive than standard ones as it increases the payoff by x.

Question 7

What is the final payoff of a gap call and a gap put?

Answer 7

Gap call: S-K1 when S>K2
Gap put: K1-S when S<K2

Question 8

What is a Cliquet Option?

Answer 8

This is a series of call or put options with rules determining how the strike is determined.
It is a series of ‘pre-purchased’ ATM options with a premium determined in advance.
When one option expires a new similar ATM comes into existence (at reset date).
Its main advantage is that a Cliquet cost is known in advance for all maturities (strike prices are not tho).

Question 9

When does it make sense to buy a Cliquet Option? Why?

Answer 9

When volatility is expected to rise. Because the ‘reset’ feature gives the investors more chances to get money.
This is convenient as a passive investment for a medium-term investor.

Question 10

Given lower and higher volatility, when is a Cliquet cheaper or more expensive?

Answer 10

Lower volatility: Cliquet is more expensive than buying calls annually.
Higher volatility: Cliquet is cheaper.

Question 11

What is a Compound Option? Which are the 4 types?

Answer 11

An option whose first underlying is an option. The first option is the option to buy/sell an option. And the second option is the option to buy/sell the underlying. Only if both are ITM the compound option arrives to the end.
(1) A call on a call.
(2) A call on a put.
(3) A put on a put.
(4) A put on a call.

Question 12

What costs more a plain vanilla cost or a call on a call? Why?

Answer 12

A call on a call, because it provides the option holder with more flexibility. The holder has the opportunity to benefit from two price movements in the underlying asset.

Question 13

What is a Chooser (As You Like) Option?

Answer 13

It gives the holder the possibility to choose, up to a given time before expiration, if at expiration the option will be a call or a put. It has 2 periods: expiration and decision day (prior to expiration).

Question 14

What are the 2 types of Chooser Options?

Answer 14

(1) Simple: both options are European and with the same strike price.
(2) Similar to a compound option if not.

Question 15

What is the value of a Chooser option at t=0, at t=1 and a time between 0 and 1?

Answer 15

At t=0 Chooser costs the same as a plain vanilla call/put.
At t=1 Chooser costs the same as a straddle (simultaneous purchase of a call and a put).
At 0<t<1 Chooser costs more than a call but less than a straddle.

Question 16

What is a Barrier Option?

Answer 16

It is an option whose pricing/hedging is also determined by an extra parameter - the option barrier (H).
The option comes into existence if the stock price hits the barrier. (1) In (or knock-in) option.
Option dies if the stock hits the barriers (2) Out (or knock-out) option.
The barrier can have different positions concerning the underlying: stock price must hit the barrier from below (3) up option or from above (4) down option.

Question 17

What are the 8 Barrier Option types?

Answer 17

(1) Up-and-in.
(2) Up-and-out.
(3) Down-and-in.
(4) Down-and-out.
Each can be either a call or a put, leading to 8 alternatives in total.

Question 18

What is the sum of a knock-in and a knock-out option? Why? Is this sum more or less expensive than a plain vanilla option?

Answer 18

The sum is the plain vanilla option (either a call or a put). The effects of a knock-in and knock-out options cancel each other out. The sum should be exactly the price of a call or a put.

Question 19

Why would you buy a barrier option?

Answer 19

It is the perfect asset for those who want the payoff of a call/put option but don’t want to pay for all the upside/downside potential.

The closer is the barrier to the the stock price the lower the price for out options and the higher the price for in options.

Question 20

How can we price the barrier option in closed-form?

Answer 20

For calls, we know that
c= c(ui) + c(uo) and
c = c(di) + c(do)
For puts, we know that:
p = p(ui) + (uo) and
p= p(di) + p(do)

Question 21

When does the stock price beach the barrier in the 2 period model?

Answer 21

Only if it moves up in the first period. The barrier options are path dependent. We treat each price path separately and check whether the barrier is breached or not.

Question 22

What is a Binary Option?

Answer 22

Binary or Digital option is any option with a discontinuous payoff structure.

Question 23

What are the 2 types of binary calls?

Answer 23

(1) Cash-or-nothing call:
payoff = Q if St>K or 0
value: c = Qe-rT N(d2)
N(d2) is the probability of being in the money.
(2) Asset or nothing call:
payoff = St if St>K or 0
value: c=Ste^(-qt) N(d1)
N(d1) is the probability of getting the underlying.

Question 24

What kind of payoff do you recreate by going long an asset-or-nothing call and going short a cash-or-nothing call with payoff K?

Answer 24

A payoff of a plain vanilla call.

Question 25

What are the 2 types of binary puts?

Answer 25

(1) Cash-or-nothing put:
payoff Q if St<K or 0
value: p=Qe^(-rT) N(-d2)
(2) Asset-or-nothing put:
payoff St if St<K, otherwise 0
value: p = St e^(-qT) N(-d1).

Question 26

What kind of payoff do you recreate by going long an cash-or-nothing put and going short asset-or-nothing put with payoff K?

Answer 26

A payoff of a plain vanilla put.

Question 27

What is the payoff of going long a call and a put cash-or-nothing?

Answer 27

A form of financing that gives K for sure regardless of S.
c + p = Ke^(-rT).

Question 28

Why are binary options very rare in practice among professionals?

Answer 28

They are very easy to understand and price but very difficult to hedge.