Revised Options

Question 1

What is the equation for put-call parity?

Answer 1

S + P = Call + X/(1+r)

Question 2

What is put-call-forward parity?

Answer 2

F/(1+r) + P = Call + X/(1+r)

Question 3

How do you use options to create a synthetic forward?

Draw a diagram showing potential payoffs

Answer 3

This is when you take a long call (upside) and short put (downside) at the same X.

Question 4

Why would you want to create a synthetic forward? Draw an example

Answer 4

1. Hedge out a short forward
2. Create a long forward
3. Take advantage of overpriced forwards (sell forward)

Question 5

Why would you want to create a short synthetic forward?

Answer 5

1. Hedge a long forward
2. Arbitrage an underpriced forward
3. Create short forward

Question 6

How can you create a synthetic long call position?

Answer 6

Using P-C parity…
S + P = Call + X/(1+r)
Call = S + P - X(/1+r)
Therefore a synthetic long call is a long stock, long put,

Question 7

How can you create a synthetic long put?

Answer 7

S + P = C + X/(1+r)
Therefore P = C - S + X/(1+r)
Long a call, short the stock

Question 8

Describe Delta

Answer 8

Delta measures the change in option value for a change in the price of the underlying. This is always positive for calls, negative for puts

Question 9

Describe gamma

Answer 9

Gamma measures the change in delta for the change in underlying price - this is always positive for long options

Question 10

Describe vega

Answer 10

Vega measures the chance in option price for a change in vol - always positive for long options

Question 11

Describe theta

Answer 11

Measures the value of an options price for changes in time - always negative for long options

Question 12

What are the primary purposes of covered calls?

Answer 12

1) Yield enhancement - sell OTM calls
2) Position reduction - sell ITM calls
3) Position exit at a target price

Question 13

Why does it make sense to buy longer dated puts? Draw an explanation

Answer 13

Option values decay faster closer to expiration, therefore you could sell early if you didn’t need the insurance anymore

Question 14

Describe the delta profiles of a covered call, also draw

Answer 14

Covered call will start with a delta of 1 when you own the stock. You will receive negative delta from selling the call. Calls increase delta as price increases (more in the money). Therefore, as calls are more ITM the total portfolio delta will approach 0. Upside is capped, downside is unlimited.

Question 15

Describe the delta profile on a protective put, also draw

Answer 15

Protective puts start with a delta of 1 when you own the stock. You then buy a put which has negative delta. The more prices decrease, the higher the put delta is and the closer to 0 delta the entire portfolio is. Upside is unlimited, downside is capped

Question 16

What is the biggest difference between using covered calls and using a short forward contract.

Answer 16

Both will reduce the delta of a portfolio. Covered calls reduce delta on the upside, whereas short forward reduces delta across the spectrum

Question 17

Why would you buy a call on a short underlying position? Draw an example

Answer 17

A short underlying position has a negative delta of one. A long call will have a positive delta that increases as the stock price increases. Essentially you are mitigating the downside of your short as big price increases cause short losses, but the call can recoup some

Question 18

Why would you sell a put on a short underlying position? Draw an example

Answer 18

A short underlying position has a delta of negative one and a short put will have a positive delta. As prices drop, the short put will increase in delta, offsetting the short position. This means that upside is capped below the put strike price, but you have unlimited downside. This is the opposite of a covered call.

Question 19

What is the defining characteristic of a bull spread?

Answer 19

A bull spread is a positive delta position (gains as prices increase). It can be done using calls or puts.

Question 20

What is the defining characteristics of a bear spread?

Answer 20

A bear spread has negative delta.

Question 21

How do you construct a basic bull spread using calls?

Answer 21

Bull spreads need positive delta. Therefore, the call you buy must have higher delta (lower priced). To help fund the position, you will sell a call at a higher price.

Question 22

How do you construct a basic bull spread using puts?

Answer 22

A bull spread needs positive delta. Therefore, the put you sell must have higher delta than the put you buy. Higher delta for a put means a higher strike price (closer). You would sell a put near current prices and buy a put at a much lower price.

Question 23

How do you construct a basic bear spread using puts?

Answer 23

A bear spread needs negative delta. Puts have negative delta already, so our put purchase must have more negative delta than our put sale. Delta on put options increases as strike is higher, as it is more ITM.

Question 24

How do you construct a basic bear spread using calls?

Answer 24

A bear spread has negative delta. Calls have positive. Therefore, we must sell calls with higher delta. high delta call options are more ITM, therefore the strike price will be lower.

Question 25

You have an ITM call option and you’re looking to do better than just selling it. How can you use a call bull spread to make more money? Assume you have a call that you bought for $1.50 strike 40, it is worth $8,30 today, Spot is 48, and calls at 45 are worth 4.42

Answer 25

You could sell a call at a higher price which could cut off some upside.
You have a profit of $8.30 - 1.5 = $6.8.
You could sell a higher call at 45 for 4.42.
If the price drops drastically to take your first call out of the money, you would still make 4.42-1.50
You would cut your max profit from unlimited to 5 + 4.42 - 1.5

Question 26

What is a straddle strategy and why would you use it?

Answer 26

This is when you buy a call and a put at the same strike price (as close to ATM as possible). This is a play on price volatility. The delta is essentially 0 but gamma and vega are high.

Question 27

What is a collar and why would you use it? How is it difference than a bull spread? Draw a collar

Answer 27

A collar combined a covered call with a long put option.
You long exposure through the stock, with limited upside due to the covered call. You also own a put which limited downside. You could also use this with a protective put and a short call. you have long exposure with upside capped with the new short call. Downside is capped with the put. You could use this to lock in previous gains or mitigate vs adverse events. This is different than a bull spread because in a collar you own the underlying.

Question 28

What changes as the spread of a collar changes?

Answer 28

As the spread converges, the delta will approach zero. This is intuitive as you don’t benefit from any movement in the underlying. If you put a full collar ATM, you will earn the risk free rate.

Question 29

What is a calendar spread? Long vs short? Why would you do it? Draw an example

Answer 29

This is when you buy and sell the same type of option with different expirations. Long is when you buy long and sell short. Short position means you’re short the long dated option. The purpose of this is to play thetha assuming the near term option decays faster. In general you want to be short the option with higher theta.

Question 30

How do you move implied annual vol to monthly?

Answer 30

Monthly = Annual / (sqrt(252/21))
Annual = Monthly * (sqrt(252/21))

Question 31

Why does volatility depend on the strike price?

Answer 31

1. Demand for insurance (higher volatility in OTM puts)

2. Bullish sentiment (OTM calls)

Question 32

What does volatility skew measure? What does it mean?

Answer 32

Vol skew is the implied vol for puts - calls, it measures the increased IV on puts. Typically means somewhat bearish if steepness is increasing

Question 33

What is a long delta hedged risk reversal?

Answer 33

This is when you’re long an OTM call and a short OTM put at a lower price, but at the same expiration. This indicates that you believe implied volatility is too high in the puts compared to the calls. Both positions are positive delta so you need to sell the underlying short.

Question 34

Explain the term structure of volatility

Answer 34

It is in contango meaning that it increases for longer time horizons. In periods of stress this can invert.

Question 35

You are bearish on a stock and expect its volatility to decrease - what options strategy should you use?

Answer 35

You should write calls to capture excess vol premium

Question 36

You are bearish on a stock and don’t have a view on volatility - what options strategy should you use?

Answer 36

You should either 1. Take a synthetic short by selling calls and buying puts or 2. Collar your long positions or 3. Go short risk reversal if you can

Question 37

You are bearish a stock and expected volatility to increase - what options strategy should you use?

Answer 37

You should buy puts to protect yourself in a cheap way

Question 38

You are neutral on a stock and believe vol is going to decrease - what should you do?

Answer 38

You should use a short straddle (write)

Question 39

You are neutral on a stock and believe vol is not going to change - what should you do?

Answer 39

You should use a calendar spread to take advantage of thetha as other greeks have low risk

Question 40

You are neutral on a stock and believe vol is going up - what should you do?

Answer 40

You should buy a straddle

Question 41

You are bullish on a stock and believe vol is going down - what should you do?

Answer 41

You should sell puts to capture the vol premium

Question 42

You are bullish on a stock and believe vol is going to stay the same - what should you do?

Answer 42

1. Synthetic long - buy call sell put

2. Long risk reversal - buy OTM call and sell OTM put with no delta (short underlying)

Question 43

You are bullish on a stock and believe vol is going up - what should you do?

Answer 43

buy calls as they are probably cheap

Question 44

What are the complications with delta hedging?

Answer 44

1. Only a linear approx
2. Delta changes with underlying and time and can change quickly
3. Units must be rounded