Options

Question 1

Covered Call

Answer 1

a party that already owns shares sells a call option, giving another party the right to buy their shares at the exercise price.

Question 2

Naked Call
Naked Put
Fiduciary Put

Answer 2

When someone creates (writes) a call without owning the underlying asset, it is known as a “naked” call.
In a Naked Put, the writer has not put the cash aside in an escrow to buy the shares if the put is exercised. The opposite of this would be a ‘Fiduciary Put’ in which is cash is put aside.

Question 3

Protective Put

Answer 3

When someone simultaneously holds a Long position in an asset and a Long position
in a put option on that asset

buying a put option to protect against the underlying falling in value, while retaining upside.

Maximum loss at expiry = S0 – X + p0
Breakeven stock price at expiry = S0 + p0
Maximum profit = unlimited

Question 4

Covered Call - Investment objectives

Answer 4

1. Yield Enhancement - with limited upside to generate extra cash flows. Strike price set above current price
2. Reducing a Position at a Favourable Price - earning Call Premium + Strike Price, Strike Price is set below current price
3. Target Price Realization - Strike price near the target price

Question 5

Who is Long and Short in Options?

Answer 5

The buyer of an option (pays premium) is Long.
The seller of an option (receives premium) is Short.

Question 6

Synthetic Long Forward Position

Answer 6

Long Call and Short Put position - in other words Buy a call option and Sell a Put

Assumption P0 and C0 i.e. Call and Put Premiums are same as per Put-Call Parity

c0 – p0 = S0 – PV(X), which can be rearranged to S0 + p0 = c0 + PV(X).

Assumption: Underlying pays no dividend

Question 7

Shape of Profit vs. Strike Price graph for Short and Long positions

Question 8

Collar

Answer 8

Zero cost collar is Call Premium equals Put Premium - can be done by playing with Strike Price

Investor is long in the underlying and Sells a call and uses the premium to buy Put options (Protective Put + Covered Call)

Max loss and profit is limited and pre-determined

A collar position is economically in between pure equity and fixed income exposure

Question 9

Straddle (long straddle)

Answer 9

Buy equal no. of call options and put options at the same X - Strike Price

Upfront cash outflow due to premiums for calls and puts

*betting on volatility / change in price of So

Buy the Put and Call options at the same price closest to the current price of the underlying

We will have two break-even prices - the price of the So will need to increase or decrease by the Po + Co

Question 10

Short Straddle

Answer 10

Sell Put and Call options

Enjoy cash inflow from premiums

*betting on price of So to remain stable and not change

Question 11

Bull Call Spread

Answer 11

With a view towards rising price of the underlying

Buy a Call option and write/sell a Call option (higher X price than Call buy) to fund the premium (subsidise) for buying the Call option

Upside is limited

Bull spreads use long options on the lower strike and short options (write higher price options - Bull) on the higher strike.

Question 12

Bull Put Spread

Answer 12

With a view towards rising price of the underlying

Sell a Put Option to earn premium and Buy a Put option to limit downside risk

Bull spreads use long options on the lower strike and short options (write higher price options - Bull) on the higher strike.

Question 13

Bear Put Spread

Answer 13

With a view towards declining price of the underlying

Buy a Put option at a higher strike and Sell a Put option at a lower price to Subsidise

Bear spreads use short options on the lower strike price (Bear) and long options on the
higher strike price.

Question 14

Bear Call Spread

Answer 14

With a view towards declining price of the underlying

Sell a Call option at a lower strike and Buy a Call option at a higher price for Protection

Question 15

Debit Spread

Answer 15

Cash Outflow - Spread strategy where Buying an option is more expensive than Selling an option

Question 16

Credit Spread

Answer 16

Cash Inflow - Spread strategy where Selling an option generates more money than buying an option

Question 17

Delta for Future and Forwards

Answer 17

Futures and forwards on underlyings that pay no yield (e.g., nondividend paying stocks) are
essentially proxies for the underlying, so they also have deltas of +1 (if long) and –1 (if short).

Question 18

Synthetic Short Forward position

Answer 18

selling a call and buying a put at the same strike price and maturity.

Question 19

Long and Short Straddle

Answer 19

A long straddle is an option combination in which one buys both puts and calls, with the same exercise price and same expiration date, on the same underlying asset.
If someone writes both options, it is a short straddle.

A straddle is an example of a directional play on the underlying volatility.
Increased volatility - long straddle
decreased volatility - short straddle

buyer believes the ‘true’ volatility is higher than the market consensus

Question 20

Calendar Spread

Answer 20

A strategy in which one sells an option and buys the same type of option but with different expiration dates, on the same underlying asset and with the same strike,

When the investor buys the more distant call and sells the near-term call, it is a long calendar spread. (Expectation implied volatility will remain unchanged)

The investor could also buy a near-term call and sell a longer-dated one, known as a short calendar spread.

Calendar spreads can also be done with puts; the investor would still buy a long-maturity put and sell a near-term put with the same strike and underlying to create a long calendar spread.

As discussed previously, a portion of the option premium is time value. Time value decays over time and approaches zero as the option expiration date nears.

Taking advantage of this time decay is a primary motivation behind a calendar spread. Time decay is more pronounced for a short-term option than for one with a long time until expiration.

A calendar spread trade seeks to exploit this characteristic by purchasing a longer-term option and writing a shorter-term option.

Big move in underlying or decrease in implied volatility will help short calendar spread

stable market or increase in implied volatility will help long calendar spread

Overall, calendar spreads are sensitive to movement of the underlying and also to changes in implied volatility

Question 21

Position Delta

Answer 21

Unless told otherwise, assume that a traded stock option contract is a right over 100 shares. So a long position in an XYZ call option contract, where the option delta is +0.65, would have a position delta of 100 × +0.65 = +65.

A holding of 1,000 shares in XYZ, plus a long position in 10 XYZ put contracts (delta = –0.6), has a position delta of (1,000 × +1) + (10 × 100 × –0.6) = 1,000 – 600 = 400.

Some of the stock’s exposure is being offset by the negative exposure given by the puts.
If the stock price falls $1, then the shares lose $1,000, but the net position value will only fall $400.

Forward contract based hedge
position delta of number of shares × (delta of long stock + delta of short forward) = number of shares × (+1 + –1) = 0, and would be completely hedged

Question 22

Volatility Skew

Answer 22

A volatility skew is where implied volatility increases for more OTM puts, and decreases for more OTM calls. This is explained by OTM puts being desirable as insurance against market declines (so their values are bid up by higher demand, and higher values imply higher volatility), while the demand for OTM calls is low.
Deviations in the skew from historical levels can be used to draw conclusions about market sentiment:

A sharp increase in the level of the skew, plus a surge in the absolute level of implied volatility, is an indicator that market sentiment is turning bearish.

Higher implied volatilities (relative to historical levels) for OTM calls indicate that investors are bullish, so the demand for OTM calls to take on upside exposure is strong.

Question 23

Risk Reversal & Delta Hedge

Answer 23

Trading strategies that attempt to profit from the existence of an implied volatility skew and from changes in its shape over time. A common strategy is to take a long or short position in a risk reversal, which is then delta hedged.

Using OTM options, a combination of long (short) calls and short (long) puts on the same underlying with the same expiration is a long (short) risk reversal. In particular, when a trader thinks that the put implied volatility is too high relative to the call implied volatility, she creates a long risk reversal, by selling the OTM put and buying the same expiration OTM call. The options position is then delta-hedged by selling the underlying asset.

The trader is not aiming to profit from the movement in the overall level in implied volatility. In fact, depending on the strikes of the put and the call, the trade could be vega-neutral.
For the trade to be profitable, the trader expects that the call will rise more (or decrease less) in implied volatility terms relative to the put.

Question 24

Term Structure of Volatility

Answer 24

There is a term structure of volatility, where implied volatilities differ across option maturities (contango is quite common, with longer-dated options having
higher implied volatilities).

Question 25

Implied Volatility Surface

Answer 25

An implied volatility surface uses a three dimensional graph, with

Implied volatility on the z-axis,
to examine the joint influence of
maturity (x-axis) and
strike price (y-axis).