Chapter 3 - Insurance collars and other strategies Flashcards
what is crucial to remember when compyting payoffs and profits for diagrams etc=
All values are in future value. This means that all initial amounts, or amounts payed earlier than t=T must account for interest.
what is the effect of owning asset and buying a put as insurance
Creates a floor in regards to how much we can lose.
what can we say about the payoff and profit diagrams of “asset + put” vs “call”
payoff diagrams are not the same. This is because of how the initial investments differ.
Profits are the same however.
if we buy call, we end up with asset IF stock price is above strike price K.
If below K, we dont get asset.
If we buy asset + put, we keep the asset if it is above K, same as with the call. We force sell it (exercising put) if S is below K.
Thus, the position at expiration is the same. But the timing of investments differ. Howver, since the positions are equal at the end, they must cost the same in future value terms, and therefore the profits are equal.
what do we call it when the insurance seller is insured (options)?
Covered writing
opposite of covered writing
Naked writing
what is covered writing
Writing options when you also have a position in the underlying that acts as insurance.
what is the equivalent of a covered call?
A written put.
we have limited gains, because the call option will be exercised if asset increase beyond strike price, and we also have potential for large losses. If the asset increase a lot in value, we will collect the shitty premium, but be forced to give away our asset.
At expiration, if S < K, the call will not be exercised, so we end up with premium call + asset.
For the written put, if S < K, we’d be forced to buy the shitty asset, so we end up with: put premium + asset.
In other words, same outcome.
If S > K at expiration, the call is exercised, forcing us to sell. For the writte nput, we wll not be forced to buy, so in either case we end up with the premiums.
There is the stock price at t=0, the P, the C and the stock price at t=T that work together here, along with interest.
is covered call writing a safe position?
no. It is a bet of low volatility
what is a covered put
writing a put against a short position in the underlying.
If the put is exercised, it is because the asset declined in value. We will be forced to buy it. We have also shorted the asset. Thus, the short position takes care of the losses we get from buying the shitty asset.
We actually use the shares from the written put to return shares from the short.
However, we also lose money should the stock appreaciate.
The covered put only makes constant cash whenever the stock price goes down. In such case, it gets the premium, and nothing more.
This is the same aswith the covered call, but for the upside. Covered calls make premium profit when the stock goes up.
elaborate on synthetic forwards
mimic a long forward position by using options.
The aim of a long forward position is to end up with the asset no matter what, and at a price known in advance.
We buy a call and write a put at the same strike price. The call makes sure that if the stock price appreciate, we can buy it for less than its future level.
The written put makes sure that we will be forced to buy the asset at the strike price should the asset drop.
This position is insured sort of, and if strikes are the same, the price at which we acquire the assets will be deterministic.
IMPORTANT: There is a premium here, since we buy call (require premium) and sell put (acquire premium). We can use this to relate the synthetic long forward contract to the pricing of puts and calls.
What are the 2 diffreneces between synthetic and actual forward contract?
1) Synthetic pays premium, regular forward have no premium
2) Regular forward pay forward price. Synthetic pay the strike price.
These must be related, so that arbitrage is not possible.
if we set the strike price high, something else must be low to balance it out. This would be the premiums. Same goes for hte opposite way.
what happens if we set strike prices equal to the forward price for a synthetic long forward contract?
In order to not create an arbitrage opportunity, the profit of synthetic must b eteh same as profit for the regular forward.
Since strike is the same as forward price, and the regular forward has no premium, the premiums of the synthetic long forward contract must cancel each other out perfectly.
what is the put call parity equation
C - P = PV(F_{0,T} - K)
A way of saying this is that “The final positions are the same (asset in our keep) so cost is the same. THe cost of the forward is forward price. The cost of the ssynth is premium diff + strike price”.
what is no arbitrage
if two positions have the same payoff, they must have the same cost
what are spreads?
Spreads refer to positions consisting of only calls, or only puts, but some are bought andsome are written
how can we achieve lower cost than either a long forward+put or a call option?
bull spread.
Buy a call, and sell an equivalent call with a higher strike price. This creates a gap. The written call force us to sell asset if the stock appreciate a lot, but if this happens, we’d already have been protected by the call we buy at lower strike.
essentially, with a bull spread, we give away some of the profit and as a consequence we get a lower cost of hte position.
can bull spreads by built from puts?
Yes. sell a high strike put and buy a low strike put
elaborate on box spreads
synthetic long and short forwards at different prices. Guarantees cash flow in the future. Costly, but no risk.
elab on collars
purchase of a put, write a call. Call must have higher strike price than the put.
Opposite (buy call sell put) is the written collar.
Collars are a natural short position.
