Chapter 3 - Insurance, Collars and other strategies Flashcards
what happens if we add a position in the underlying to a put option?
elaborate in regards to payoff vs profit
The combined effect acts like a call option.
When accounting for the premium, the interest rate loss, and the position in the underlying (its payoff), we get a result that we have a certain level of the underlying where the payoff from the put is equal to the difference in payoff of the initial and current position in the underlying asset. Because of the premium on the option, this will be a negative amount for us. this level represent the premium we’d pay for the call option.
Actually, thisis not true. Understand the payoff.
For the put+long asset, we pay for the asset and the put. The payoff is equal to the value of hte long asset and the put.
For the call, we only pay for the premium, and the payoff is therefore equal to the option value only.
Thus, from a payoff POV (what we’d get from liquidating the position), the long+put is worth much more.
HOWEVER, the profit case is different. The profit of the long+put is equal to a regular call.
the payoff a long+put is not the same as for the call option. How can we change this?
We can add a bond to shift the curve vertically.
Since the profits are the same, the payoff is only some vertical adjustment away from equating them.
explain the essence of put-call parity
in general, one could say that put-call parity balance the prices of puts and calls based on the current risk free in regards to how much risk free rate you sacrifice by taking the asset position and how much risk free rate you benefit from the call+bond position
what is floor and cap
floor is referred to taking a put position to insure a long position.
cap is taking a call position to insure a short position
elaborate on interest rate considerations
There is a lot of epmhasis on the interest rate we earn in various scenarios.
for instance, if we short a stock, we are selling the shit and receiving liquidity in the form of cash. We can invest this cash to receive the risk free interest rate.
In all cases where we are not immedietly investing the cash, we need to consider the benefit of earning this interest.
In general, we say that there can be a benefit in earning an interest rate, while disadvantage to not be able to receive it. typically, the prices of for instance calls and puts will balance these so that no arbitrage is possible.
elaborate on who sells insurance
first of all, we need to understand that in order for people to be ableto buy insurance, someone must sell it. So who does it?
elaborate on some typical insurance “sells” cases
Covered writing. It is typical that if you own asset, you can write puts on it. You are covered, and you can collect premium on it.
Note how it applies to both calls and puts. You need to own the asset to be covered, as both calls and puts involve the seller having to essentially give away the shares.
what is the distinction between “option overwriting” and “covered write”?
Option overwriting refers to writing options on an asset you already own, while a covered write actually refer to buying asset and writing the put at the same time.
elaborate on naked writing
Writer of the option does not have a position in the underlying.
elaborate on covered calls writing
you own the asset, and write calls on it as well.
If the asset increase in value, you earn no money on the stock because you have to give it away. You earn the premium, but loose the asset.
If the asset decrease in value, we collect the premium and keep the asset. in such a case, we loose money on the asset, but earn premium.
The profit at expiration:
We decompose it to the two parts: the asset and the option call
The call profit consists of the premium multuplied by the rate, and the potential loss we have to pay if the asset increase in value beoyond the strike price. This value is equal to (StockPrice@expiration - strike price). It is actually a cost for us IF this value is positive. If negative, we dont pay anything.
the asset require the placement of money, and the asset will be worth something at the end of the period.
StockPrice@exp - initialStockPrice x rate.
So, if we buy the stock at 1000, and the strike is 1000, and the expiration price is 1100:
1100 - 1.02 x 1000 - 100 + C x 1.02
80 - 100 + Cx1.02
Can do break even analysis
Cx1.02 = 20
C = 20/1.02
C = 19.61
As long as the Call premium was larger than 19.61 we make money on it.
Writign covered calls is the same as writing puts. Same profit.
elaborate on covered puts
If you write a put, and at the same time enter a short position in the underlyinf, the following happens:
1) Should the asset decrease in value, we gain from the short position but loose on the option.
2) Should the asset increase in value, we collect the premium from the put, but loose on the short position.
what is actually covered, what does it mean to be covered in covered calls and puts?
Being covered does not refer to being fully hedged or whatever.
Being covered refers to having a way to “pay for” the shares should we be required to fulfill our obligation as the options seller.
Consider covered puts: Recall that a put contract is an obligation from the seller, where he is forced to buy the shares from you, if you want to, for a pre-specified price (strike price).
A put exercise involve the buyer actually selling the shares to the writer. Therefore, the writer receive the shares. Typically, the buyer of the put need to have sufficient funds ready to buy the shares at market price, which is then used to sell to the writer for the strike price, and results in profit.
So, for covered puts, we are looking for a way to hedge our case as the writer if we need to exercise. If we need to exercise, we essentially loose cash equivalent to the difference between the strike price and market price at expiration. If we have a short position in the underlying, we make cash if the stock drops.
however, if we write covered puts, and the strike is above the current stock price, the short position will not offset the entire position. However, the price of the put will balance it out.
but it is important to understand that covered puts are not necessarily entirely offset from the short position.
Consider covered calls: Now we are looking for ways to hedge our losses if we are forced to sell our shares for a fixed price. Our loss in this scenario is equal to the difference between the current stock price and the strike price. why? because we need to acquire the shares, which cost us equal to the current stock price, and then we need to immediately sell them for the pre specified price.
So, we loose the movement in the asset beyond the strike. If the strike was equal to the stock price at the point in time when we wrote the call, then a regular long position in the asset will bank us the money differnece.
If the strike is below the stock price at the point when we write the covered call, even a long position in the asset will not cover the losses by itself. However, if the call is OTM when we write it, the long position in the asset will more than cover for the losses. The balancing factor is the premium we can expect.
essence of put call parity
Put call parity tells us the difference in option price when they have the same time to expiration and strike price.
elaborate on synthetic forwards
We can create/mimic a forward contract on an asset by buying a call and selling a put.
writing the put obligates us to purchase and asset for some pre specified price if the price goes bad, while the call option allows us to purchase the asset for a favorable price if the price goes up.
Consider the strike price for them. If the asset value is above or below determine whether we will exercise the call or the put will be exercised. If asset value goes above the strike, we make linear money. If below, we loose linear money. The outcome is a linear profit curve (assuming the same strike).
The profit is also determines by the premium difference. We receive for the put but pay for the call. This is cash we’d receive risk free rate for.
Recall that forward contracts does not have premium.
But why does it resemble a forward contract?
- At expiration, one of 2 things will happen. Either WE exercise the call, and purchase the asset for the strike price. OR, someone exercise their put option, and WE are forced to buy their asset for the strike price.
- In either case, WE end up purchasing the asset for the strike price.
We refer to this as synthetic because it has differneces, but work relatively the same. These differences are :
- Forward contracts do not have premiums, but this one has
- The forward price and the strike price are two fundamentally different things. They can be compared, but are not the same.
Elaborate on why the forward price is not the same as the expected future realized price
the forward price reflect the value/loss of delaying the payment and transaction, but balanced with the guaranteed deal. Therefore, from the asset holder perspective, the forward price is very likely lower than the value at this point, but this is not the point of the deal. The point of the deal is that he has already found someone who has agreed to buy it. The value here is what would happen if the value of the asset would have tanked instead. There would be no good buyers, so having the guaranteed trade is extremely beneficial in these scenarios.
From the asset buyer perspective, the forward price is typically lower than the realized future price, which would be beneficial for him, but in some cases it is extremely opposite. He might be forced to purchase apple shares for 10$ a share should all of their products be banned etc.
Therefore, the question is, what should the forward value reflect? Since the asset buyer will have funds available until the expiration, he will earn money on it, assuming he is rational. if he invest it in risky securities, he will be fucked should he not be able to fulfill the forward contract. Therefore, the only rational option are risk free ones. You could keep the cash at hand, but this would not be rational, as you could earn the risk free rate otherwise.
As a resuklt, the forward price should be something like this: currentAssetValue(1+riskfreeRateAnnual/periods)^periods
When we let periods go towards infinity, we approach e^(riskFreeRateAnnualperiods), and of course we need to multiply this by the original asset value
NOt necessariyl a question, but
“key takeaways from forward contracts”
It is a risk minimizer at heart. Because of this, its dynamics mimic the thought of reducing risk exposure.
Both parties may benefit in regards to risk exposure, but whether the forward price will overshoot or undershoot the realized price depends on the risk profile of the underlying asset. Depreciating assets, like cars and boats and planes etc, have a very different risk profile than the concept of stocks. The forward price of a car will likely be higher than the actual realized price, because hte risk free rate is larger than the appreciation of the car.
Currencies, gold, and other commodities are considered relatively stable.
relate options prices to the synthetic forward contract
Recall that the synthetic forward contract is created by going long a call and writing a put. The whole idea is that we are locking ourself into purchasing the underlying at the strike price. If its current value is brlow strike, we will not exercie our option right, but the other trader will exercise his put option. The put option force us to buy HIS shares.
If current price is above strike, the other trader will not sell us his shares, he is better off selling shares at market price. However, we will exercise OUR right to buy shares from whoever we bought the call from.
The natural comparison is the price relative to the forward price. Naturally, it is beneficial for us to purchase the shares/assets for a price lower than the forward price. So if the strike price is very low, it looks like a bargain because we are buying asset lower than that of the forward price, and we know that the forward price is already a “perfect deal” in regards to only considering risk free asset on top of current asset price.
But in finance, assuming no arbitrage, such an advantage would be taken advantage of. This would balance it out. But what is the variable? The metrics like strike price, expiration, underlying are all fixed parameters. It is only the price of the call option and the price of the put option that are variable. It would only make sense if the difference between the premium we collect and the premium we pay is exactly equal to the opposite of the difference between the forward price and the strike price. Meaning, if we have the price advantage in regards to a low strike price, we will have an equal but opposite disadvantage in the premiums.
elaborate on the distinction between synthetic forwards and regular forwards
on the distinction between synthetic forward contract and regular forward contract:
Forward contracts have no premium.
Forward contracts have no strike prices, because this concept doesn’t make any sense when considering forwards. Only the forward price makes sense, and this price is purely computed based on the added benefit of being able to wait before fulfilling the deal.
Since a synthetic forward involve options, there is the concept of strike prices. And since there is options, there are premiums to account for as well.
The only case where the premium is the same for the call and put, is whenever the strike price is equal to the forward price. In such case, there is no benefit from either party in the deal in regards to risk free profit. I would pay him the same as he would pay me, and the benefit would be equal.
Once the strikes are not equal to the forward price, it will be in the favor of one party. The other guy, who buys the put, want the strike to be high, because this will obligate me to purchase his assets for a high price. for me, I want the strike to be low because then the other guy will sell me his assets for low price.
We know that a synthetic forward can create the same payoff as a regular forward. What can we conclude frm this?
Put call parity.
the net cost of buying an index at some future time using the synthetic forward must equal the cost of doing it with the forward.
The value of the regular forwards contract is just simply the present value of the forward price. There is no premium.
PV(F).
And this must equate the cost of the call less the benefit of the put plus the price we’re locking into (strike).
PV(ForwardPrice) = Call(K) - Put(K) + PV(K)
We can rewrite this to solve for the difference in premiums:
Call(K, T) - Put(K, T) = PV(ForwardPrice(T)) - PV(K)
Call(K,T) - Put(K,T) = PV(ForwardPrice(T) - K)
The difference in premium is equal to the difference in forward price and strike price.
We can note the connection to the put call parity as explained in corporate finance. That one use C-P = S - PV(K), where S is stock price and PV(K) is the bond we’re buying to get the risk free cash at hand to fulfill the deal. They argued that a position in the underlying and the put is worth the same as going long the call and using to bond to pay it. And it is, still the same, it is just that now we are sending the cash for the asset at the end, while in corp the asset position was established early on.
what is off-market forward?
Forward contract where the price is non-zero. In other words, the price of the contract is not equal to the no-arbitrage price.
There is some sort of compensation here.
In general, these are special needs like cash flow management etc that require sometimes custom settings.
conceptually, what does it mean that two portfolios has the same profit?
They must have the same payoff at expiration, and the same cost.
what is an option spread?
An option spread is a position consisting of either only calls or only puts. However, some are pruchased and some are written.
elaborate on buying a forward contract vs call option, when they have the same strike and expiration
The call option makes money if the asset value is greater than the strike price/forward price. The same happens with the forward contract. Their payoff is the same.
If the asset value is lower than the strike/forward price at expiration, the call option has 0 value, meaning 0 payoff, while the forward contract has a payoff value. We are tied to the deal.
Considering profit, we know that:
forward contract has no premium, and require only PV(forward price). Profit is equal to PV(asset value) - PV(forward price).
For the call option, there is the premium as well. But what should it be worth?
We use put call parity to find this.
Call - Put = PV(forward price) - PV(K)
Call = PV(forward price) - PV(K) + Put
In words, the call is worht the same as the present value of the forward contract plus the put. why plus the put? It is a hedge that limits its profit losses exactly like the call option does.
bull spread
Recall a spread: Buying and selling same option type but at different strike price.
Bull spread is just that we expect the stock to move up.
you buy a call, and then sell a call at a higher strike price, but otherwise all is the same.
Doing so essentially means that you give away a portion of hte profits, should the asset appreciate a lot in value.
We basically define a range in the interval between the strike prices, which become our target zone where we make money. All profit above the strike price of the option we wrote will offset because while we earn on the one we bought, we loose on the one we wrote.
define bull spread wiht puts
recall how puts and calls are just opposite. Calls give you the right to buy shares at fixed price. Puts give you the right to sell shares at fixed price. The profit curves therefore are very related.
If we buy a low strike put and write a high strike put, the following happens:
You make money on the net credit. Since we sell the one with the higher strike, this gives us more premium that we give away for hte lower strike put. So we net the benefit of the premium.
if we sell a high strike put, and but a low strike put, we make money on the net premium. But only if the asset value go beyond the high strike. If we end up in the range between strike prices, the one who buys our put will exercise, and we are forced to buy his shares. If the stock really tank, then our own protective put kicks in and offsets the loss beyond the low strike.
If the stock go above high strike, then happy days: we receive the full net premium.
opposite of bull spread
bear spread
elaborate on bear spread
the idea is that we believe the asset will drop in value. We are therefore looking for ways to exploit this using spreads. Spreads are cases where we buy and sell the same type of option but with differnet strike price.
elaborate on box spreads
Box spread is defined as creating a long synthetic forward at one price, and creating a short synthetic forward at another price.
the benefit of the box spread is that it guarnetees a cash flow in the future. If you’d only go short the synthetic forward we’d receive a fixed payoff, but we dont know about the profit. When we also go long a synthetic forward, there is a price difference between what we pay and what we get.
Recall that a synthetic forward (long) is achieved by going long a call, and writing a put, at the same strike price. The strike price acts as the balance point. If the asset value is larger than the strike, we exervise the call and receive the shares/asset at the strike price.
If the asset value is below the strike, the counterparty to our put option will exercise his right, which will force us to buy his shares at the strike. In either case, we end up with the assets at the strike price. Whether it is ultimately favorable for us depends on the asset value. Recall also that the point of such a position is not to be speculative, it is mainly about risk management.
Going short a synthetic forward involve writing the call and buying the put. At this position, if the asset value appreciate above strike price, the counterparty to our call will exercise, and he will buy our asset for the strike. If the asset depreciate below strike, we can exercise our put option that we bought, and force someone to buy our shares (the right to sell our shares for the strike). Going short a synthetic forward involve having an asset, and selling it for the strike price regardless of the stock movement.
KEY:
So, when we are talking about box spreads, and we say that a box spread is defined as going long one synthetic forward, and going short one synthetic forward, at different strike prices, we will make sure that we receive a certain cash flow from the short position, while getting the asset back from the long position. The payoff of this box spread is only positive if the strike price for the long position is lower than the strike price for the short position. However, the profit (which includes the premiums) is likely close to 0 in a no-arbitrage environment. Interesting part is that using a box spread, we can therefore make sure that we get a certain cash flow by paying the premium. In perfect markets (no fees) I suppose this would be a zero-value transaction.
Furthermore, this all means that a box spread is simply a tool for borrowing money or lending money. The premiums are multiplied by the risk free rate compounding using continuous compounding, and this must equal the difference in strike prices, the cash flow we receive with certainty.
long vs short box spread
Long box spread refer to paying a premium today and receiving the cash flow later. Therefore, you take the position of the lender.
Short box spread receive the net premium, but have to pay the difference later. Therefore, a short box spread position is about borrowing money.
use case of box spreads
Box spreads have the same workings as a risk free bond. However, the gain is classified as capital gain, not interest gain. Therefore, it can be used to offset taxes.
Say you sell shares for a loss. This is capital gain loss, which can be used to deduct taxes. But we need to have some gains for this to work. And regular interest income does not qualify. However, since the box spread is the same as a risk free bond, but with capital gain instead of interest income, we can use this to acquire non taxable risk free income.
It is not strictly speaking legal, but very hard to catch. The use of box spread is completely legal, but the illegal part happens if you write the gain as capital gain rather than interest income.
what is a ratio spread
buying m options and selling n options. Same type and expiration, differnet strike between the options you buy and write. So m options have the same strike, and the n options have another strike.
The benefit of this is that one can create pay later insurance.
elaborate on collars
buy a put, write a call. The call must have higher strike price.
If the asset go high, we loose.
If the asset go low or in between, we gain.
We can reverse this (sale of put and purchase of call) to get the “written collar”.
what is a zero cost collar
A zero cost collar is a collar where the premium for the call and the put are equal.
