Hedging with options
Second last step before I conclude this options and futures trading course
Refer to attached images
The Delta value can be interpreted of the ability of the option stay in or out of money. If it is one it is deep in the money or very low for being deep out of the money. See the chart to see how it is graphed. there is a positive and negative on the delta. For A seven dollar strike price of a call option in sleeping. If adult is .5 for a long call or you buy the call, The seller will have a negative delta because Long call which is like holding a long future position. If the price rises from seven dollars to eight dollars, the holder of the option will make a profit which becomes positive Delta. The seller of the option will incur a loss if the price rises. There is a negative sign for the Delta on the seller of the option. The Delta can be negative or positive depending on the profitability.
For a put the opposite is true for a call option. If you purchase a put as in Long put, The Delta will be negative but will be positive. If holding a put the Delta will be a positive sign well shorting. This is like holding a short futures position for the future price falls, you will make a profit. Holder of the put will make a profit were Delta is negative. The Delta measures the relationship between the change in the future as price and the premium. You can interpret it as a probability. You can also assign a negative or positive what are you sold or purchased a call or put
Referred to the relationship of seven dollars sleeping call lambda futures
and expiration diagram
Lamda is the volatility effect
There is a seven dollars strike price in soybean. You can calculate the lambda from the website calculator. The lambda Will vary depending days to expiry or at the money or deep in or out of the money.
If you have 60 days to expiry, the lambda Will be at its highest at the money. Lambda measures the impact of the change of volatility in the premium. The option at the money is more sensitive to volatility. THis makes intuitive sense when you look at the interpretation of the option that is deep in the money or out of the money. It makes sense when it is more sensitive to an option that is at the money because when volatility changes at the money, you can move in or out of the money which is critical to a trader. If the volatility goes out where you are at the money volatility increases the chance of being in or out of the money. If you’re deep out of the money.
If your crude oil call option strike price $50 per barrel, this gives you the right to go along at $50 a barrel. If you just price is $40, you are deep out of the money. If the implied volatility goes up The option option deep all the money will not be overlooked sensitive. It will respond but it will not be as responsive as if it was at the money. It also makes sense that the further you are from expiry, it will be more sensitive to to volatility. If the volatility goes the impression is more sensitive.
Greek components are never stable as a change all the time.
The theta measures the sensitivity of premium to time. Since options are and eroding asset. Certain options will be more sensitive to time than others. Those options can be those that are at the money. If you look at the value of time erosion you will find options that are at the money, Their time will erode more quickly versus options that are deep in or out of the money. These are the same reasons as with volatility. Time and volatility can have a bigger impact on the premium.
Another is how gamma measures how the Delta changes. Delta is in constant so if you take the second derivative, we see how the Delta changes with the futures price. It is also the case that the options at the money I’m going to have more deltas that are sensitive. We talked about the importance of Delta to hedger because when you hedge one over the Delta will give you the number number of positions that will give you a hedge ratio of one. If Delta is .5 you will need 2 contracts. If you’re trying to decide which option to hedge with. This is a decision you have to make with hedging with futures, It was more straightforward where you have an open cash position which is liquidated in February. Typically choose the March futures which expires after our cash position was to be completed. When you hedge with options you have a range of strike prices. Not only do you have the month but you have to choose the strike. And airline will has their jet fuel requirements, they use the options market so they have to choose the right month and right strike price.
So if you pick an option with the strike at the money, Delta will jump around to greater extent as opposed to an option that was deep in the money or deposit the money. This will affect the hedgers choice. If you choose one that is in the money is more expensive but the Delta will be more stable.
Hedging with options
Hedgers like options because is like buying insurance. When you Hedge with options you can eat your cake and have it too. If there is significant price moves in a favourable direction throw the option away. Airlines hedge against rises in fuel costs. The benefit with hedging with options as you throw the option away, becomes worthless but you can buy the fuel at a lower price. If you have the futures position, The profit or loss will never offset the profit or loss on the cash. This is not the case with options because the most you can lose the is your premium. It would have gives commercial firms more versatility. There is no free lunch here because you have to pay the premium while futures you don’t pay. Options to provide insurance in that you establish a floor or ceiling price. If you are an airline you are interested in the ceiling price which is the maximum fuel. You can use options to set a ceiling price if you short cash. If you are long cash because you’re worried about a price fall, in other words a hedger who owns the asset. You don’t want to have to sell at a price going through the floor. Swatches establishing floor or ceiling price. When has been with options, you take a cash position and an options position, you create a synthetic options position. Think of the floor price as a flat spot for the synthetic position of the ceiling and pricing of the flat of the spot of that synthetic position. With futures you trying to lock in at that cash price. With futures with the matrix for housing, you had today’s cash price which is your objective. When he asks to calculate the outcome, the outcome of the hedge is relative to cash price today. The objective of options is to establish a floor or ceiling price.
Or still has used to use the futures markets instead of the options market.
Pros and cons of using options versus futures refer to attached table
For futures you have margin calls. Some hedgers had to pull the plug or banks had to pull the plug to get out of the hedge halfway through. Sometimes the market will go around. Futures have no premium so to start is at minimum cost. The cost to initiate a trade is very insignificant. The futures you try to lock in a cash price which is subject to the bassist risk. The basis change can detract from the hedge.
With options you have many strategies. There are no margin calls but a negative is that you have to pay the premium. Instead of locking in a price call me to try to establish at your floor or ceiling depending if you have a long or short position. If you short cash, you have to buy the asset at some future date so you try to set a maximum price. This is why want a ceiling. If you’re trying to long cash do you want to sell the asset at some future date so this is why you set a floor. You can choose to set this floor by choosing the appropriate strike price. If you want to low ceiling you will have to pay a higher premium which is costly. You can choose where the floor or ceiling is subject to basis risk. There are a number of strategies including selling options or combine these with cash positions.
The issue with the options you have to pay the premium, as you know the price has to move A certain amount to get the premium back. Sometimes it’s better to use the futures contract rather than options. If the kick shows up then you want to have options rather than futures.
If an airline what’s the price of fuel to drop to $20 a barrel. But they buy protection against the rise in price so they throw that away. So then they buy the teacher at a much lower price today. If they had futures contracts, The futures had your locking in today’s price. So if today’s price is $40 a barrel but if the price goes to 20, you still pay 40 but you insuring against the price rise to 50. This is the story of futures. With options if the price is 40, the price close to 20 you pay 20+ whatever the premium is. So you pay 20+ something iwhich is a lot better than paying 40. This is why options a superior than futures. If the price rises what you’re trying to protect against, you may be better off with the futures over options because there’s no premium with futures. So you’re trying to protect one sure I can start rising price. If you hold futures contract you will profit there so the rising market will offset Price you pay in the cash market while there is no premium to worry about.
Refer to hedging with options versus futures table which is attached
Cash position will either be long or short. If you short cash you want to buy futures. or the alternative is Buy a call. Short cash you’re following the airline example where they buy call options. If you long cash you sell futures and buy puts. You would have to assess the outcome of the futures versus the option to see you for better result. If you short cash you have to buy a call because you were worried about a rise in price. How do you profit from the rising price in the options market, you buy a call. If you want cash, you need to sell a future because you worry about a price fall, how do you profit from a price for all the options market, buy to put.
Example referred to long cash in the attached images.
You long cash could be farmers who are hedging. You are a cotton producer with harvest coming in so you long cash. The current price is not too bad now so you are exposes to a fall on the price so you long cash. There’s a 45° line where there is today’s price so so set basis at zero to keep problem more manageable. If you long cash The price rises, you are moving up the 45° angle of long cash so your effective sales price becomes higher. So if the price Falls your effective sales price drops. In this problem we are working towards a price floor or price ceiling. Former wants to establish a floor because they worry about the price of cotton falling. So when you long cashew you establish a price floor Due to a price drop so you also need to buy a put. For an airline they will buy a call because they worry about buying fuel at a future date due to a higher price. The farmer buys a call due to price fall in their asset like cotton. With the payoff chart but you have to worry about the premium. You will have 2 assets with a Long cash position and a long put those result in a hedge position.
You will need to combine them so referred to the long cash and buy put to establish a floor price diagram attached
There is an orange line that looks like a long call.now you’ve created a synthetic call by buying a put. With the synthetic call you have a floor price but if the price rises you just ride the orange profit line.unlike a future position where one position neutralizes the other. This is true on the left side when prices fall. If the long 45° angle is profiting while the 45° long cash goes down, one neutralizes the other to establish a floor price. If the price rises, add the premium to get $35 or anything above that you will make a profit.
The Orange line is a vertical is the verdict sum of the two. When you add the straight-line to the kink line which is the strike price. Therefore when you add the two together, it will be kinked to the same spot so focus on the spot of $30 which is the current cash position. Do you want cash but you have some oil so to protect yourself you buy a put which has a strike of $27. It is below the current price of $27. The premium is what you pay the five dollars which is what you pay for the put for a $5 premium. When you look at $27 which is it is kinked , The price happens to fall from $30-$27, you will move down the cash line of three dollars. You are at the money. You will not get your premium back. If the price falls to $27 how does the effective sales price compared to $30 which is lower. It felt three dollars and you The five dollars for the premium, so you are now down to eight dollars. So the effective price is eight dollars lower than the axis which relates to the current cash price. Do you have establish the fourth floor price of eight dollars under the current price of $30 which is $22. Another way to calculate the floor prices which is a strike of 27 minus the premium of five dollars. Note the basis is zero. Those becomes $22 so what is done with the hedge will stop the show floor price of $22 to give you the minimum price which will sell our oil for. If the price rises to $35, you sell it for $30 because you have to subtract the premium. If the price goes to 35, so oil in the market for 35 but subtract The five dollar premium. This is why Cross is at zero since you get your premium back. Anything above 35 then you’r effective price will be be in positive range since it u is over $30. If the price goes to $45 you would see a $10 addition to the current price of 30 for the price to be 40. If it goes to 45 we end up with 40 because of the five dollar premium.
If you look at all the strike prices, there will be one that will give you the lowest floor. You are choosing the strike for protection based on the floor price. In this example you want A higher floor price since you’re long cash. The premium will be higher so the Orange line will be shifted to the right more which moves the floor price up. As the price rises, it will have to increase by the price of the premium. You are establishing a higher floor price but the insurance gets more expensive. If the price goes in a favorable direction, you are better off to buy a cheaper option. If you Buy an option that will be thrown away, you want to pay a premium of only four dollars versus eight dollars per barrel.The trade-off is if you want more protection higher insurance but if you don’t need it you’re better off to buy cheaper insurance.
Short cash example so referred too short cash and buy call to establish a ceiling price
Note The horizontal axis change underline price at expiry. So you’re calculating the effective purchase price not effective sales price. You are buying the asset here. So the short cash it goes in different direction if the price falls so you are trying to establish a lower effective purchase price. Previous example you were looking for a higher sales effective price. But again no labeling change. You have a short cash position combined with long call because of the short cash, you have to buy the cash in the future so you worry about a price increase. In the futures market you buy call options. Will have a payoff shirt for the call option with the premium. Do you have the short cash and long call with your two assets in the portfolio. The yellow line is a long put which becomes a combined synthetic long put. The Airline are worried about prices rising in oil but they wanted to fall. Here they create a synthetic put some of the price does fall goes into the range of lower effective purchase price. This is in the range of your eaten cake in having it to on left side. You add the white line to the Orange line so some will be kinked at the same spot of 33+5. It starts at 30 but goes to 33 which is a strike which is three dollars plus the premium of five dollars which is eight dollars. This becomes our ceiling price. The strike which is 33+5 premium. And the previous example it was a strike minus the premium. Basis is assime to be zero. It is possible the Airline will pay a higher price than the $30. The price of oil goes up your pay a higher price of $30 but you have a ceiling which is $30 +8 dollars equaling $38. This is the strike plus premium equaling $38. The price is $30 but they bought insurance but they won’t pay more than $38 knowing basis risk. If the price falls to $25, cost of five dollar premium but they still pay $30. If Price continues to fall below $25 moving up the 45° line there’s affect the purchase price could be as low as $15 under the 30 so their effective purchase price is $20 including the five dollar premium. If it ends up at 15 they still have to pay the five dollar premium on top of that.
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