Options pricing and put call purity intro to arbitrage

(Last Updated On: July 16, 2015)

Options pricing and put call purity intro to arbitrage

Attached images parity

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Refer to the images in the money:: options at 50,000 pounds cents per pound

All calls are circled in the money. You need to remind yourself how to calculate intrinsic value and time value. If you choose a mate call with the strike price of $54 which is expensive. It is in the money because the underlying futures price for March is $56.55, You’re buying the right to go along at $54 so it’s in the money. If you buy the right to go along at $.54 where the future is 56.55 you could exercise that option right away to earn 2.55 cents per pound which equals the intrinsic value. The total premium is is 4.05. You subtract 2.55 from the total which gives you time value of 1.5 cents on the march call.

If you look at strike price of 59, the strike is above the future price of 56.55 so it is out of the money. Therefore your intrinsic value zero since it is either zero or positive. So the time value is equal to the premium which is 1.7 cents per pound. Those two strike prices the same delivery month, at the time value different slightly where one is deep in the money and the other is far  out of the money. Time values will be similar.

 

In the money: T-bond, $100,000

The one circled are in the money. The future for deCember is 101–19, if you buy strike price 98 or hundred you’ll be in the money. The march future is 100–14 where 102 store 104 strike price is out of the money. For June there is no in the money.

 

For the put side it is the reverse. Those that are in the money they  usually have a high premium since they have intrinsic in time value. If the premium is low usually means it’s out of the money.

 

For T-bond on if you have a strike price on an expensive put option, strike is 104 with a  March contract, The mar futures is 114 so it is in the money. The total premium is 4344 or 4-22 When you calculate the total premium the options are priced in 64ths not 32nds. Each point is worth $15.62 so multiply 22 times 15.62 Plus $4000 will equal $4344. This is the total premium

Intrinsic value is the strike minus the the futures because is a put option. It will be reversed if it is the call option. You take the strike price of 104-(100-14) futures prices and 32nds. This will equal three – 18÷32 equaling $3562. Each 32nd is equal to 31.25  The time values than equal to $4344 -$3562 equaling $782

 

Intrinsic value means return you would receive if you exercise the option immediately and then reversed your futures position. It is returned to the holder of the option if it is exercised immediately. When you exercise you get a futures position then you reverse the futures position to take the opposite futures position.

 

Time value is profit to the writer of the option.  This is long as the option stays out of the money. Times all he has to do the uncertainty where prices are going.

Intrinsic value is difference between the strike in the futures price today.

If you have an intrinsic value of 3000 writer will not sell it for less than $3000, but they may also ask for some time value to account for the uncertainty regarding future price changes. If It is out of the money, reflects the possibility it will move in the money where the writer of the option will start losing. If it is in the money it is the probability it will stay in the money versus out of the money. The writer of the option Max profit will be is the premium. If there’s no time value it makes no sense to write an option.

 

In the money: yen options at 12 1/2 million Japanese yen

Remember when looking at quotes they are in cents per hundred yen.

If you look at attached image you’ll see the futures December put (right to sell) at .010205 jan .01024 December 1015 put strike it will have no intrinsic value so it will be all time value. I’m value is .64 cents per ¥100 equaling .000064 per yen Times 12 1/2 million yen equaling $800. This is the same as the premium because there is no intrinsic value.

 

Put Call parity

There is an important relationship between the culprit premium with the same strike price

If the pricing relationship doesn’t hold our arbitrage opportunities

(Call premium minus put premium) equals (Futures price minus strike price)

 

There are some underlying factors that determine the premium. If you have a call and put for the same strike price in the same futures month, there will be a lot in common. The only differences there is the right to go long and the others The right to go short. The prices are related which is the put call parity. Where is arbitrage relationship here. An example leading to the Black Scholes  formula.

Take a given strike price in a given delivery month, you take the difference between call and put premium, that should equal to the difference of futures price and strike price. If it does not there is a arbitrage opportunity. The put call. He comes from the call and put have factors in common to the Black Scholes formula. You have the underlying volatility, the difference between the strike and future, etc. is an important arbitrage activity going on in the markets to ensure the put call parity holds. It does not hold you can earn a riskless return by taking an arbitrage position in the call market or put market or in the futures market. If you take three positions, the put call parity does not hold you can take on positions without any risk. This will drive all prices back to their relationship call put parity . The same reason for looking at the carry charge market if the June future was above the December future compared to the storage cost, you could have a arbitrage kick in. You could buy December sell June it would bring me back to the storage cost.

Need to take a look at the markets for arbitrage opportunity to see if call put parity holds.

 

Referred to the call parity example attached

For soybean price the future prices is 571 three quarters strike price is six dollars call premium

May soybean: underline futures is $5.71 three quarters six dollars strike price call is 16 three-quarter cent put his $.43

[Call premium minus put premium )equals (futures price minus strike price)

[16 3/4-43] equals [$5.71 3/4-6 dollars)

-26 three quarters equals -28 one quarter

These are almost the same but there will be some transaction costs. With the difference of two cents, the parity premium does hold.

Louis reassure ourselves this does hold? We could look at various arbitrage opportunities. You could take different prices of the put a call and futures prices to earn an arbitrage return.

Arbitrage example: arbitrage futures and options and assume futures doesn’t change in price

Futures long at $5.71 three quarters short At $5.71 three quarters equal zero cents

Call short at 16 three-quarter cents expires at zero equals 16 three quarters

Put long at $.43 expires at 28 one quarter cents equals -14 three-quarter sense

Net total is +2 cents

 

When you long futures at $5.71 three quarters, call short at 16 three quarters cents, Put long at $.43, these three positions are your arbitrage call. Question becomes what happens when the prices change to our profit or loss. If the futures price does not change, you are nothing on the future position but ignoring transaction costs. If you sell the call where the strike price is six dollars in the future is $5.71, will the option Be exercised? It is not in the money. The call option gives you the right to go along at six dollars. In this case you are buying high selling low. You need to ask yourself if you want to Buy at at strike sell the future since this is what you’re doing when you buy a call option. If you buy a put question becomes do you want to sell The strike and buy at the futures. With the three positions the call does not move into the money and expires worthless so you sold for $.16. You breakeven on the futures position, you sell a call at 16 and three-quarter cents since the price did not change so you keep your premium as a writer, and you bought a put option with a strike of six dollars. The futures has become $5.71 three quarters. Is that option in the money? It is in the money.  Put you are buying the right to sell. You want to sell strike at six dollars and buy the futures for $5.71 three quarters.

The intrinsic value becomes 28 1/4 cents. The time is eroding here so  so you can safely ignore it. You can profit because you can exercise the option. You then reverse the futures position at 571. You pay $.43 for this option. You get back $.28 and a quarter so you’re not returning his -$.14. He made a positive four $.16 on the short call because you kept The premium. You earn some return on the put but you don’t get the premium that that time has eroded on you. You will not get that back so you get two cents gain. So what brings you back to the put call parity of two cents. So the three positions equal the call put parity.

if the three positions netted a large number with a call put parity would not hold. You can earn a profit by taking those three positions. It is not worth it for two cents because of transaction costs.

 

If you allow the futures price to go to $5.65 from $5.71

You go long and the futures market the price is following you will lose six in three-quarter cents. You sell a call for the six dollars strike. We said the call was out of the money when the price was $5.71. When it goes to $5.65 it’s further away from being in the money. It still expires worthless so you will retain your $.16. You’ll lose a little bit less on the put option because you bought at the right to sell at six dollars. It was in the money at $5.71 but it falls to $5.65, is deeper than money. So you are on $.35 instead of $.28 you only lose eight cents. You’ll net two cents

So no matter what you’ll always come back at two cents.

 

Refer to arbitrage Pay off chart

This will be helpful to you when you start to hedging with options. When hedging with options you combine with cash prices that is nice to see it in graphics.

The long futures line is the payoff chart which is roughly 45°. If you’ve along put,  you pay $.43 for the put then the long put will look like the blue  line. It is kinked at the six dollars. If it hit sixth dollars then it goes in the money, You’ll start earning some return back. When the price falls you start moving up the Long put line. When it’s $5.57 which is the difference between the strike in the premium of $.43.

You also have a call option so you need to overlay on that chart as well.

We take our three arbitrage positions we draw a payoff charge for each of them. We need to convince ourselves that there is an arbitrage position here. The call premium was at 16 and three-quarter cents it had a six dollar strike which is the same as the long put. This  Is the point of the coal put parity. If the price was at $5.71 but felt $5.57 but you kept your premium so when the price rises it’s at the money. When it rises higher than six then it becomes in the money because the buyer is getting the right.

We have our arbitrage position we can use the attached graph to doublecheck our results no matter what happens you’ll end up with two cents.

If the price settles at $5.57.  You label a point on the payoff graph need to check the return on each pay off and have them up. If it settles at $5.57, your long put will give zero return. You sell the call as long as the price stays below six dollars, it is out of the money. As long as it’s out of the money, you keep the full premium. If point b on top which is the return of the short call. You can draw a vertical line through points a B and C.  At point B make $.16 three quarters. At point c you breakeven. For point a, You need to take the difference between $5.71 and $5.51. You lose 14 three-quarter cents on the futures as you move down the 45° long future line. Your net gain becomes two cents.

 

If you draw a Payoff with a long put option, you know the shape of it so that will be a good head start. Because you know you’re buying the option there is going to be a flat spot where it is negative if it stays out of the money. If it stays out of the money you will lose money because the premium. Just remember it becomes a 45° line once moved into the money. It should cross is the difference between the strike and Price minus the premium which is your break even point.

In the short call, both along put, if you sell a call or put, you’ll hit a flat spot because of a positive return as long as it stays out of the money. On the lower flat spot is negative.

If you buy a call option it will have have a flat spot in negative range where the premium you pay.

 

Go long in the futures market, if you look at the short call and long put in remove the future. Both short  call and long put create a synthetic short future. Combining both lines you’ll have a downward sloping line. You’re looking for a risk-free arbitrage position where you use a synthetic short future, you want to buy futures for the risk free arbitrage position.

 

 

Sent from my iPhone

 

Options pricing and put call purity intro to arbitrage

 

Refer to the images in the money:: options at 50,000 pounds cents per pound

 

All calls are circled in the money. You need to remind yourself how to calculate intrinsic value and time value. If you choose a mate call with the strike price of $54 which is expensive. It is in the money because the underlying futures price for March is $56.55, You’re buying the right to go along at $54 so it’s in the money. If you buy the right to go along at $.54 where the future is 56.55 you could exercise that option right away to earn 2.55 cents per pound which equals the intrinsic value. The total premium is is 4.05. You subtract 2.55 from the total which gives you time value of 1.5 cents on the march call.

If you look at strike price of 59, the strike is above the future price of 56.55 so it is out of the money. Therefore your intrinsic value zero since it is either zero or positive. So the time value is equal to the premium which is 1.7 cents per pound. Those two strike prices the same delivery month, at the time value different slightly where one is deep in the money and the other is far  out of the money. Time values will be similar.

 

In the money: T-bond, $100,000

The one circled are in the money. The future for deCember is 101–19, if you buy strike price 98 or hundred you’ll be in the money. The march future is 100–14 where 102 store 104 strike price is out of the money. For June there is no in the money.

 

For the put side it is the reverse. Those that are in the money they  usually have a high premium since they have intrinsic in time value. If the premium is low usually means it’s out of the money.

 

For T-bond on if you have a strike price on an expensive put option, strike is 104 with a  March contract, The mar futures is 114 so it is in the money. The total premium is 4344 or 4-22 When you calculate the total premium the options are priced in 64ths not 32nds. Each point is worth $15.62 so multiply 22 times 15.62 Plus $4000 will equal $4344. This is the total premium

Intrinsic value is the strike minus the the futures because is a put option. It will be reversed if it is the call option. You take the strike price of 104-(100-14) futures prices and 32nds. This will equal three – 18÷32 equaling $3562. Each 32nd is equal to 31.25  The time values than equal to $4344 -$3562 equaling $782

 

Intrinsic value means return you would receive if you exercise the option immediately and then reversed your futures position. It is returned to the holder of the option if it is exercised immediately. When you exercise you get a futures position then you reverse the futures position to take the opposite futures position.

 

Time value is profit to the writer of the option.  This is long as the option stays out of the money. Times all he has to do the uncertainty where prices are going.

Intrinsic value is difference between the strike in the futures price today.

If you have an intrinsic value of 3000 writer will not sell it for less than $3000, but they may also ask for some time value to account for the uncertainty regarding future price changes. If It is out of the money, reflects the possibility it will move in the money where the writer of the option will start losing. If it is in the money it is the probability it will stay in the money versus out of the money. The writer of the option Max profit will be is the premium. If there’s no time value it makes no sense to write an option.

 

In the money: yen options at 12 1/2 million Japanese yen

Remember when looking at quotes they are in cents per hundred yen.

If you look at attached image you’ll see the futures December put (right to sell) at .010205 jan .01024 December 1015 put strike it will have no intrinsic value so it will be all time value. I’m value is .64 cents per ¥100 equaling .000064 per yen Times 12 1/2 million yen equaling $800. This is the same as the premium because there is no intrinsic value.

 

Put Call parity

There is an important relationship between the culprit premium with the same strike price

If the pricing relationship doesn’t hold our arbitrage opportunities

(Call premium minus put premium) equals (Futures price minus strike price)

 

There are some underlying factors that determine the premium. If you have a call and put for the same strike price in the same futures month, there will be a lot in common. The only differences there is the right to go long and the others The right to go short. The prices are related which is the put call parity. Where is arbitrage relationship here. An example leading to the Black Scholes  formula.

Take a given strike price in a given delivery month, you take the difference between call and put premium, that should equal to the difference of futures price and strike price. If it does not there is a arbitrage opportunity. The put call. He comes from the call and put have factors in common to the Black Scholes formula. You have the underlying volatility, the difference between the strike and future, etc. is an important arbitrage activity going on in the markets to ensure the put call parity holds. It does not hold you can earn a riskless return by taking an arbitrage position in the call market or put market or in the futures market. If you take three positions, the put call parity does not hold you can take on positions without any risk. This will drive all prices back to their relationship call put parity . The same reason for looking at the carry charge market if the June future was above the December future compared to the storage cost, you could have a arbitrage kick in. You could buy December sell June it would bring me back to the storage cost.

Need to take a look at the markets for arbitrage opportunity to see if call put parity holds.

 

Referred to the call parity example attached

For soybean price the future prices is 571 three quarters strike price is six dollars call premium

May soybean: underline futures is $5.71 three quarters six dollars strike price call is 16 three-quarter cent put his $.43

[Call premium minus put premium )equals (futures price minus strike price)

[16 3/4-43] equals [$5.71 3/4-6 dollars)

-26 three quarters equals -28 one quarter

These are almost the same but there will be some transaction costs. With the difference of two cents, the parity premium does hold.

Louis reassure ourselves this does hold? We could look at various arbitrage opportunities. You could take different prices of the put a call and futures prices to earn an arbitrage return.

Arbitrage example: arbitrage futures and options and assume futures doesn’t change in price

Futures long at $5.71 three quarters short At $5.71 three quarters equal zero cents

Call short at 16 three-quarter cents expires at zero equals 16 three quarters

Put long at $.43 expires at 28 one quarter cents equals -14 three-quarter sense

Net total is +2 cents

 

When you long futures at $5.71 three quarters, call short at 16 three quarters cents, Put long at $.43, these three positions are your arbitrage call. Question becomes what happens when the prices change to our profit or loss. If the futures price does not change, you are nothing on the future position but ignoring transaction costs. If you sell the call where the strike price is six dollars in the future is $5.71, will the option Be exercised? It is not in the money. The call option gives you the right to go along at six dollars. In this case you are buying high selling low. You need to ask yourself if you want to Buy at at strike sell the future since this is what you’re doing when you buy a call option. If you buy a put question becomes do you want to sell The strike and buy at the futures. With the three positions the call does not move into the money and expires worthless so you sold for $.16. You breakeven on the futures position, you sell a call at 16 and three-quarter cents since the price did not change so you keep your premium as a writer, and you bought a put option with a strike of six dollars. The futures has become $5.71 three quarters. Is that option in the money? It is in the money.  Put you are buying the right to sell. You want to sell strike at six dollars and buy the futures for $5.71 three quarters.

The intrinsic value becomes 28 1/4 cents. The time is eroding here so  so you can safely ignore it. You can profit because you can exercise the option. You then reverse the futures position at 571. You pay $.43 for this option. You get back $.28 and a quarter so you’re not returning his -$.14. He made a positive four $.16 on the short call because you kept The premium. You earn some return on the put but you don’t get the premium that that time has eroded on you. You will not get that back so you get two cents gain. So what brings you back to the put call parity of two cents. So the three positions equal the call put parity.

if the three positions netted a large number with a call put parity would not hold. You can earn a profit by taking those three positions. It is not worth it for two cents because of transaction costs.

 

If you allow the futures price to go to $5.65 from $5.71

You go long and the futures market the price is following you will lose six in three-quarter cents. You sell a call for the six dollars strike. We said the call was out of the money when the price was $5.71. When it goes to $5.65 it’s further away from being in the money. It still expires worthless so you will retain your $.16. You’ll lose a little bit less on the put option because you bought at the right to sell at six dollars. It was in the money at $5.71 but it falls to $5.65, is deeper than money. So you are on $.35 instead of $.28 you only lose eight cents. You’ll net two cents

So no matter what you’ll always come back at two cents.

 

Refer to arbitrage Pay off chart

This will be helpful to you when you start to hedging with options. When hedging with options you combine with cash prices that is nice to see it in graphics.

The long futures line is the payoff chart which is roughly 45°. If you’ve along put,  you pay $.43 for the put then the long put will look like the blue  line. It is kinked at the six dollars. If it hit sixth dollars then it goes in the money, You’ll start earning some return back. When the price falls you start moving up the Long put line. When it’s $5.57 which is the difference between the strike in the premium of $.43.

You also have a call option so you need to overlay on that chart as well.

We take our three arbitrage positions we draw a payoff charge for each of them. We need to convince ourselves that there is an arbitrage position here. The call premium was at 16 and three-quarter cents it had a six dollar strike which is the same as the long put. This  Is the point of the coal put parity. If the price was at $5.71 but felt $5.57 but you kept your premium so when the price rises it’s at the money. When it rises higher than six then it becomes in the money because the buyer is getting the right.

We have our arbitrage position we can use the attached graph to doublecheck our results no matter what happens you’ll end up with two cents.

If the price settles at $5.57.  You label a point on the payoff graph need to check the return on each pay off and have them up. If it settles at $5.57, your long put will give zero return. You sell the call as long as the price stays below six dollars, it is out of the money. As long as it’s out of the money, you keep the full premium. If point b on top which is the return of the short call. You can draw a vertical line through points a B and C.  At point B make $.16 three quarters. At point c you breakeven. For point a, You need to take the difference between $5.71 and $5.51. You lose 14 three-quarter cents on the futures as you move down the 45° long future line. Your net gain becomes two cents.

 

If you draw a Payoff with a long put option, you know the shape of it so that will be a good head start. Because you know you’re buying the option there is going to be a flat spot where it is negative if it stays out of the money. If it stays out of the money you will lose money because the premium. Just remember it becomes a 45° line once moved into the money. It should cross is the difference between the strike and Price minus the premium which is your break even point.

In the short call, both along put, if you sell a call or put, you’ll hit a flat spot because of a positive return as long as it stays out of the money. On the lower flat spot is negative.

If you buy a call option it will have have a flat spot in negative range where the premium you pay.

 

Go long in the futures market, if you look at the short call and long put in remove the future. Both short  call and long put create a synthetic short future. Combining both lines you’ll have a downward sloping line. You’re looking for a risk-free arbitrage position where you use a synthetic short future, you want to buy futures for the risk free arbitrage position.

 

 

Sent from my iPhone

 

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Hi i there My name is Bryan Downing. I am part of a company called QuantLabs.Net This is specifically a company with a high profile blog about technology, trading, financial, investment, quant, etc. It posts things on how to do job interviews with large companies like Morgan Stanley, Bloomberg, Citibank, and IBM. It also posts different unique tips and tricks on Java, C++, or C programming. It posts about different techniques in learning about Matlab and building models or strategies. There is a lot here if you are into venturing into the financial world like quant or technical analysis. It also discusses the future generation of trading and programming Specialties: C++, Java, C#, Matlab, quant, models, strategies, technical analysis, linux, windows P.S. I have been known to be the worst typist. Do not be offended by it as I like to bang stuff out and put priorty of what I do over typing. Maybe one day I can get a full time copy editor to help out. Do note I prefer videos as they are much easier to produce so check out my many video at youtube.com/quantlabs