SERVING THE QUANTITATIVE FINANCE COMMUNITY

ACD
Posts: 107
Joined: April 19th, 2004, 8:09 am

QuoteOriginally posted by: listbut what is the price ? is it something between 0 and 50 ?-------------------------------------------------------------------------------example 1if the real probability of 50 = 1 and prob of 200 = 0. Then with prob 1 call option equal to 0example 2if the real probability of 50 = 0 and prob of 200 = 1. Then with prob 1 call option equal to 50example 3if the real probability of 50 is close to 1 say 0.999 and prob of 200 = 0.001 . Then with prob 0. 999 call option will be equal to 0. This 3 example shows that to say something about the price we need to know the stock distribution. If you do not know it we could not say anything about call option price on theoretical level.Examples 1 & 2 violate the no arbitrage assumption since the stock is deterministic. In 1 I short the stock and go long the bond to get free money and reverse this in example 2, therefore you cannot use the BS framework as the price is not uniquely determined. There are an infinite number of combinations that will give the option payoff. e.g. in example 2 I can buy $5 worth of stock and$90 of bond and have a payoff of $100, this implied a price of$95 or buy $100 dollars of stock and sell$100 of the bond and get a payoff of $100, this implies a price of$0 (the arbitrage situation), you can't say the call has a price of $50 since this is not the only portfolio giving the desired payoff.In 3 this is not true anymore, there is now a risk (albeit small) arising from the stock, I can now give you a unique price that if you think it should be more I can sell you the option at that price and hedge buy buying the stock and get a guaranteed profit, if you think it's lower I can buy the option from you and hedge the option by selling the stock to get a guaranteed profit. Even if the small probability event occurs I do not lose money.The problem seems to be that you think the random scenario price should converge to the deterministic scenario one (which actually doesn't exist) as the probability of an event approaches 1, you have not justification to think that since that situation cause a violation of the BS assumptions. Last edited by ACD on August 30th, 2011, 10:00 pm, edited 1 time in total. ACD Posts: 107 Joined: April 19th, 2004, 8:09 am ### option hedging remarks QuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportional Last edited by ACD on August 30th, 2011, 10:00 pm, edited 1 time in total. list Topic Author Posts: 2041 Joined: October 26th, 2005, 2:08 pm ### option hedging remarks QuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example. TinMan Posts: 613 Joined: September 21st, 2006, 9:42 am ### option hedging remarks QuoteOriginally posted by: list QuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.What about two options on the same stock but with different strikes? TinMan Posts: 613 Joined: September 21st, 2006, 9:42 am ### option hedging remarks QuoteOriginally posted by: bearishWow! I think we just hit rock bottom. Guess you never know what will happen if you take your eyes off a thread for a few hours around here...It's a false bottom, I predict a breakout to the downside. daveangel Posts: 17031 Joined: October 20th, 2003, 4:05 pm ### option hedging remarks QuoteOriginally posted by: listQuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.all you had to do was come up with one number ... thats all. then I would have decided whether to buy, sell or walk away. knowledge comes, wisdom lingers ACD Posts: 107 Joined: April 19th, 2004, 8:09 am ### option hedging remarks QuoteOriginally posted by: list QuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.Nothing wrong with that definition, all I am saying is that you have no justification to think it applies to a stock and it's option. Their rates of return are not equal, the option is more leveraged, therefore it is only proportional to the stock in rate of return. In your own example the rates do not match, you match when the option expires in the money, but not when it expires out of the money (where the option return is -100% and the stock -50% <- this is the example by the way). Last edited by ACD on August 30th, 2011, 10:00 pm, edited 1 time in total. list Topic Author Posts: 2041 Joined: October 26th, 2005, 2:08 pm ### option hedging remarks QuoteOriginally posted by: ACDQuoteOriginally posted by: listbut what is the price ? is it something between 0 and 50 ?-------------------------------------------------------------------------------example 1if the real probability of 50 = 1 and prob of 200 = 0. Then with prob 1 call option equal to 0example 2if the real probability of 50 = 0 and prob of 200 = 1. Then with prob 1 call option equal to 50example 3if the real probability of 50 is close to 1 say 0.999 and prob of 200 = 0.001 . Then with prob 0. 999 call option will be equal to 0. This 3 example shows that to say something about the price we need to know the stock distribution. If you do not know it we could not say anything about call option price on theoretical level.Examples 1 & 2 violate the no arbitrage assumption since the stock is deterministic. In 1 I short the stock and go long the bond to get free money and reverse this in example 2, therefore you cannot use the BS framework as the price is not uniquely determined. There are an infinite number of combinations that will give the option payoff. e.g. in example 2 I can buy$5 worth of stock and $90 of bond and have a payoff of$100, this implied a price of $95 or buy$100 dollars of stock and sell $100 of the bond and get a payoff of$100, this implies a price of $0 (the arbitrage situation), you can't say the call has a price of$50 since this is not the only portfolio giving the desired payoff.In 3 this is not true anymore, there is now a risk (albeit small) arising from the stock, I can now give you a unique price that if you think it should be more I can sell you the option at that price and hedge buy buying the stock and get a guaranteed profit, if you think it's lower I can buy the option from you and hedge the option by selling the stock to get a guaranteed profit. Even if the small probability event occurs I do not lose money.The problem seems to be that you think the random scenario price should converge to the deterministic scenario one (which actually doesn't exist) as the probability of an event approaches 1, you have not justification to think that since that situation cause a violation of the BS assumptions.The example of the 1,2 types indeed do not relate to the financial market. They are like arithmetic before calculus. You need to comprehend the main underlying idea: a trader that have possibility of the same return with different probabilities always choose the maximum probability choice.

list
Topic Author
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### option hedging remarks

QuoteOriginally posted by: TinManQuoteOriginally posted by: list QuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.What about two options on the same stock but with different strikes?you can look at http://papers.ssrn.com/sol3/papers.cfm? ... _id=500303 page 19for continuous case and for binomial scheme with the same states and distributions you apply above design twice.

list
Topic Author
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### option hedging remarks

QuoteOriginally posted by: daveangelQuoteOriginally posted by: listQuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.all you had to do was come up with one number ... thats all. then I would have decided whether to buy, sell or walk away.The way how to choose a price and what type of the risk information can be attached to this numbe is explained in the above message @ Wed Aug 31, 11 12:49 PM .

TinMan
Posts: 613
Joined: September 21st, 2006, 9:42 am

### option hedging remarks

QuoteOriginally posted by: listQuoteOriginally posted by: TinManQuoteOriginally posted by: list QuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.What about two options on the same stock but with different strikes?you can look at http://papers.ssrn.com/sol3/papers.cfm? ... _id=500303 page 19for continuous case and for binomial scheme with the same states and distributions you apply above design twice.But if two options with different strikes both have the same rate of return as the stock then they must have the same rate of return as each other.How can this be?And for once try to answer a straight question without linking to another one of your 'papers'.

ACD
Posts: 107
Joined: April 19th, 2004, 8:09 am

### option hedging remarks

QuoteOriginally posted by: listThe example of the 1,2 types indeed do not relate to the financial market. They are like arithmetic before calculus. You need to comprehend the main underlying idea: a trader that have possibility of the same return with different probabilities always choose the maximum probability choice.Then you need to check your arithmetic, as I pointed out earlier:QuoteOriginally posted by: listexample 2if the real probability of 50 = 0 and prob of 200 = 1Does not imply the following:QuoteOriginally posted by: listThen with prob 1 call option equal to 50.Your whole argument starts on the basis that this result is self evident when it is false. You've been given two counter examples showing this to be false (I can come up with many more, there are an infinite number of them).QuoteOriginally posted by: ACDThere are an infinite number of combinations that will give the option payoff. e.g. in example 2 I can buy $5 worth of stock and$90 of bond and have a payoff of $100, this implied a price of$95 or buy $100 dollars of stock and sell$100 of the bond and get a payoff of $100, this implies a price of$0 (the arbitrage situation), you can't say the call has a price of \$50 since this is not the only portfolio giving the desired payoff.

TinMan
Posts: 613
Joined: September 21st, 2006, 9:42 am

### option hedging remarks

QuoteOriginally posted by: listQuoteOriginally posted by: daveangelQuoteOriginally posted by: listQuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.all you had to do was come up with one number ... thats all. then I would have decided whether to buy, sell or walk away.The way how to choose a price and what type of the risk information can be attached to this numbe is explained in the above message @ Wed Aug 31, 11 12:49 PM .Then apply it and give the price.

list
Topic Author
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### option hedging remarks

QuoteNothing wrong with that definition, all I am saying is that you have no justification to think it applies to a stock and it's option. Their rates of return are not equal, the option is more leveraged, therefore it is only proportional to the stock in rate of return. In your own example the rates do not match, you match when the option expires in the money, but not when it expires out of the money (where the option return is -100% and the stock -50% <- this is the example by the way).Indeed, random stock and its options have different risk characteristics. Hence, the market choice of the sport price does not straightforward and expected return on option and on its underlying are different. This difference is some kind of the price on higher risky option and also stdv on option and underlying stock are different. These primary distinctions affect on option pricing.

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### option hedging remarks

QuoteOriginally posted by: TinManQuoteOriginally posted by: listQuoteOriginally posted by: daveangelQuoteOriginally posted by: listQuoteOriginally posted by: ACDQuoteOriginally posted by: listI used the principle that states that two investments are equal fro t to T when rates of return are equal. What justification do you have to apply this to the stock and the option? The option is more leveraged, therefore rates of return are not equal... they are only proportionalAs a pricing low i used the principle. Two investments are equal on [ 0 , T ] if and only if they offer equal rates of return at any moment within [ 0 , T ] and applied it for each scenario. If you think that such definition misses something it is sufficient to present an example.all you had to do was come up with one number ... thats all. then I would have decided whether to buy, sell or walk away.The way how to choose a price and what type of the risk information can be attached to this numbe is explained in the above message @ Wed Aug 31, 11 12:49 PM .Then apply it and give the price.one gets the feeling that "list" is all talk and no trousers... put the price out there, lets see if you get hit or lifted... or indeed if we all just walk away.
knowledge comes, wisdom lingers

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