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option hedging remark*

September 2nd, 2011, 9:41 pm

This was a long message and frankly I did not read it first.1) You have two equations for the present price of the option which are not equal. /// I might be do not understand your point but if you think that your statement do not adequate to the definition of the option price. Market option price is a function of a scenario. If scenario belongs to the set { S ( T , x ) > K }, C ( t ) is defined by equation. Otherwise it is 0. Solution of the equation for different omega might be different or equal numbers.///2) Both equations require knowledge of the future. Which means they cannot be used in the present.This remark does not look good but nevertheless one can note that if we ignore future distribution at T as it is with binomial scheme then it might be binomial solution can look the best reasonable. If we use real distribution of the stock at T we can find better explanation for the price. I am tired to write long messages but it might be makes sense to present an example. Let two stocks A , B take two values 2 and 5 at T. A takes 2 with probability 0.2 and 5 with 0.8. B takes 2 with probability 0.9 and 5 with pr 0.1. Assume that set of scenario { A = 2 } belongs to the set { B = 2 } in other words if { A = 2 } occurs then { B = 2 } occurs too. Similarly set of scenarios { B = 5 } belongs to the set { A = 5 }. Binomial scheme suggests the same price for either option with K say 4 . Investor sells B and for the same money buys A, i.e. at t he begins with 0. There are 3 types of the final events when 0 = C ( t ) = when { A = 2 , B = 2} , { A = 5 , B = 5 } and { A = 5 , B = 2}. For the 1st two scenarios Investor arrives at 0 outcomes while for the 3rd he will get positive profit. Thus with positive probability which one can easy calculate Investor has profit. Repeat independently this game Investor arrives at positive profit with probability as close to 1 as he wish. 3) To say that prices can be derived from this equation the return must match under every scenario not just those where the option expires with a value greater than zero. /// Sorry, I could not understand this. If you wish use numbers to clarify your point.I will read remainder tomorrow and try to respond.
 
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TinMan
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option hedging remark*

September 2nd, 2011, 11:58 pm

QuoteOriginally posted by: frenchXQuoteOriginally posted by: daveangelWe have tried ignoring him - he keeps popping up and writing the same drivel week in, week out... pathetic.I agree that this is problematic. What I would do to stop him is to point explicitely a mathematical error in his paper. The man cannot be reasonned but in front of fact it might be different. Pointing out his very mistake should also help him to progress (at least I hope ...)A case in point, ACD has repeatedly posted where he is incorrect, has patiently posted counterexamples to his ridiculous notions, and he has been ignored over and over again.The idea that we should deal with him on his own terms and try to decipher his inane ramblings is ridiculous.Let's call a spade a spade, the guy is an idiot.Now you can choose to indulge him if you wish, but there are plenty of productive threads in the student forum that are derailed because he spouts his gibberish.Show me where anyone who has challenged him has been unreasonable with anyone else who posts in the student forum.This is not a case of needing to be patient with someone who is missing some subtlety of the subject.He has decided that everyone else here has no idea what they are talking about and so posts the same inane nonsense over and over again.@Paul, you say you commend him, would you say the same if it was homeopathy he was defending in the face of all evidence?Because that's what he is, a financial homeopath.In fact anyone here who pleads for more patience with him, I challenge you to set him straight.I guarantee you'll fail.
 
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option hedging remark*

September 3rd, 2011, 12:57 am

Why don't you address this problem with your results. Also I've given you a derivation of the price for the call option in the example daveangel gave you, feel free to find a mistake in a definition or in a formula there there... The ball is in your court.------------------------------------------------------------------------------------------------------------------------------------------------------------Finally the example you were given in previous thread:Assume the following:1) Transaction costs are zero2) We have 2 times t (now) and T (some point in the future when the call expires)3) Interest rates are zero (i.e. there exists a zero coupon bond with the following price, B(t)=B(T)=1, its price in the future is known)4) There exists a stock S with current price 100 (S(t)=100), in the future its value is given by a Bernoulli distribution, at time T it can take value S(T)=200 with probability p or S(T)=50 with probability (1-p). Where p is in (0,1) pick any value you like for p, the rest of us don't need one (note that 0 & 1 are excluded since they permit arbitrage between the stock and the bond).5) There is a European call option available that has strike 100, that is at time T it's value is C(T)=max(S(T)-100,0).6) From (3) & (4) C(T)=100 if S(T)=100 and C(T)=0 if S(T)=50We need to find C(t), please show where the fault in the following line of reasoning is:1) If we purchase 66 2/3 of S at time t and sell 33 1/3 of the bond B at time t then we have spent in total 33 1/3 (66 2/3 - 33 1/3 = 33 1/3) which is its present value2) At time T the bond purchase will still be worth 33 1/3 (interest rate is zero), the stock purchase is worth either 133 1/3 or 33.33 (it has either doubled in value S(T)=200 or halved S(T)=50 respectively).3) The value of our portfolio at time T is either 100 if S(T)=200 (133 1/3 - 33 1/3 = 100) or 0 if S(T)=50 (33 1/3 - 33 1/3 = 0). These are the same values are the payoff of the option./// up to this everything is perfect ///4) No other combination of the stock and bond will replicate the payoff of the options under the assumptions above. /// it is not proved it might be true or false. If you stated this you need to prove it///5) The present value of the call must therefore equal that of the portfolio at time t giving C(t)=33 1/3If we define price as a deterministic number depending on t , S ( t ) you are right. If not statement 4) is incorrect. This is what is important before we construct a portfolio we need a formal definition of the option price. If we say that binomial scheme is a formal definition of the option and we then construct a portfolio which you described everything look fine. And this synthetic replication looks like an important property of the option price. Nevertheless, one can argue upon your definition and therefore the significance of the perfect replication will be diminished. Arguments to the binomial formula were presented earlier. Formally, to reject mathematical construction it is sufficient to show that statement does not make sense in a particular situation. You do not find a particular spot where something wrong. In above example such confusing moment is that the common sense suggests that if real probability of the state 200 is close to 1 and close to 0 the option price must be different while above method of pricing explicitly defines price 33 1/3 even if we takes a limit when p tends to 0 or 1.
Last edited by list on September 2nd, 2011, 10:00 pm, edited 1 time in total.
 
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option hedging remark*

September 3rd, 2011, 1:03 am

QuoteOriginally posted by: TinManQuoteOriginally posted by: frenchXQuoteOriginally posted by: daveangelWe have tried ignoring him - he keeps popping up and writing the same drivel week in, week out... pathetic.I agree that this is problematic. What I would do to stop him is to point explicitely a mathematical error in his paper. The man cannot be reasonned but in front of fact it might be different. Pointing out his very mistake should also help him to progress (at least I hope ...)A case in point, ACD has repeatedly posted where he is incorrect, has patiently posted counterexamples to his ridiculous notions, and he has been ignored over and over again.The idea that we should deal with him on his own terms and try to decipher his inane ramblings is ridiculous.Let's call a spade a spade, the guy is an idiot.Now you can choose to indulge him if you wish, but there are plenty of productive threads in the student forum that are derailed because he spouts his gibberish.Show me where anyone who has challenged him has been unreasonable with anyone else who posts in the student forum.This is not a case of needing to be patient with someone who is missing some subtlety of the subject.He has decided that everyone else here has no idea what they are talking about and so posts the same inane nonsense over and over again.@Paul, you say you commend him, would you say the same if it was homeopathy he was defending in the face of all evidence?Because that's what he is, a financial homeopath.In fact anyone here who pleads for more patience with him, I challenge you to set him straight.I guarantee you'll fail.I just responded on ACD post. If you wish you can read it. I explained that I did not read it first because it look too long and a number others were shorter. But I also could not understand why you so nervous. You personally at least as it seems to me did not lose anything up to now.
 
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Paul
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option hedging remark*

September 4th, 2011, 7:23 am

@TinMan I'm commending him for his relative calm in the face on this onslaught!P
 
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daveangel
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option hedging remark*

September 4th, 2011, 8:40 am

Quote Formally, to reject mathematical construction it is sufficient to show that statement does not make sense in a particular situation. You do not find a particular spot where something wrong. In above example such confusing moment is that the common sense suggests that if real probability of the state 200 is close to 1 and close to 0 the option price must be different while above method of pricing explicitly defines price 33 1/3 even if we takes a limit when p tends to 0 or 1.for a brief moment I thought it was all clear to you then I realised that you were quoting ACD but in your very own inimitable style. If you can come up with a price that is higher than 331/3 to buy the option or lower than 331/3 to sell the option and still make a profit given the two possible states of the stock at maturity then feel free to let us know what the price is. Other than that, please stop polluting these forums.
knowledge comes, wisdom lingers
 
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option hedging remark*

September 4th, 2011, 10:41 am

QuoteOriginally posted by: daveangelQuote Formally, to reject mathematical construction it is sufficient to show that statement does not make sense in a particular situation. You do not find a particular spot where something wrong. In above example such confusing moment is that the common sense suggests that if real probability of the state 200 is close to 1 and close to 0 the option price must be different while above method of pricing explicitly defines price 33 1/3 even if we takes a limit when p tends to 0 or 1.for a brief moment I thought it was all clear to you then I realised that you were quoting ACD but in your very own inimitable style. If you can come up with a price that is higher than 331/3 to buy the option or lower than 331/3 to sell the option and still make a profit given the two possible states of the stock at maturity then feel free to let us know what the price is. Other than that, please stop polluting these forums.It is a big difference between definitions of the options price as the benchmark fixed = perfect = 'no free lunch' and market spot price which was discussed above. In the first case the primary characteristic of the perfect price is its no-arbitrage. The second approach adds to any spot market ( or agreed ) price the risk value one of quantified characteristics of which is probability to lose premium. Actually it does not reject any idea of choice premium including 'no arbitrage' price. But note that without risk to lose premium the price=number is incomplete. In such a way one component BS price admits 'better-worse' quality while in two component price definition = ( spot , risk ) we obviously lose such a possibility. The essence of my arguments against BS pricing is that to show that the 'perfect' price is risky based on the stochastic definition. On other hand i also tried to present examples that show that say binomial pricing does not always correspond our common sense of the price : to buy calls for the same price which with 99% and 1 % gives you the right to buy underlying of the option. If then binomial price is drawn from dynamic hedging or inverse binomial price serves to derive dynamic hedging the doubts about hedging goes from binomial price definition.The question whether 33 1/3 is correct or to present others: higher or lower number is incorrect if we interpret price as a stochastic process. It is from my point of view about the same as to say that to day the no arbitrage market has established stock price S ( t ) and therefore at T we would have S ( T ) = S ( t ) B^-1 ( t , T ). Though this example is too subjective.
 
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option hedging remark*

September 4th, 2011, 10:41 am

Last edited by list on September 3rd, 2011, 10:00 pm, edited 1 time in total.
 
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daveangel
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option hedging remark*

September 4th, 2011, 11:40 am

Quote On other hand i also tried to present examples that show that say binomial pricing does not always correspond our common sense of the price : to buy calls for the same price which with 99% and 1 % gives you the right to buy underlying of the option. I have asked you over and over again to tell me what price you think this option should trade at if you think 33.3333 is not the right price. Please tell me what it is otherwise please do not comment further.
knowledge comes, wisdom lingers
 
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option hedging remark*

September 4th, 2011, 1:55 pm

QuoteOriginally posted by: daveangelQuote On other hand i also tried to present examples that show that say binomial pricing does not always correspond our common sense of the price : to buy calls for the same price which with 99% and 1 % gives you the right to buy underlying of the option. I have asked you over and over again to tell me what price you think this option should trade at if you think 33.3333 is not the right price. Please tell me what it is otherwise please do not comment further.Market price in the example is a rv C ( t , o ) = { 0 , 50 } with probabilities p , 1 ? p. These values come from the definition of market price. The market price depends on the parameter p.An investor who think that the spot market price = premium of the option is 33 1/3 will lose his premium with probability 1-p and will gain 50-33 1/3 with probability p. For different p, say 0.1 or 0.9 risk characteristics of the price 33 1/3 will be different. This is basic risk characteristics of the price 33 1/3. We can calculate mean, variance of return and based on our rules take a decision whether to buy or not this option for 33 1/3 price.Consider more complex example because 2 states at T is a simplest illustration. Let S ( t ) = 2.5 and S ( T ) = { 0.5 , 1 , 2, 4 } with correspondent distribution { 0.1 , 0.3 , 0.2 , 0.4 } , K = 2. I do not know how to present benchmark solution in this case. Other approach defines the market price at t of the call option C ( t , omega ) as a rv taking values { 0 , 1.25 } with probabilities { 0.6 , 0.4}. Here 1.25 comes from the equation ( 4 ? 2 ) / x = 4 / 2If one chose the premium=spot market price equal C ( t ) = 1 then rate of return on the call investment is a rv taking value 0 with prob 0.6 and ( 4 ? 2 )/1.25 = 16/5 with prob 0.4. Expected return is (16/5)*0.4 = 32/25.We can calculate stdv of the return. If we agree with such risk characteristics of the investment we can buy option if no we can determine lower price which risk will be consistent with our strategy. If we have other ?real world? distribution of the stock we get in general other risk characteristics of the investment in call.
 
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frolloos
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option hedging remark*

September 4th, 2011, 2:07 pm

i have a suspicion that List is in the 'real world' (not meant sarcastically) when he should be in the risk-neutral world. it seems that you, list, are making things way too complex and not accepting the fact that pricing is based on certain assumptions. of course you can doubt whether those assumptions hold, but that's the next step.what is the price of a forward?
Last edited by frolloos on September 3rd, 2011, 10:00 pm, edited 1 time in total.
 
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Alan
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option hedging remark*

September 4th, 2011, 2:22 pm

Quotefrom list:Formally, to reject mathematical construction it is sufficient to show that statement does not make sense in a particular situation. You do not find a particular spot where something wrong. In above example such confusing moment is that the common sense suggests that if real probability of the state 200 is close to 1 and close to 0 the option price must be different while above method of pricing explicitly defines price 33 1/3 even if we takes a limit when p tends to 0 or 1.While I know from trying several years ago that list is likely immune to this argument, it is a useful thought experiment for students to actually set up this scenario in the real-world and then ask: what would happen in the real-world? By 'this scenario', I mean set up a hypothetical real-world situation where " the probability of the state 200 is close to 1 and the probability of the state 50 close to 0". Here is one way. On some Friday, suppose some stock in a company with listed options trades at $100. By the Friday close, I, a fabulously rich investor acquire control of thiscompany. After the close, (after-hours) trading is halted and I announce the following tender offer for the remaining shares -- solely to resolve the 'paradox' of list.Here are the terms of the offer: After the tender deadline passes (and so the shares are tendered), I will spin a (specially constructed) roulette wheel with 100 slots, numbered 0-99. If a 0 comes up, I willpay 50 for the tendered shares and if any other number comes up, I will pay 200 for the tendered shares.After that payment, I will destroy the company's assets, de-list it, dissolve it, etc -- it is gone!Assume the call options, striking at 100 and expiring a week later, will cash settle with a payment of nothing or 100 in these two roulette states (states=slot 0, slot >0). [These final option terms are due to an adminstrative fiat ruling by the CBOE, made over the weekend in response to my offer.If you want, you can also assume the obvious analogous rulting is made with respect to puts and all strikes.]The stock is halted throughout the weekend and trading will resume at 9:30 am Monday morning. For students:1. What will actually happen at the Monday opening* to the stock and option prices? 2. How does this resolve list's confusion? -----------------------------------------------------------------------------------------------------------------------------------------------* Exchange rules require the option market makers to open the options with 2-sided quotes,within prescribed limits, promptly after the opening of the underlying security in the primary market .
Last edited by Alan on September 3rd, 2011, 10:00 pm, edited 1 time in total.
 
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ACD
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option hedging remark*

September 4th, 2011, 3:14 pm

QuoteOriginally posted by: list3) The value of our portfolio at time T is either 100 if S(T)=200 (133 1/3 - 33 1/3 = 100) or 0 if S(T)=50 (33 1/3 - 33 1/3 = 0). These are the same values are the payoff of the option./// up to this everything is perfect ///4) No other combination of the stock and bond will replicate the payoff of the options under the assumptions above. /// it is not proved it might be true or false. If you stated this you need to prove it///Ok let's prove it, at time T we have one of two outcomes: {B(T)=1, S(T)=50, C(T)=0} or {B(T)=1, S(T)=200, C(T)=100}. I am trying to create a combination of the stock and bond that replicate the value of the option at time T. This gives the unknowns x & y which are the units of each I purchase respectively, giving the equation:x * S(T) + y * B(T) = C(T)This must hold in both scenarios giving the following system of linear equations:x * 50 + y * 1 = 0x * 200 + y * 1 = 100Subtracting the first equation from the second we have:x * 150 = 100 => x=2/3Subtracting 4 times the first equation from the second we have:y * (-3) = 100 => y = -33 1/3As this is a linear equation there is either 0 solutions (not true since we have a solution), 1 solution (possible since we have a solution) or an infinite number of solutions (possible if the second equation is a multiple of the first). Since we solved the equations by gaussian elimination and found a unique solution the third case is not possible. We therefore have unique solutions for x and y. This tells us to buy 2/3 of a stock for each option and to borrow -33 1/3 to fund this purchase. Since we have the values for S(t) and B(t) this gives a present value of the portfolio which will equal C(t) since it replicates it and is unique:x * S(t) + y * B(t) = 2/3 * 100 - 33 1/3 * 1 = 33 1/3 = C(t)Statement 4 is proven. Unless there is now a problem with statement 5, you are stuck, the price is proven to be 33 1/3 under the assumptions.QuoteOriginally posted by: listIf we define price as a deterministic number depending on t , S ( t ) you are right. If not statement 4) is incorrect.I've just proven statement 4 meaning that your conjecture here is wrong...QuoteOriginally posted by: listFormally, to reject mathematical construction it is sufficient to show that statement does not make sense in a particular situation.This is wrong too, to reject a mathematic construction you show is to be false. You can't reject it simply because you don't understand it. I hope this will help you see where you are going wrong.
Last edited by ACD on September 3rd, 2011, 10:00 pm, edited 1 time in total.
 
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frenchX
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option hedging remark*

September 4th, 2011, 3:46 pm

@ACD: First I admire your patience Sir and I have to say it was one of the clearest explanation I have seen so far, so I think you did all the possible and it's not honestly possible to contest your point.
 
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tagoma
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option hedging remark*

September 5th, 2011, 10:14 am

QuoteOriginally posted by: HansiWhen you've hit the bottom please, stop digging.good morning, china !
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