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rweinsh
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volatility of exotics

May 26th, 2011, 7:43 pm

When I pricing exotic options(barrier and asian),what kind of volatility should I use?Implied volatility of vanilla or historical volatility of the underlying?Or do exotics have their own implied volatility?Thanks
 
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acastaldo
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volatility of exotics

May 26th, 2011, 8:52 pm

A good way to do it is to use a stochastic volatility model which attempts to match the current Implied Volatility surface for vanillas (as you know there is not a single IV for all vanillas, it varies by strike and maturity, resulting in a 2-dimensional surface rather than a single estimate).
 
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pimpel
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volatility of exotics

May 27th, 2011, 6:58 am

QuoteOriginally posted by: acastaldoA good way to do it is to use a stochastic volatility model which attempts to match the current Implied Volatility surface for vanillas (as you know there is not a single IV for all vanillas, it varies by strike and maturity, resulting in a 2-dimensional surface rather than a single estimate).Are you sure? Which do you think is the best? Maybe something else? There is no simple answer.
 
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rweinsh
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volatility of exotics

May 27th, 2011, 9:39 am

Actually,I would ask those who deal with exotics what is the difference between a volatility of vanilla option (say,30 day ATM call) and a volatility of exotic (say,30 day ATM up&out call).How does the volatility depend on level of barrier?Thanks
 
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pimpel
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volatility of exotics

May 27th, 2011, 9:56 am

QuoteOriginally posted by: rweinshActually,I would ask those who deal with exotics what is the difference between a volatility of vanilla option (say,30 day ATM call) and a volatility of exotic (say,30 day ATM up&out call).How does the volatility depend on level of barrier?ThanksFirst question suggests, that you ask about single volatility parameter to be put into valuation formula for the exotic. Since the price/volatility relationship for exotics is non-linear, quite often you can find two different levels of vol yielding the same price of option from the model. That is why sonsidering single point vol makes no sense.Second question - vol is different around strike and different around barrier. Everything depends whether it is simple knock-out or reverse knock-out. You should rather think about prices, as those include the option price taken from the model and the cost of hedging model imperfections.
 
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rweinsh
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volatility of exotics

May 27th, 2011, 10:21 am

to:Pimpel you said:" Since the price/volatility relationship for exotics is non-linear, quite often you can find two different levels of vol yielding the same price of option from the model."I do not think I`ve understood you.Would you be so kind to give me an example where I can put into a formula two different levels of volatility and get the same price of an option
 
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pimpel
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volatility of exotics

May 27th, 2011, 10:33 am

QuoteOriginally posted by: rweinshto:Pimpel you said:" Since the price/volatility relationship for exotics is non-linear, quite often you can find two different levels of vol yielding the same price of option from the model."I do not think I`ve understood you.Would you be so kind to give me an example where I can put into a formula two different levels of volatility and get the same price of an optionTake a formula for up&out call, Spot = 100, Strike = 100, Barrier = 120, Maturity = 0.25, r = 5%, q= 3%. Plot prices against vol from the region <5%; 40%>. Surprised?
 
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ronm
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volatility of exotics

May 27th, 2011, 10:37 am

Quotewhat is the difference between a volatility of vanilla option (say,30 day ATM call) and a volatility of exotic (say,30 day ATM up&out call)If I think in this way propably, I may get some meaningful answer:In pricing many exotic options, you need to work with some **modified version of volatility i.e. Sigma** to be feed into the pricing formula. This may involve some arithmatics with raw sigma, underlying price, or other known inputs. This in not the case for vanilla option (atleast if I go with BS formula). This modified Sigma can be thought of volatility of exotic.Thanks,
 
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rweinsh
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volatility of exotics

May 27th, 2011, 11:23 am

QuoteOriginally posted by: pimpelQuoteOriginally posted by: rweinshto:Pimpel you said:" Since the price/volatility relationship for exotics is non-linear, quite often you can find two different levels of vol yielding the same price of option from the model."I do not think I`ve understood you.Would you be so kind to give me an example where I can put into a formula two different levels of volatility and get the same price of an optionTake a formula for up&out call, Spot = 100, Strike = 100, Barrier = 120, Maturity = 0.25, r = 5%, q= 3%. Plot prices against vol from the region <5%; 40%>. Surprised?It is interesting but not useful.I do not believe that any underlying and its vanillas have 45% vol,and its up&out call has less than 5%I was talking about real situation,when we have volatility surface for vanillas and we are trying to estimate volatility to put into the formula for pricing exotic (for ex. your 100,100,120,0.25 up&out call).Lets say,we are talking about crude oil and its vanilla implied volatility (ATM) is 35%,and say we have a smile (at the barrier level we have 37.5%)Can we put into the formula for our up& out call 37.5%? Or should we put in something else?
 
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rweinsh
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volatility of exotics

May 27th, 2011, 11:37 am

QuoteOriginally posted by: ronmQuotewhat is the difference between a volatility of vanilla option (say,30 day ATM call) and a volatility of exotic (say,30 day ATM up&out call)If I think in this way propably, I may get some meaningful answer:In pricing many exotic options, you need to work with some **modified version of volatility i.e. Sigma** to be feed into the pricing formula. This may involve some arithmatics with raw sigma, underlying price, or other known inputs. This in not the case for vanilla option (atleast if I go with BS formula). This modified Sigma can be thought of volatility of exotic.Thanks,I`ve never heard about that .Where can I get an explanation what sigma is and a formula to calculate/estimate that,please?
 
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pimpel
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volatility of exotics

May 27th, 2011, 11:53 am

QuoteOriginally posted by: rweinshQuoteOriginally posted by: ronmQuotewhat is the difference between a volatility of vanilla option (say,30 day ATM call) and a volatility of exotic (say,30 day ATM up&out call)If I think in this way propably, I may get some meaningful answer:In pricing many exotic options, you need to work with some **modified version of volatility i.e. Sigma** to be feed into the pricing formula. This may involve some arithmatics with raw sigma, underlying price, or other known inputs. This in not the case for vanilla option (atleast if I go with BS formula). This modified Sigma can be thought of volatility of exotic.Thanks,I`ve never heard about that .Where can I get an explanation what sigma is and a formula to calculate/estimate that,please?I think Rebonato's book is biggest in volume on the topic. But I would rather encourage you to make a graph I asked and think it over. If you still don't understand what I asked you read Paul Wilmott on Quantitative Finance. Maybe you will understand then, that the implied volatility exists only for options, which have strictly monotonic relationship between vol and price. The example I give you has a quadratic form (you would see a parabola). Vanillas are quoted by means of implied vol, but exotics by price, since there is no prevailing model, like B-S for vanillas. I like Rebonato's sentence about implied vol, something like "the wrong number, to put into wrong formula, to get the right price".
 
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rweinsh
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volatility of exotics

May 27th, 2011, 12:30 pm

QuoteOriginally posted by: pimpelQuoteOriginally posted by: rweinshQuoteOriginally posted by: ronmQuotewhat is the difference between a volatility of vanilla option (say,30 day ATM call) and a volatility of exotic (say,30 day ATM up&out call)If I think in this way propably, I may get some meaningful answer:In pricing many exotic options, you need to work with some **modified version of volatility i.e. Sigma** to be feed into the pricing formula. This may involve some arithmatics with raw sigma, underlying price, or other known inputs. This in not the case for vanilla option (atleast if I go with BS formula). This modified Sigma can be thought of volatility of exotic.Thanks,I`ve never heard about that .Where can I get an explanation what sigma is and a formula to calculate/estimate that,please?I think Rebonato's book is biggest in volume on the topic. But I would rather encourage you to make a graph I asked and think it over. If you still don't understand what I asked you read Paul Wilmott on Quantitative Finance. Maybe you will understand then, that the implied volatility exists only for options, which have strictly monotonic relationship between vol and price. The example I give you has a quadratic form (you would see a parabola). Vanillas are quoted by means of implied vol, but exotics by price, since there is no prevailing model, like B-S for vanillas. I like Rebonato's sentence about implied vol, something like "the wrong number, to put into wrong formula, to get the right price".I understood that...But I am trying to understand how market maker prices those exotics?(for vanilla he may use "wrong number" like implied volatility with "wrong formula")
 
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pimpel
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volatility of exotics

May 27th, 2011, 12:41 pm

QuoteOriginally posted by: rweinshI understood that...But I am trying to understand how market maker prices those exotics?(for vanilla he may use "wrong number" like implied volatility with "wrong formula")Then nobody will give you the answer. It depends on the exotic (list is huge) and the underlying (not that narrow either) and frequently for every pair different models are used. For the same pair, two market makers may have different models. There is no methodology set.
 
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pimpel
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volatility of exotics

May 27th, 2011, 12:49 pm

QuoteOriginally posted by: rweinshI understood that...But I am trying to understand how market maker prices those exotics?(for vanilla he may use "wrong number" like implied volatility with "wrong formula")Let's discuss the other way. Assume people say, it is Heston as the best. You meet someone, who gives you initial capital for starting a hedge fund. I come to you and ask for the price of up&out call on crude oil. You calibrate your model to vanillas, run the model on trade parameters I asked and you get the answer from your model it is worth 7% of the volume. Would you write such option for me at this price? How would you hedge it? Which instruments would you buy/sell and in what amounts to cover your risk? What would you do if it happened, that it is not the Heston you should use, but rather some fancy Levy process is governing your underlying and vanillas written on it?
 
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rweinsh
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volatility of exotics

May 27th, 2011, 1:18 pm

QuoteOriginally posted by: pimpelQuoteOriginally posted by: rweinshI understood that...But I am trying to understand how market maker prices those exotics?(for vanilla he may use "wrong number" like implied volatility with "wrong formula")Let's discuss the other way. Assume people say, it is Heston as the best. You meet someone, who gives you initial capital for starting a hedge fund. I come to you and ask for the price of up&out call on crude oil. You calibrate your model to vanillas, run the model on trade parameters I asked and you get the answer from your model it is worth 7% of the volume. Would you write such option for me at this price? How would you hedge it? Which instruments would you buy/sell and in what amounts to cover your risk? What would you do if it happened, that it is not the Heston you should use, but rather some fancy Levy process is governing your underlying and vanillas written on it?So my question should be asked as following:What model do you/market maker usually use for Euro/dollar(currency) barrier(or asian) options?Or just ask /them a quote?Is that right?