# Please help me with an exit strategy



## shooter (21 April 2008)

Hi all

I've been paper trading options for few months now and I still haven’t figure out an exit strategy. 

Recently I encountered the probability density function for the lognormal random walk derived from a stochastic differential equation.  Apparently this can be used to calculate the probability of the underlying asset price being in a certain range at a certain time. So I can estimate the probability of winning given that I know the range which makes a profit.    

From the look of this equation it requires the current asset price, the volatility and the drift rate also known as the expected return or the growth rate. These variables are also used in the binomial pricing model as well. I would like to know how to calculate the last two variables, the volatility and the drift rate (anyone who use the binomial pricing calculation probably familiar with them) .  I don’t know whether I should be using the implied volatility or the historical volatility for the volatility. These variables seem all subjective.

I am aware that quantitative methods do not always match the reality due to the oversimplification of the model and other issues. But I’d like to have it as an approximation and a safety net. Please let me know if there are any good exit strategies. I much appreciate it.     

Cheers


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## CFD (21 April 2008)

I have none of the answers you seek, but thought I would suggest that you need to advise which moves you are trading, time frames etc.


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## wayneL (21 April 2008)

shooter said:


> Hi all
> 
> I've been paper trading options for few months now and I still haven’t figure out an exit strategy.
> 
> ...



Take probability with a liberal dose of salt as volatility is an imperfect input, whether implied or historical. Implied is the markets forward expectation of vols so probably better than historical.

The problem with volatility and probability is that volatility is a measure of day to day price moves and NOT a measure of trendiness. A "less than expected" volatiltiy trend can still move you past OTM strikes and mess up your  probability assumptions.

If you want to do it, software is your best bet unless you really want to do the maths, but as I said before, liberal doses of salt.


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## shooter (21 April 2008)

wayneL said:


> Take probability with a liberal dose of salt as volatility is an imperfect input, whether implied or historical. Implied is the markets forward expectation of vols so probably better than historical.




Yeh I agree.. it is just impossible to determine the asset volatility with a high degree of accuracy.Also the model assumes that volatility is invariant with respect to a priod of time and this is clearly not the case in reality. I can't really trust IV either since it is a quantity implied by the derivative market (please correct me if I'm wrong) and I don't really know how much this reflects the real volatility of the underlying asset. It's funny how there is a numerous way of calculating the quantity. I don't know which calculation is the best one. May be there is no best one. 

I still wonder how ppl use binomial pricing model. It requires the same quantities as for this probability calculation.  



wayneL said:


> The problem with volatility and probability is that volatility is a measure of day to day price moves and NOT a measure of trendiness.




I think the drift rate is the trendiness in the probability equation. Come to think of it. I might be able to ignore this quantity as long as it's a short term as the stochastic differential equation suggests that volatility plays a much bigger role than the drift rate in a short period of time. Sorry to think in a mathematical way here.. it just that the current book that I am reading is quite mathematical.. I will learn more practical stuff to balance myself later.  

I guess I just have to try and see whether this equation is practical or not. I probably have to check the sensitivity of the equation to the volatility. If the sensitivity is low then it might be useful, if it's high, I probably won't even bother testing.   




wayneL said:


> If you want to do it, software is your best bet unless you really want to do the maths, but as I said before, liberal doses of salt.



Hahaha..  I think I am going to code myself .. I  am really cheap...  unless there is a free one somewhere. It's going to be a pain!


Cheers


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## wayneL (21 April 2008)

shooter said:


> Yeh I agree.. it is just impossible to determine the asset volatility with a high degree of accuracy.Also the model assumes that volatility is invariant with respect to a priod of time and this is clearly not the case in reality. I can't really trust IV either since it is a quantity implied by the derivative market (please correct me if I'm wrong) and I don't really know how much this reflects the real volatility of the underlying asset. It's funny how there is a numerous way of calculating the quantity. I don't know which calculation is the best one. May be there is no best one.
> 
> I still wonder how ppl use binomial pricing *model*. It requires the same quantities as for this probability calculation.



The key word in the above statement is bolded in red. Binomial pricing is just a model, and a model is... well, just a model.

Models are notoriously inaccurate at times; quite a lot of the time really, hence the phenomenon of IV skew/smile etc. The market knows more about risk than the model. But, it's the best we have, and does a pretty good job combined with practical nuances applied by humans.

In the end, as a retail trader you have to make your own volatility projection, assess the delta/gamma risks, chuck in a bit of T/A, soothsaying, gut feeling, whatever; and decide whether the price on offer is fair.



shooter said:


> Hahaha..  I think I am going to code myself .. I  am really cheap...  unless there is a free one somewhere. It's going to be a pain!
> Cheers



Good luck, it's quite a mammoth task.


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## cuttlefish (21 April 2008)

If paper trading options and you're planning on trading with ASX ETO's then I'd recommend having a close look at the intraday MM spreads to get an idea of the slippage you'll be facing - its a significant factor to consider imo.


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## shooter (22 April 2008)

Hi Cuttlefish 



cuttlefish said:


> If paper trading options and you're planning on trading with ASX ETO's then I'd recommend having a close look at the intraday MM spreads to get an idea of the slippage you'll be facing - its a significant factor to consider imo.




I will take your advice. But first I need to ask a questions ( I forgot to mention and stress that I really belong to the newbie's lounge). Whats MM spreads stand for ???  I don't know most of the abbreviation in ASF and having a hard time reading threads.    

 Thanks


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## wayneL (22 April 2008)

shooter said:


> Hi Cuttlefish
> 
> 
> 
> ...



Shooter,

You may be interested in this: https://www.donfishback.com/blog/2008/04/18/new-visual-method-for-analyzing-volatility-and-movement/

Cheers

PS MM spread = bid/ask spread


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## shooter (22 April 2008)

wayneL said:


> Shooter,
> 
> You may be interested in this: https://www.donfishback.com/blog/2008/04/18/new-visual-method-for-analyzing-volatility-and-movement/
> 
> ...




Yes It looks very interesting! Thanks WayneL.


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## shooter (1 May 2008)

I encountered an interesting article through wiki. This talks about a brief history related to Black Scholes equation and its practicability.  

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075

It says that before  the Black Scholes Merton formula, by using simple arbitrage principles, traders were able to hege options more robustly than with Black Scholes Merton formula. Also it mentions that there is a way to perform dynamic hedging just by using put and call parity. I am very eager to find out how to hedge without the equation constructed based on unrealistic assumptions.


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## wayneL (1 May 2008)

shooter said:


> I encountered an interesting article through wiki. This talks about a brief history related to Black Scholes equation and its practicability.
> 
> http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075
> 
> It says that before  the Black Scholes Merton formula, by using simple arbitrage principles, traders were able to hege options more robustly than with Black Scholes Merton formula. Also it mentions that there is a way to perform dynamic hedging just by using put and call parity. I am very eager to find out how to hedge without the equation constructed based on unrealistic assumptions.



You'll have to find a rocket scientist to help with that one. 

It's a field more applicable to market makers than retail traders... unless you really want to hold a bunch of short gamma.


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## shooter (1 May 2008)

wayneL said:


> You'll have to find a rocket scientist to help with that one.
> 
> It's a field more applicable to market makers than retail traders... unless you really want to hold a bunch of short gamma.




Oh..  OK.  I don't usually like short gamma strategies so it may be a waste of time investigating further. There are few references on the article related to hedging without Black Scholes equation.. I might have a look at them just for interest. By the way I'm not a rocket scientist but I was trainning to be a mathematical physicist. I don't know if that is going to help.. but probably not ..  my knowledge in finance is too shallow.


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## wayneL (1 May 2008)

shooter said:


> Oh..  OK.  I don't usually like short gamma strategies so it may be a waste of time investigating further. There are few references on the article related to hedging without Black Scholes equation.. I might have a look at them just for interest. By the way I'm not a rocket scientist but I was trainning to be a mathematical physicist.* I don't know if that is going to help*.. but probably not ..  my knowledge in finance is too shallow.




Ah, now I see the interest in the mathematical side. It certainly won't hurt 

Just a point to bear in mind, most highly mathematical option tomes are directed sqaurely at market makers and don't have a lot of relevance to we retail traders.

You might like Cottles book "Options, The Hidden Reality" @ www.riskdoctor.com He walks the line between MM and retail trader quite well. With your theoretical background, it should be a much easier read for you than most of us.


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## shooter (1 May 2008)

wayneL said:


> You might like Cottles book "Options, The Hidden Reality" @ www.riskdoctor.com He walks the line between MM and retail trader quite well. With your theoretical background, it should be a much easier read for you than most of us.




hmm...  It seems that the link to order the free introductory course is not working and I can't receive it. I will try again later. 

I've been reading Quantitative Finance by Paul Wilmott and I borrowed finance books that are substantially heavy on mathematics. To be honest, I don't see the practicability of most of the stuff in those books ( but they are interesting ). Perhaps, the best I can do is to identify the flaws in  the model to learn the danger of using strategies that heavily rely on theoretical indicators such as greeks. 

The learning process is so slow especially my current job is not related to finance at all. I wish to grow as a trader. What job position will it make me a trading guru??

Cheers


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## wayneL (2 May 2008)

shooter said:


> hmm...  It seems that the link to order the free introductory course is not working and I can't receive it. I will try again later.
> 
> I've been reading Quantitative Finance by Paul Wilmott and I borrowed finance books that are substantially heavy on mathematics. To be honest, I don't see the practicability of most of the stuff in those books ( but they are interesting ). Perhaps, the best I can do is to identify the flaws in  the model to learn the danger of using strategies that heavily rely on theoretical indicators such as greeks.



Yep, academic interest only.

But I wouldn't go and call the Greeks a theoretical indicator, more of a pricing nuance in a non-linear system. They certainly are theoretical, but only because of the dynamism of Implied Volatility. Knowledge of the minute of the relevant option pricing model in use won't make much difference to your trading IMO.

The things you really want to know about the Greeks, is how they are going to apply to a proposed or existing trade. As an example, if you want maximum gamma, it pays to know where that is and whether it is sufficient for the trade in mind, or knowing what your total delta exposure is etc etc.

That's real time knowledge you need. 

Let's say you want to buy call options instead of 1000 long stock. What strike and expiry do you choose, and how many contracts? The greeks will help you evaluate this and will highlight which additional risk you have traded in return for the amelioration of other risks and addition potential reward.

It's not a precise science and is entirely different to the market maker who is generally trying to flatten risk out as much as possible.


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## shooter (8 May 2008)

wayneL said:


> The things you really want to know about the Greeks, is how they are going to apply to a proposed or existing trade. As an example, if you want maximum gamma, it pays to know where that is and whether it is sufficient for the trade in mind, or knowing what your total delta exposure is etc etc.



Yes indeed.. Speaking of greeks I've been working on a strategy, basically it is a call or put spread but I'm trying to eliminate the vega risk and keep the total gamma positive (well.. I'd like to know whether it is possible in practice). Based on Black Scholes equation keeping the total gamma positive while the total vega zero is not possible since 

vega(k1) = vega(k2) <-> gamma(k1) = gamma(k2) 

Where k1 and k2 are strike prices and <-> means if and only if. This condition ensures that vega and gamma are traded off equally hence if the total vega is zero, the total gamma becomes zero simultaneously. 

However in practice, because of the volatility skew, the condition is not satisfied and it is posible to have the total vega zero and the total gamma positive. But then again they are just theoretical quantities based on B.S. equation which involves unrealistic assumptions in its derivation. I need to know whether the condition applies to the "real" risk (not theoretical). 

I am wondering if there is any arbitrage principle that makes the real vega and gamma trade off each other completely and hence satisfying the condition. If there is then it will convince me that keeping the total gamma positive while the total vega zero is indeed impossible.

May be I should investigate calender spread to see if this can be done.. hmmm


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