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BlackScholesMerton Process and Volatility

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pierre baral

BlackScholesMerton Process and Volatility

Hello,

I'm trying to code a basic pricer for european warrants with discrete dividend, but it's not so easy. (I'm not in the finance) ;-)

I want to use the BlackScholesMerton Process but it needs a volatility.

Is it the historical volatility which is calculated on a year (~260d)? Do I need to recalculate it for each day or just at the settlement date?

Or is it the implied volatility (how to calculate it then)?

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Marcin Pawlik

Re: BlackScholesMerton Process and Volatility

2010/10/14 pierre baral <[hidden email]>:
> Hello,
>
> I'm trying to code a basic pricer for european warrants with discrete
> dividend, but it's not so easy. (I'm not in the finance) ;-)
>
> I want to use the BlackScholesMerton Process but it needs a volatility.
>
> Is it the historical volatility which is calculated on a year (~260d)? Do I
> need to recalculate it for each day or just at the settlement date?

You can use it as a proxy if you don't have implied vol. Of course you
can use any other estimator. Some of them are implemented in QuantLib
e.g. GarmanKlass.

> Or is it the implied volatility (how to calculate it then)?

Implied vol is taken "from the market". If there are options on your
underlying listed on an exchange you can use their prices in order to
"imply" volatility. These implied volatilities are dependent on strike
and maturity. In most cases you'll need to interpolate or extrapolate
them in order to get the vol you need.
The proper way of interpolation is another issue. Generally it
accepted - correct me if I'm wrong - that in time one interpolates
variance (i.e. volatility^2 x time-to-maturity).

M.

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experiences on the web. Be a part of the beta today.
http://p.sf.net/sfu/beautyoftheweb
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pierre baral

Re: BlackScholesMerton Process and Volatility

Ok so I need to use an estimator such as GarmanKlass. It takes historical prices and returns the implied volatility. t's okay I can do what I want.

However is this the easiest way to do it?

I just want to estimate/forecast the price of a stock for the following day and then to get the future price of my warrant.

2010/10/14 Marcin Pawlik <[hidden email]>

2010/10/14 pierre baral <[hidden email]>:

> Hello,
>
> I'm trying to code a basic pricer for european warrants with discrete
> dividend, but it's not so easy. (I'm not in the finance) ;-)
>
> I want to use the BlackScholesMerton Process but it needs a volatility.
>
> Is it the historical volatility which is calculated on a year (~260d)? Do I
> need to recalculate it for each day or just at the settlement date?

You can use it as a proxy if you don't have implied vol. Of course you
can use any other estimator. Some of them are implemented in QuantLib
e.g. GarmanKlass.

> Or is it the implied volatility (how to calculate it then)?

Implied vol is taken "from the market". If there are options on your
underlying listed on an exchange you can use their prices in order to
"imply" volatility. These implied volatilities are dependent on strike
and maturity. In most cases you'll need to interpolate or extrapolate
them in order to get the vol you need.
The proper way of interpolation is another issue. Generally it
accepted - correct me if I'm wrong - that in time one interpolates
variance (i.e. volatility^2 x time-to-maturity).

M.

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Simon Ibbotson-2

Re: BlackScholesMerton Process and Volatility

Okay, here’s a sequence of questions:

1) Why (for what purpose) do you need to price the warrant?

2) Are there any warrant prices / quotes that you can see in the market?

3) Are there any option prices / quotes (on the stock) that you can see in the market?

4) Why do you want to use discrete dividend model and the BSM process?

Once you’ve answered these, we can look at the best way to do it…

From: pierre baral [mailto:[hidden email]]
Sent: 19 October 2010 14:13
To: [hidden email]
Subject: Re: [Quantlib-users] BlackScholesMerton Process and Volatility

2010/10/14 Marcin Pawlik <[hidden email]>

2010/10/14 pierre baral <[hidden email]>:

> Hello,
>
> I'm trying to code a basic pricer for european warrants with discrete
> dividend, but it's not so easy. (I'm not in the finance) ;-)
>
> I want to use the BlackScholesMerton Process but it needs a volatility.
>
> Is it the historical volatility which is calculated on a year (~260d)? Do I
> need to recalculate it for each day or just at the settlement date?

You can use it as a proxy if you don't have implied vol. Of course you
can use any other estimator. Some of them are implemented in QuantLib
e.g. GarmanKlass.

> Or is it the implied volatility (how to calculate it then)?

Implied vol is taken "from the market". If there are options on your
underlying listed on an exchange you can use their prices in order to
"imply" volatility. These implied volatilities are dependent on strike
and maturity. In most cases you'll need to interpolate or extrapolate
them in order to get the vol you need.
The proper way of interpolation is another issue. Generally it
accepted - correct me if I'm wrong - that in time one interpolates
variance (i.e. volatility^2 x time-to-maturity).

M.

This communication and any attachments contains information which is confidential and may be subject to legal privilege. It is for intended recipients only. If you are not the intended recipient you must not copy, distribute, publish, rely on or otherwise use it without our consent. Some of our communications may contain confidential information which it could be a criminal offence for you to disclose or use without authority. If you have received this email in error please notify [hidden email] immediately and delete the email from your computer.

The FSA reserves the right to monitor all email communications for compliance with legal, regulatory and professional standards.

This email is not intended to nor should it be taken to create any legal relations or contractual relationships. This email has originated from

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London
E14 5HS
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Registered Office as above

Switchboard: 020 7066 1000
Web Site: http://www.fsa.gov.uk
*****************************************************************

pierre baral

Re: BlackScholesMerton Process and Volatility

Ok let's try to answer, sorry in advance for my poor english :-)

First, here is the data I have:
- The quotes (open/close/high/low) of the unrderlying stock since at least 1 year.
- The quotes of the warrant I have choose since its first quote.
- All the information about the warrant except the volatility (type, maturity, settlement, underlying, strike, dividend...).

I want to forecast/know the exact price of my warrant at day+1.

Let's take an example:
It's Monday, the price of my cisco stock is 50$ for one share.
The price of a call warrant is 0.40$ the Monday.

Now I suppose tuesday, my share will be at 52$. With all the information I have on the warrant (except the volatility I need to calculate), I want to forecast/know the exact (and future) price of my warrant for tuesday ... :)

To do that I need to calculate the volatility (io::volatility)? How to do it?
Marcin says I can use the GarmanKlass model to have it.
Is there another way that would be easier with all the information I have? Is there an example to know how to use the GarmanKlass model ?

PS: 4) Why do you want to use discrete dividend model and the BSM process?
Well, I use european warrants, I suppose the market maker use the BSM process? For the discrete dividend model... that was a supposition =)

2010/10/19 Simon Ibbotson <[hidden email]>

Okay, here’s a sequence of questions:

1)       Why (for what purpose) do you need to price the warrant?

2)       Are there any warrant prices / quotes that you can see in the market?

3)       Are there any option prices / quotes (on the stock) that you can see in the market?

4)       Why do you want to use discrete dividend model and the BSM process?

Once you’ve answered these, we can look at the best way to do it…

From: pierre baral [mailto:[hidden email]]
Sent: 19 October 2010 14:13
To: [hidden email]
Subject: Re: [Quantlib-users] BlackScholesMerton Process and Volatility

Ok so I need to use an estimator such as GarmanKlass. It takes historical prices and returns the implied volatility. t's okay I can do what I want.

However is this the easiest way to do it?

I just want to estimate/forecast the price of a stock for the following day and then to get the future price of my warrant.

2010/10/14 Marcin Pawlik <[hidden email]>

2010/10/14 pierre baral <[hidden email]>:

> Hello,
>
> I'm trying to code a basic pricer for european warrants with discrete
> dividend, but it's not so easy. (I'm not in the finance) ;-)
>
> I want to use the BlackScholesMerton Process but it needs a volatility.
>
> Is it the historical volatility which is calculated on a year (~260d)? Do I
> need to recalculate it for each day or just at the settlement date?

You can use it as a proxy if you don't have implied vol. Of course you
can use any other estimator. Some of them are implemented in QuantLib
e.g. GarmanKlass.

> Or is it the implied volatility (how to calculate it then)?

Implied vol is taken "from the market". If there are options on your
underlying listed on an exchange you can use their prices in order to
"imply" volatility. These implied volatilities are dependent on strike
and maturity. In most cases you'll need to interpolate or extrapolate
them in order to get the vol you need.
The proper way of interpolation is another issue. Generally it
accepted - correct me if I'm wrong - that in time one interpolates
variance (i.e. volatility^2 x time-to-maturity).

M.

This communication and any attachments contains information which is confidential and may be subject to legal privilege. It is for intended recipients only. If you are not the intended recipient you must not copy, distribute, publish, rely on or otherwise use it without our consent. Some of our communications may contain confidential information which it could be a criminal offence for you to disclose or use without authority. If you have received this email in error please notify [hidden email] immediately and delete the email from your computer.

The FSA reserves the right to monitor all email communications for compliance with legal, regulatory and professional standards.

This email is not intended to nor should it be taken to create any legal relations or contractual relationships. This email has originated from

The Financial Services Authority (FSA)
25 The North Colonnade,
Canary Wharf,
London
E14 5HS
United Kingdom

Registered as a Limited Company in England and Wales No.1920623.
Registered Office as above

Switchboard: 020 7066 1000
Web Site: http://www.fsa.gov.uk
*****************************************************************

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Marcin Pawlik

Re: BlackScholesMerton Process and Volatility

On 4 November 2010 21:41, pierre baral <[hidden email]> wrote:
> Ok let's try to answer, sorry in advance for my poor english :-)
>
> First, here is the data I have:
> - The quotes (open/close/high/low) of the unrderlying stock since at least 1
> year.
> - The quotes of the warrant I have choose since its first quote.
> - All the information about the warrant except the volatility (type,
> maturity, settlement, underlying, strike, dividend...).

Interest rates?

> To do that I need to calculate the volatility (io::volatility)? How to do
> it?

You can choose between the two:
1. Get the implied volatility (based on the market prices of options)
- I've described this more or less in my previous message. Let us know
if it wasn't clear enough.
2. Estimate it on the basis of past observations.

> Marcin says I can use the GarmanKlass model to have it.

Well, it's one of the options if you follow the second option. I named
it explicitly but from what I know it's not the most common way. In
<ql/models/volatility> you can find constantestimator.cpp. I think
it's widely used in practice if the first method fails.

> Is there another way that would be easier with all the information I have?
> Is there an example to know how to use the GarmanKlass model ?

Actually, I'm not so sure. Perhaps it will be easier to find a
constant estimator example. You should look into test-suite directory.

M.

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David G. Thomson, author of the best-selling book "Blueprint to a
Billion" shares his insights and actions to help propel your
business during the next growth cycle. Listen Now!
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Marcin Pawlik

Re: BlackScholesMerton Process and Volatility

In reply to this post by pierre baral

Pierre,
I'm not much familiar with warrants but why don't you use implied vols
for CISCO stock in your calculations?
If you don't have access to professional fin. data providers you can
use data provided by yahoo, I think.
Just take a look:
http://finance.yahoo.com/q/op?s=CSCO

M.

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Billion" shares his insights and actions to help propel your
business during the next growth cycle. Listen Now!
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