Comparision between binomial and BSM model

[harry_summy]

Dear David

I have created one spreadsheet where I am valuing put and call option with undernoted assumption.
( please see uploaded excel spreadsheet as well)stock 150
Strike 100
Volatility 5%
Rf 5%
T 1
With the above assumption, I am getting call price of Rs.54.88 with both binomial and BSM method, but when I am increasing the volatility, I am getting a slight price differencial (i.e. when volatility is 20%, price of call becomes 54.97.

My question: But when the same volatility jump is applied over to put valuation using binomial and BSM, I am getting a huge price difference. i.e. at
stock 75
Strike 100
Volatility 5%
Rf 5%
T 1

above assumption, I am getting same value for put option using binomial and BSM model, but when I am rasing the volatility to 20%, I am getting a huge price differential with Binomial it is 21.07 and with BSM it is 14.39.

1. What is the causative factor for such a huge difference?
2. Which model is optimum to use in real market situation?
3.When Stock=strike why put option have zero value but call option still positive through BSM model. even when I am having strike price of 100 and stock price of 75, I am getting a positive call value call=max(s-x,0).
4. Is option value and option premium different?
5.Which model the market participants are using mostly?

Regards,
Harish

 

[Avishek]

Greetings Harish,

I am sure that David will come up with better concepts and ideas behind your query. But, I would like to provide my inputs as well to make the forum more interactive. Would also expect you to provide your ideas to my queries or concepts in days to come.

Well, I am uploading another spreadsheet of mine (check the added spreadsheets at different volatility levels). Really impressive stuff and to be frank I faced a similar issue previous year.

1) Check the time factor. In your case, for the call option, you had taken time as 1 year, but in the binomial tree, you have used (1/4). Again, while you calculated the value of d1 and d2, you took it as 1. So there was a major imbalance. In my calculation I took time as 1/4 and used it throughout. Same thing goes with the put option. In that case I used time as 1 throughout. The differential is negligible. Hope this is what you were looking for. You were on the right path though! :coolsmile:

2) I shall leave this for David as I would be more biased about my firm. ;-)

3) I suppose this can be clarified via Put-Call Parity if not anything else. You can download the Bionic Turtle 2008 Book-2 (Market Discipline) - Page 50 for better clarity.

Hi David - Is there any other concept behind this or is it the simple calculation using:

"c + K.e^– rT = p + S"

4) Yes, I see Option Value differently from Option Premium. Premium is the price you pay to buy the Option (whether call or put) while the Option Value would be the "execution price" of the call or put only if you are ever in a position to execute it before expiry.

5) It would be answered once David replies to your second pointer.

Do come up with more queries and doubts and I shall provide my views as well.

Good Day, Avi.

 

[harry_summy]

Thanks Avi for the prompt reply. I think its great learning and sharing platform. regarding your views;

1) Time factor: in BSM I am using 1 year and in Binomial, I am creating four lattices each of 3 months to get more accurate or closer valuation to that of the BSM. and See in my spreadshit I have tallied the price obtained from BSM and price obtained from Binomial. I am doing a PV at each note for the intrinsic value of the option, creating four notes which eventually giving me value for the one year and perfectly tallied with the value obtained in BSM.

My query is that why the BSM and binomilal give almost same value at lower volatility say at 2% and why there is huge difference, particularly in case of put option when i raise the same volatility to 20%. Try this with my excel sheet.

2) regarding d1 and d2 being one, If you can see in excelsheet I have taken normsdist of the d1 and d2. One important point here is that for any value of d1 and d2 greater than 3.09=(0.9990), you will wihout seeing z-table can put value as 1 for d1 and d2. So no calculation mistake here.

I hope David will through some more light on my queries. Anyway thank. I would definitely like to share some more ideas on that.

Regards,
Harish

 

[harry_summy]

Dear Avi and David

I am uploading a fresh excel spreadsheet. I was getting a huge differential in case of put value due to my mistake in spreadsheet. Sorry for the inconvenicne. Now I could tally both results with almost same results using both BSM and binomial model

It automatically replies to my query 1}

For rest of my quries, I still to hear from David.

Regards,
Harish

Please see fresh spreadsheet