Actuarial Outpost > MFE spring 07 # 15 - BS with discrete dividends
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#1
04-29-2009, 06:29 PM
 Chocolate Muffins And Pie Member Join Date: Jan 2008 Posts: 223
spring 07 # 15 - BS with discrete dividends

For the life of me I can never understand this problem. In ASM there are many problems about discrete dividends, where you can solve it by using S'=S-PV(divs) and using the forward volatility in d1.

In this problem they just give volatility with no mention of it being a forward volatility, but using it as-is yields the correct answer. What am I not understanding?
#2
04-29-2009, 06:32 PM
 Chocolate Muffins And Pie Member Join Date: Jan 2008 Posts: 223

the problem is:

six month european put on stock
K=50
S=50
dividend of 1.50 paid at t=4 months
volatility=.3
continous interest rate r=.05

Setting S'=S-1.5exp(-.05*4/12) and using .3 as the volatility yields 4.19
#3
04-29-2009, 06:47 PM
 colby2152 Note Contributor SOA Join Date: Feb 2006 Location: Virginia Studying for FAP College: PSU '07 Favorite beer: Oskar Blues Old Chub Scotch Ale Posts: 4,175

Quote:
 Originally Posted by Chocolate Muffins And Pie For the life of me I can never understand this problem. In ASM there are many problems about discrete dividends, where you can solve it by using S'=S-PV(divs) and using the forward volatility in d1. In this problem they just give volatility with no mention of it being a forward volatility, but using it as-is yields the correct answer. What am I not understanding?
If only one volatility is given, then you must assume that the stated volatility is the forward volatility on the stock.
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#4
04-30-2009, 08:00 AM
 am_vanquish Member SOA Join Date: Mar 2007 Studying for the zombie apocalpyse Favorite beer: Smithwick's Posts: 656

Is the OP referring to using Schroder's Method to switch between the Forward and Stock volatilities? Also, wasn't that removed from the syllabus? Therefore, we can trust that whatever volatility is provided can be used as-is.

Is this correct?
#5
04-30-2009, 10:06 AM
 colby2152 Note Contributor SOA Join Date: Feb 2006 Location: Virginia Studying for FAP College: PSU '07 Favorite beer: Oskar Blues Old Chub Scotch Ale Posts: 4,175

Quote:
 Originally Posted by am_vanquish Is the OP referring to using Schroder's Method to switch between the Forward and Stock volatilities? Also, wasn't that removed from the syllabus? Therefore, we can trust that whatever volatility is provided can be used as-is. Is this correct?
Yes, Schroder's method was removed from the syllabus.
__________________
How to explain actuarial exams to someone else...
Good Einstein quote - "One had to cram all this stuff into one's mind for the examinations, whether one liked it or not. This coercion had such a deterring effect on me that, after I had passed the final examination, I found the consideration of any scientific problems distasteful to me for an entire year."
#6
04-30-2009, 10:17 AM
 ActuarialHeroOfTime Member Join Date: Mar 2009 Posts: 313

Is it? some of the TIA exams have binomial trees based on forward prices (usually ask you to price an american call w a discrete div in there), where you haveto obtain

sigma_F = sigma_S*S(0)/F(0)

and determine u, d, p* using that. are these just outdated questions?

Though Ive never seen a problem where volatility must be adjusted in the BS Framework

Last edited by ActuarialHeroOfTime; 04-30-2009 at 10:40 AM..
#7
04-30-2009, 10:43 AM
 chopsticks Member SOA AAA Join Date: Jan 2009 Studying for ever Posts: 310

Schroder's method was on the exam for November 2008, but they were taken off the syllabus for May 2009.
#8
04-30-2009, 10:50 AM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 5,327

Oh good so I didn't waste 3 hours on it last night
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