spring 07 # 15 - BS with discrete dividends

[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?

[Chocolate Muffins And Pie]

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

[colby2152]

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.

[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?

[colby2152]

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.:tup:

[ActuarialHeroOfTime]

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 are these just outdated questions?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

[chopsticks]

Schroder's method was on the exam for November 2008, but they were taken off the syllabus for May 2009.

[Actuarialsuck]

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