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#1
04-14-2008, 07:02 PM
 macTEN Member Join Date: Feb 2007 Posts: 205
Help _Delta hedging

Ive been trying to get this simple concept straight but i keep getting confused.
this is what im thinking.....
To hedge a written call we at time 0 :
1. we recv $C_{0}$
2. we buy $\Delta_{0}S_{0}$ 3. we borrow $\Delta_{0}S_{0}-C_{0}$

At time one we have $C_{1}, \Delta_{1}, S_{1}$.
what is the cash flow at time of rehedging,
what is the market-to-market gain or loss,
what exactly doe it mean to be self-finaced.
and how does this all relate to overnight profit
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#2
04-15-2008, 08:19 AM
 macTEN Member Join Date: Feb 2007 Posts: 205

Is it possible for the SOA to test us on delta-hedging on "Dividend paying stocks" ?
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#3
04-15-2008, 09:32 AM
 bjz99 Member Join Date: Apr 2007 Location: Earth? Studying for zombie survival Favorite beer: one with drinkability Posts: 951

You sell the call, buy Delta shares (I don't know how to do the fancy lettering) and you lend C0-Delta*S0 (Negative value implies borrow). After one day, I think of it this way (let me know if it helps). I'll say C1>C0, Delta1> Delta0, and that S1>S0. Since I sold the call for less than it's worth today, I lost C1-C0 on it. Since I bought the stock for less than it's worth today, I made Delta*(S1-S0) on it. Then factor in the interest on the money lent/borrowed to get your overnight profit.

I believe the self-financing aspect means that if the stock moves one standard deviation, there won't be a profit or loss and you don't need to re-hedge, but don't quote me on that part.

Last edited by bjz99; 04-15-2008 at 10:49 AM..
#4
04-15-2008, 01:38 PM
 macTEN Member Join Date: Feb 2007 Posts: 205

Thanks bjz99
This is what gets me confused.
I quote " Assuming that the position is fully financed, the "cash flow" at the time of rehedging- where cash flow includes mark-to-market gains and loses-eqauls the overnight profit or loss" pg 192 3rd ed.

ie $-(C_{1}-C_{0})+\Delta_{0}(S_{1}-S_{0})-(e^{r/365}-1)(\Delta_{0}S_{0}-C_{0})$="cash flow"

what is the cash flow?
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#5
04-15-2008, 02:13 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 6,197

Cash flow is the amount of cash that changes hands. If you borrow \$1, you have a dollar of cash flow. By this definition, you can see that the statement you made is almost by definition; you are fully financing the portfolio, so you borrow the amount you lost in a day and lend the amount you gain in a day.
#6
04-15-2008, 02:40 PM
 macTEN Member Join Date: Feb 2007 Posts: 205

I see now
I was reading too much into that statement.
what is means it that at time 1. the money you have to put in or out ie cash flow is equal to profit/loss. therefore we do not need to make anymore investments it fully financed.

I totally Misinterpreted that line. thanks Abe and bjz99
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