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#1




Paul Wilmott, Chapt. 10
My question pertains to the equation that's shown as:
When I work out the left side of this equation, I get: So this seems to imply that = 0 Is this correct? If so, why do we assume it's 0? 
#2




What do the V's represent?

#3




Quote:
 When plugging in the upper bound of "T" you get 0.  When plugging in the lower bound of "t0" you get  Therefore, we get the integral by doing upper bound  lower bound Here are the details of how we know this: Important realization: At expiration, the value of an option is its payoff. This is obvious, but important. Because at time T.....we must have Vi = Va. The value at expiration is equal to the payoff, and the volatility parameter used does not matter at expiration! In other words  at expiration, our value (if we use a call as an example) is max(STK,0) and the same value regardless of sigma. So at expiration time T, Vi = Va. Therefore, when we plug in at the upper bound T for our integration, that part will cancel out. The idea is that the integral accumulates the total present value of profit. We see that for the hedging with actual volatility case, the total present value of profit is very simple  it is the difference between the OV with actual volatility and the market price. You will see this again in QFI115, so feel free to look at both sections to solidify your understanding. If you are using TIA, you will find it helpful to go to page 39 of the Section 2 DSG. This will likely clear everything up. Hopefully that helps clarify Also see here for a similar discussion: http://www.actuarialoutpost.com/actu...d.php?t=328799
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Zachary Fischer, FSA CERA TIA Instructor QFI Quant  QFI Advanced  QFI IRM  LRM  ERM Last edited by Zakfischer; 06132018 at 02:35 PM.. 
#4




Quote:

#6




Sorry, just realized the left side of the first equation I posted should've been:

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