Actuarial Outpost > SoA Fall 2014 #11 (d)
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#1
03-13-2018, 09:10 AM
 918273 Member SOA AAA Join Date: Jul 2016 Studying for QFIC Posts: 57
Fall 2014 #11 (d)

In part (c), we calculated that we need to buy 7737 calls with strike 1700, and sell 7737 calls with strike 1955, in order to delta hedge the liability.

In part (d), we're asked to calculate the total initial cost of setting up the hedge. The solution commentary states that the correct initial cost of hedging = number of options needed * cost per bull call spread. It seems obvious that this should be:

$7737 [C_{1700} - C_{1955}] = 7737 [147.15 - 59.18] \approx 680k$

However, the SOA solution multiplies that by 100 and gets an answer of 68M. We already accounted for the 100 multiplier when we determined the number of calls to buy / sell (i.e 7737). Why should we be multiplying by 100 again? This doesn't seem correct to me. Does anyone agree that this is a mistake, or can someone explain why the SOA is correct here?
#2
03-15-2018, 02:46 AM
 Bell Member Join Date: Jun 2005 Posts: 364

You have a point.

The (cost of the hedge)=(cost per bull call spread)=87.97 and the number of options needed is indeed=7,737.
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