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109 Sept 02 Q4

J

Jon Bowden

Member
This question features in the revision book as number 6 and I am having trouble with the last part.

I get that Investor B has a portfolio of value £1,079,660, with £1m in cash and 1,000,000 call options worth £0.07966 each.

If the share price instantly jumps to 120, we can recalculate the option price using Black Scholes to get f = £0.22147.

The cash stays fixed and the value of the portfolio is now £1,221,470 which is greater than the £1,200,000 Investor A has.

The solution uses delta against the change in share price to conclude Investor A is better off, but surely re-pricing the option is more accurate and in this case contradictory to the solution?

Am I doing something wrong?
 
No Jon, you're quite right. What you've done would have got full marks.

Our Revision Booklet reproduces the Examiners' answer, which is based on the rough estimate df=delta.dS.

If we knew gamma for the option, a much better estimate would be obtained from df=delta.dS + 0.5 gamma.(dS)^2 (ie Taylor's formula).

Although gamma is very small, unfortunately in this case it's enough to increase the value of Portfolio A above that of Portfolio B!
 
So there were no wrong answers. Just goes to show that as long as you do something, you stand a chance.
 
Can someone pls explain to me how we get to 79,656?

I don't understand the 1st line of the solution (q6 (iii) revision booklet 4) where it says "the original option value over 1m of stock works out to be worth 79,656"

I tried using the formula on pg 47 of the tables but Im not really getting anywhere. Pls help, thanks!
 
abumenang said:
Can someone pls explain to me how we get to 79,656?

I don't understand the 1st line of the solution (q6 (iii) revision booklet 4) where it says "the original option value over 1m of stock works out to be worth 79,656"

I tried using the formula on pg 47 of the tables but Im not really getting anywhere. Pls help, thanks!
Click to expand...

The formula for calls on page 47 is the right one to use. Using S=K=1,000,000, r=0, T-t=1, sigma=0.20 gives:

d1=0.1000, d2=-0.100 and c=79,656
 
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