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April 2024 Q9i paper A

D

David12345

Keen member
Hello,
Please can you explain how the options as mentioned in the mark scheme lead to the required payoff.

If you could break it down that would be excellent - I've seen a handful of these type of questions about replicating portfolios using options but really struggle to understand them.

Thank you:)
 
Hi David,

One nice way to create the position diagram you need is to EVERYTHING with call options from the left of your page.

Get a shouty friend and a pen and start drawing a horizontal line (left to right).

When your friend shouts "buy", start moving your pen up at 45 degrees (gradient 1).
From here, when your friend shouts "sell", start moving your pen horizontally again.

Or...

When your friend shouts "sell", start moving your pen down at 45 degrees (gradient -1).
From here, when your friend shouts "buy", start moving your pen horizontally again.

If your friend shouts "buy" when you're already going up, tell him/her to stop being a smart-arse but we can also sort this out by going from gradient 1 to gradient 2 (60 degrees, I think?).

All of this has been done with call options and the strike prices are the point where your friend shouted.

If you need to start with a slope, an upward slope of gradient 1 is sorted by buying the share, or a downward slope of gradient -1 is sorted by selling the share. BTW, a share is a call option with a strike price of K=0 (you should think about this) and so this is really your friend shouting just as you start moving your pen.

Finally, you need to get the "height" correct, which can be sorted with cash. If the final share price is less than the lowest strike of all the calls, they all expire worthless. So, if you get the "height" correct here (with the right amount of cash), all of your position diagram falls into place

Good luck!
John
 
Thanks John, that's very helpful.
Please could you write a similar thing for how Put options would work on a graph? Sep 2019 paper B Q1 asks for things in terms of put options so I don't know if call options could be used then?
Thanks
 
With put options you do everything from the right. Get your shouty friend, start drawing right-to-left and same instructions...

"buy" - go up 45 degrees
"sell" - go down 45 degrees
(with similar caveats about smartarsedness)
to start with your pen going down from right to left, buy the share
to start with your pen going up from right to left, sell the share

(with these last 2 instructions, don't stress about it seeming the wrong way round, it's not about right-to-left so much, it's about
buy share is this shape .... /
sell share is this shape ..... \
- those gradients are 45 degrees, honest!)

To get the "height" right, use a high share price where all the put options expire worthless

Good luck!
John
 
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