April 2004 Question 5

Hi All,

I've been trying to understand this question, and I just wanted to know why the building society would need to sell the call option (and limit their return). I can understand buying the put so that they can have a guaranteed payoff for the investors, but if the index grows by more than 50%, can't the society just pay the 50% over to the investors instead of limiting their own return to 50% by selling a call?

Thanks much.

 

Hi JamaicanJem

( First I hope I thought correctly about this)

The best thing to do here is to draw the profit diagram that will result in the building society making neither profit nor loss. This profit diagram will give rise to the payoff diagram shown.

Profit diagrams are a good way of replicating payoffs using Options since they just require adding graphs. It is clear that you will need two Options, one short, the other long. So whether you long the Call and Short the put or vice versa still gives ''neither profit nor loss''[I first drew two diagrams]

i.e;

- short put strike (x) + long call (1.5)
And
- long put strike (x) + short call (1.5)

And we realise that this happens only if the premiums are the same i.e Ct=Pt.

The rest is calculating the prices, these should be the same since the strikes are the same i.e c(1.5) AND p(x).

For the primary part of your question, if you just long the put struck at x, you will lose the premium when the index is ; x≤ST.

I think about it as a problem requiring a ROBUST payoff, which tends to be the addition of a concave and convex payoff.

 

Hi Edwin,

Thanks for the reply. I've actually been trying to get the gist of adding graphs, but I'm terrible at it! I drew the long put and the short call but I really can't get them together to look like the payoff diagram. So if in fact I draw the diagram which guarantees no profit or loss, then I should be able to see that I need a long put and short call or vice versa?

Regards.

 

Yes, you can Google ''Option Strategies'', this is a Mathematics of finance topic not discussed in CT8 but that's been asked in most previous CT8 papers I saw.(e.g this question and April 2004 question 10 e.t.c)

There are a number of Options Strategies; Spreads, Butterflies, Strangles...e.t.c I found that knowing how to replicate them by adding graphs and using a ''payoff'' profile is of great help to some CT8 questions (you may agree that Sep 08, question 8 (v) was horribly the worst!!!) But a modicum of understanding Option Strategies does help.

Most of CT8 difficult questions come from staff that's not covered in the CT8 NOTES , these are normally hard using CT8 resources but are otherwise easy when using other techniques.(e.g Unfamiliar derivatives, like cash/Asset or nothing Options_September 2008 question 8 e.t.c, Power Options_September 2010 question 5 (iii) e.t.c)
It HELPS to have the book;(''Options, Futures and other Derivatives by John C. Hull any edition will do)However it is still possible to pass without it.

Good luck to both of us.

 

This question has a full model solution in Revision Notes. what i do not understand is that the model solution says 'since exam questions involving calculations based on a binomial tree normally tell you how many periods to use, this suggests we should use the BS Model'.
But we do know there are 3 years dont we? so can we use the 3-period binomial model as well? u and d for each year can be calculated according to the formulae p.45 of the tables.
(i've tried a 3-period binomial model to arrive at x=102%, which is odd at first sight yet makes sense because of the high volatility and of the 'no profit' condition).

i just dont quite follow why the model choice is Black-Scholes here. my reasoning is that the annual volatility of the share over 3 years is unlikely to stay the same, so i'd go for binomial.

 

i know! my result x = 102% relies on the assumption of the binomial model that the share price will be as high as So 1.3^3 which is unrealistic. so the BS model could be better. phew... if this question was the exam id probably spend too much time on it trying out different approaches.

 

If the examiners want you to use a tree, then they say normally so. In other words, the question always includes the phrase "binomial tree" or "binomial model" or says something like, "the share can either move up from S to S*u or down to S*d".