Tom is under-educated
Jun. 18th, 2005 03:28 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
fivemackI can't remember whether it was Further Group Theory or Number Theory that I took when I could have been taking Martingales and Financial Mathematics. Both have been useful in my life, but in this situation appear less so.
My bank wants to sell me the following deal:
* Let X be the current value of the FTSE 100 index
* Let Y be the value of the FTSE 100 index on 15 June 2010
* On 15 June 2006, they give me £3168
* On 15 June 2010, if Y<X, they give me £7000. If Y>X, they give me 0.75*((Y-X)/X) * £7000
All the figures for money the bank gives me are after tax.
This looks to me like a classic sort of option-pricing problem. How do I figure out what a fair price for the deal ought to be?
Current rate for a five-year bond is 4.0% after tax; I'm sure there's some sort of bond-lengthening derivative equivalent to 'I will pay you on 15 June 2010 the amount of money you'd have then if you'd bought the best-on-the-then-market 4-year bond in 15 June 2006', but I don't know what it would be called or what it's value is agreed to be.
Equally, I'm sure that long-term FTSE futures are a standard derivative, but I don't know how to find the relevant valuations.
My bank wants to sell me the following deal:
* Let X be the current value of the FTSE 100 index
* Let Y be the value of the FTSE 100 index on 15 June 2010
* On 15 June 2006, they give me £3168
* On 15 June 2010, if Y<X, they give me £7000. If Y>X, they give me 0.75*((Y-X)/X) * £7000
All the figures for money the bank gives me are after tax.
This looks to me like a classic sort of option-pricing problem. How do I figure out what a fair price for the deal ought to be?
Current rate for a five-year bond is 4.0% after tax; I'm sure there's some sort of bond-lengthening derivative equivalent to 'I will pay you on 15 June 2010 the amount of money you'd have then if you'd bought the best-on-the-then-market 4-year bond in 15 June 2006', but I don't know what it would be called or what it's value is agreed to be.
Equally, I'm sure that long-term FTSE futures are a standard derivative, but I don't know how to find the relevant valuations.
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Re: Huh?
Date: 2005-06-18 11:02 pm (UTC)They want £10,000 for this deal, and sell it as 'up to 30% can go in a bond, down to 70% in this guaranteed-no-absolute-loss stock market thingie'. Yes, I got the maths wrong, I get £7k back in any case, and if the FTSE has gone up 10% over the five years, I'd get 1.075*£7k.
So in worst scenario where FTSE has gone down (eg the situation I'd have been if I'd bought the equivalent to this deal five years back and it were maturing now), I have, in 2010, £7000 + £3168*risklessreturn^4.
I'm not sure how the bank actually implement the deal. I suspect they put the whole lot in an index-tracker reinvesting dividends, and are betting
a) FTSE return is >7% (3168 is 7%-tax) over one year
b) FTSE return over five years with dividends reinvested (thanks for that point!) is positive
Which is a bet I'd be moderately prepared to take. I don't have usefully formatted time-series data on ftse100, but I think the five-year returns have been reasonably positive in the medium past (though dreadfully negative for a while recently).
Thanks for explaining the details and the jargon,
Other Tom