ACID April 2000 - Option on RPI

[Gareth]

Can anyone explain why question 1(ii)(a) has used discounted RPI and strike price in the log part of:

?

In every other example of using Black's model, or the Garman-Kohlhagen formula, the ratio inside the log has always been values at expiry of the option, never the discounted values.

So i'm a little confused...

 

[examstudent]

wouldnt separation of the Log in this case reduce to a typical Black Scholes/garman kohlagehn looking d1/d2 formula

i would have thought the same was in the usual black formula where all is parametrised in terms of forward prices F which are put inside logarithm, but as F = S * exp (rt), for stocks, this reduces to typical d1/d2 found in black scholes/ gk formulae...

 

[Gareth]

i dont know, couldn't you argue that share prices or RPI indicies are effectively similar, so if you don't discount the share price, then why should u discount the RPI index?

Still unconvinced

 

[Gareth]

ST6-11 says the ratio inside the log is:

E[V_T] / X

where X is the strike price and V_T the payoff of the option. These are NOT discounted.

I'm feeling reasonably confident the examiner is wrong.

 

[examstudent]

gareth
i have seen a few cases where in d1 formula, ratio inside logarthim includes discounted strike...

look at brearley and myers "principles of corporate finance "
fifth edition page 578

look at d1 expression, the ratio inside logarithm has pv(EX)...and no r in the rest of the expression for d1.

algebraically under continuous compounding this should equal conventional formuale for d1( i.e no discounting in teh log ratio with r shoved into the second bit of d1 numerator )