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Why is the derivative price geared?

A

ActStudent

Member
April 2005
Q6. (ii)
The answer says the price of an option is usually geared, so that a change in the share price leads to a higher percentage change in the option price.

Are we talking about the delta here? According to the Black-Scholes formula, delta = phi(d_1), which is less that 1, isn't it? Is that contradictory to what the answer says?



A separate question:

Q10. (i)
The parameters determining the share price after an up-jump and down-jump should be determined by considering the standard deviation of the log price.

Why is this interpreted to mean u = exp(sigma) and d = u^-1 ?


Any help will be appreciated. Thanks!
 
Geared nature of options

If S = 100, c = 20 and delta = 0.5 then if the share price increases by 10, the call will increase by 0.5 * 10 = 5.

So the call has increased in price by 25% and yet the share has only increased by 10% - hence the geared nature of options.

See page 45 of Tables for your binomial model query.

John
 
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