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Dear sir if interest rate increases why does premium for call option goes up and rho becomes positive for call option, since put option would be preferred when interest rate increases so premium for put option should rise and it should be positive
The value of a call option is basically the current share price (Pa) less the present value of the exercise price (Pe). (As I explain in my free lectures on this, the multiplying of Pe by the term with ‘e’ in it is to discount the exercise price on a continuous basis).
If the interest rate increases then the PV of the exercise price will fall (as PV’s always will with higher interest rates) and so the value of the call option will increase.
(Having said this, because Rho on its own is only looking at the effect of changes in interest rates assuming everything else is unchanged, in practice it tends to have little affect and is the least used of the Greeks.)
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