# option price

Which statement best describes option price sensitivities? The value of a: A. call option increases as interest rates rise. B. put option increases as volatility decreases. C. put option decreases as interest rates decline. Answer = A

Why not C?

Look at put-call parity.

Sorry, still don’t understand.

if use put-call parity to think about this question, you need to assume that the right hand side of the equation doesn’t change. But when i changes, put price also changes.

My original thinking was when i increases, underlying asset(assume it’s bonds) price drops. When bond price goes down, call price decreases.

Thank you.

Call option price = S - X/(1+i) —> so if interest rate rises, X (Exercise price) will become smaller and hence (S - X) is higher.

Put option price = X/(1+i) - S —> as interest rate decrease X is higher, so (X - S) increase NOT DECREASE

So anwer is A

S + P = C + X / (1 + r)

If r increases, then either C must increase or P must decrease (or both).

If r decreases, then either C must decrease or P must increase (or both).

If i increase, call price increase, then a callable bond’s value ( which is = option free bond-the value of the call option) will decrease more than a option free bond?

does this make sense?

When interest rate increase, YTM increase and the price of the option free bond decrease

but when the bond is callable, the call option becomes more valuable as the price of the bond increase cause it is highly likely that it will be called.

And this is why we say callabe bonds are less convex cause:

P( callable bond ) = P(Option free bond ) - Option value

when Interest rate decrease, P(Option free bond ) increase and Option value Increase so they offset each other and the P of the callable bond will increase by a lesser amount.

here you have to think about the option value = Intrinsic value(option in the money) + Time Value

This put-call parity formula isn’t intended for options on bonds, where the price of the underlying is directly related to interest rates.

B - is a wrong answer because option value increases with increased volatility.

C -Put option value decreases when interest rates rises. Why put option value decreases when interest rises is because put option gives the put owner, the right to sell at X. However with an increment of interest rates, the PV of the proceeds will be lesser.Do not confuse this with bond embedded put option!!

A - Is correct because when interest rates rises, a call option gives the call owner the right to buy at price X. With an increment of interest rates, the buying price at X that you are paying will be discounted due to the increment of interest rates. Again, do not confuse this with bond embedded call option!