 # Rho

Dear:

it is said Rho is positively related to Call Option and negatively related to put option. To my knowlege, the price of Call or Put is just the discount value of payoff thru the binomial model, so Rho is the risk free rate and in the denominator, it should have and negatively related to both call/put. I mean when the Rate is high/low the Call/Put should be low/high respectively.

Thanks

look at Put Call Parity for this.

C = P + S - X/(1+rf)^T

rf increases - C increases - since less is subtracted from P + S

P = C + X/(1+rf)^T - S

rf increase causes P to decrease - since X is being discounted at a higher rate.

one way to look at it.

S0 + P0 = C0 + X/(1+Rf)

P0 = C0 - S0 + X/(1+Rf) ===> if interest rates go up, you add a little more to P0 than before as X/(1+Rf) is relatively smaller, so put goes down.

C0 = S0 + P0 - X/(1+Rf) ===> if interest rates go up, you deduct less as X/(1+Rf) is relatively smaller, so call goes up.

way to go cpk…posted at the same time!

if use the Put call parity to infer this logic, I got it but why not use the binomial model to deduct this problem becuase to calculate the price of Call or Put , the binomial is used to discount the payoff.

thanks

binomial only evaluates the Value of the option.

who exercises the option?

Call option is more valuable to the Issuer. So it increases in value when rate increases.

Put option is more valuable to the investor - and it goes down in value when rate increases. There is no motivation to put a bond back when I can reinvest the coupons from the bond at a higher rate.

this relationship is captured by the Put-Call Parity relation.

But the option is not for only the bond, It applies ot Stock also.

for further questions and deeper knowledge / understanding please go to www.google.com

thank you