Can the put call parity formula (Cost of Call + Risk Free Bond with Face Value Equal to Exercise Price = Cost of Put + Price of Stock) explain the effect of interest rates on the price of options? If Call Price + Exercise Value/(1+rfr)^T = Put Price + Stock Price: If Interest rate increases, left side of the equation increases (PV of the risk free bond will increase since the discount rate (RFR) increases), if put call parity holds then right side must decrease. Does that mean the right side (put price or stock price) must decrease for parity to hold true? Which one will decrease, stock price or put price?
I would stick to put call parity being the basis for one version of “law of one price” (no arbitrage) and not confuse yourself further. higher rates -----> lower PV for bonds and stocks, bad for puts, good for calls. thats the nuts and bolts.
Let me correct myself. If interest rates increase, the left side of the equation will stay the same, the call price will go up and PV of the bond down, and on the right side stock price will increase (dividend discount model, interest rates increase, k increases) thereby put price decreases?
da0618 Wrote: ------------------------------------------------------- > Can the put call parity formula (Cost of Call + > Risk Free Bond with Face Value Equal to Exercise > Price = Cost of Put + Price of Stock) explain the > effect of interest rates on the price of options? > > If Call Price + Exercise Value/(1+rfr)^T = Put > Price + Stock Price: > > If Interest rate increases, left side of the > equation increases (PV of the risk free bond will > increase since the discount rate (RFR) increases), > if put call parity holds then right side must > decrease. Does that mean the right side (put > price or stock price) must decrease for parity to > hold true? Which one will decrease, stock price > or put price? not at all…this is just about arbitrage to check if both options are fairly priced
> If Interest rate increases, left side of the equation increases (PV of the risk free bond will increase since the discount rate (RFR) increases), Why so? It should dcrease.
Please read my second post correcting myself, is that correct (assuming implied volatility remains constant)
Call Price = Put Price + Stock Price - Exercise Value/(1+rfr)^T so call price goes up.
We are saying the same thing right? CFA book says to remember put call parity as Call Price + Exercise Value/(1+rfr)^T = Put Price + Stock Price Therefore our equations are equal.
> If interest rates increase, the left side of the equation will stay the same, that’s not correct.
Why not? Options are price on volatility right? So a change in interest rates will only cause a proportional increase in call prices asmuch as the price of the risk free bond goes down right?
is this correct? if interest rate increases, call increase and put decrease?
da0618 Wrote: ------------------------------------------------------- > Why not? Options are price on volatility right? So > a change in interest rates will only cause a > proportional increase in call prices asmuch as the > price of the risk free bond goes down right? Have you ever heard of “greeks”…have a look
Well, the book says this is a given because when interest rates are higher, buying the call instead of a direct leveraged position in the underlying is more attractive. Also investors save money by not paying for the underlying until a later dates. I am wondering if put call parity can also explain this?
cfaiscomplex Wrote: ------------------------------------------------------- > is this correct? > > if interest rate increases, call increase and put > decrease? true
Call Price = Put Price + Stock Price - Exercise Value/(1+rfr)^T Put Price = Exercise Value/(1+rfr)^T - Stock Price + Call price int rate = 10% Call Price = $1 + $25 - $20/1.10 = $7.80 int goes up to 15% Call Price = $1 + $25 - $20/1.15 = $8.60 The put; int rate = 10% Put Price = $20/1.1 - $20 + $7.80 = $6.70 int goes up to 15% Put Price = $20/1.15 - $20 + $7.80 = $5.19 Call up, Put down.
Right, I am not trying to argue but we are saying the exact same thing…
may be, but you are not saying it right. You’re saying the left side stays the same! It doesn’t. That’s why I was trrying to help.
Your explanation did prove that call price will go up if interest rates go up, and put prices will go down if interest rates go up. HOWEVER, your formula Put Price = Exercise Value/(1+rfr)^T - Stock Price + Call price is wrong. Should be Put Price = 20/1.10 - $25 (you said $20) + $7.8 = 1 When interest rates = 10%, using your equations call price = $7.8, put price = $1. Therefore, $7.8 + ~$18.2 = $1 + $25 ( put call parity, $26 = $26)… According to Black Scholes Model, rho (sensitivity of the option price to the risk free asset), Rho(Put) = -Rho(Call), therefore there price change should be equal but in opposite directions (I’m pretty sure this is right, see http://en.wikipedia.org/wiki/Black_scholes for more info on rho). So we don’t know what the new price of the call is nor the new price of the put, but they will change by equal % amounts. Let’s say its a 5% change (does this effect the equation?) Interest Rates Go to 15% $7.8(1.05) + 20/1.15 = $1(.95) + X (Stock Price) Put call parity must hold true, New stock price = $7.8(1.05) + 20/1.15 - $1(.95) = $24.62 (stock price decreases because K-G, required return goes up but growth rate of dividend maintains? or will it increase)? Solve the put call parity formula, $7.8(1.05) + 20/1.15 = $1(.95) + $24.62 $8.19 + 17.39 = .95 + $24.62 ANSWER WHEN RATES 15% $25.57 (fiduciary call) = $25.57 (protective put) Wow…actually this was a good way for me to learn about options. Note sure if it’s all correct? Can put call parity be used to calculate the price of a stock given a change in interest rates? If Rho(Put) = -Rho(Call), then Put option decreases in the same percentage Call option increases. Would new stock price = Call0(Rho) + Strike Price/(1+ new risk free rate)^T - Put0(Rho)
man it’s beyond L1…
Hahha yeah, you’re right, but I think Black Scholes is in Level II right? Also, just read it requires a constant risk free rate, so that might cause problems.