Option Duration

derswap07

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Please explain :
” When interest rates decline, the value of call option will rise. When rates rise, value of a put option rises”
Thanks.
 
Sounds backwards.
Put-call parity says that if rates increase, the price of a call increases and the price of a put decreases. And vice-versa.
 
s2000 is correct.
Options value the future value of a security, which must be at least the cost of the risk-free rate.
i.e. Rf of 5%. Stock is $100. 1 year from now my minimum requirement for forward value is $105. Call option will be at least $5. If rate goes to 6%, forward value is $106, so call option is at least $6.
 
s2000: although you are correct, I dont think put call parity explains it. theoretically, only one term in the put call parity equation (risk free bond) can be determined based on the level of rates/strike price. the other three terms could move either way for parity to hold.
klinko88: perhaps your lower bound for option value holds for ITM/ATM strikes only? if an option is deep OTM and volatility is 0, option exercise wont happen and hence value = 0.
 
derswap07 wrote:
Please explain :
” When interest rates decline, the value of call option will rise. When rates rise, value of a put option rises”
Thanks.
I simply think call option is the option to delay buying, when rates rise, you still have something to invest at a higher rate, so call option rises …
 
oz001 wrote:s2000: although you are correct, I dont think put call parity explains it. theoretically, only one term in the put call parity equation (risk free bond) can be determined based on the level of rates/strike price. the other three terms could move either way for parity to hold.
I wasn’t trying to explain it; I was trying to illustrate it.
Put-call parity gives an easy-to-see illustration.
 
S2000magician wrote:
I wasn’t trying to explain it; I was trying to illustrate it.
Put-call parity gives an easy-to-see illustration.
how does put call parity illustrate the relationship between rate movements and direction of option price movements?
 
P + S = C + X/(1+r)^T
C = P + S - X/(1+r)^T
For C -> assume P, S are constants. Since r is at the denominator - that term reduces so term on the right increases.
==
P = C + X/(1+r)^t - S
C and S constant, smaller X term when R goes up, so P goes down.
and the terms as assumed to be constant - because of ceterus paribus conditions…
======
 
cpk123 wrote:
P + S = C + X/(1+r)^T
C = P + S - X/(1+r)^T
For C -> assume P, S are constants. Since r is at the denominator - that term reduces so term on the right increases.
==
P = C + X/(1+r)^t - S
C and S constant, smaller X term when R goes up, so P goes down.
and the terms as assumed to be constant - because of ceterus paribus conditions…
======
the ceterus paribus argument cannot include call and put prices, rather only the other inputs to the options pricing model (strike, spot, volatility, time to expiration). otherwise you would be implicitly assuming something that you are trying to prove.
C+ bond = P + S
assuming S = constant: rates rise (fall), bond price falls (rises), mathematically C/P could move up or down to maintain parity.
 
oz001 wrote:the ceterus paribus argument cannot include call and put prices, rather only the other inputs to the options pricing model (strike, spot, volatility, time to expiration). otherwise you would be implicitly assuming something that you are trying to prove.
Let’s try this again: I wasn’t trying to prove the effect of interest rates on the prices of call options and put options.
I was offering an illustration that serves as a mnemonic device to remember those effects.
Put call parity serves that purpose quite well.
 
S2000magician wrote:
Let’s try this again: I wasn’t trying to prove the effect of interest rates on the prices of call options and put options.
I was offering an illustration that serves as a mnemonic device to remember those effects.
Put call parity serves that purpose quite well.
s2000: ok, i get your mnemonic illustration. just that when you stated “put call parity says that…” i was wondering where that came from.
 
oz001 wrote:
S2000magician wrote:Let’s try this again: I wasn’t trying to prove the effect of interest rates on the prices of call options and put options.
I was offering an illustration that serves as a mnemonic device to remember those effects.
Put call parity serves that purpose quite well.
s2000: ok, i get your mnemonic illustration. just that when you stated “put call parity says that…” i was wondering where that came from.
Poor choice of wording on my part.
Sorry.
 
oz001 wrote:
s2000: although you are correct, I dont think put call parity explains it. theoretically, only one term in the put call parity equation (risk free bond) can be determined based on the level of rates/strike price. the other three terms could move either way for parity to hold.
klinko88: perhaps your lower bound for option value holds for ITM/ATM strikes only? if an option is deep OTM and volatility is 0, option exercise wont happen and hence value = 0.
I eliminated volatility for simplicity, but the logic would still apply in theory for deep OTM. Say current price is 100 and deep OTM strike is 150. You would just need an ungodly rise in the interest rate to see the impacts. For deep OTM w/ 0 volatility where IR is only raised slightly, it would still impact the option pricing model in isolation, it’s just that the 0 volatility is going to multiply it away. But I suppose theoretical option pricing models are just that.. theoretical. In reality, interest rate sensitivity (Rho) is rarely what’s impacting an options price. Volatility is still king.
 
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