Option premium

Jas0128

New Member
An equity call option and an equity put option have identical exercise prices. Does this mean that they will have identical premiums? If yes, why will they have identical premiums? If not, why won’t they have identical premiums? Hoe does your answer change if the underlying stock pays a dividend? Please explain in detail.
 

ShaktiRathore

Well-Known Member
Subscriber
hi there,

please see that the call and put options do have the same maturities otherwise its obvious that put and call option of different maturities do have different premiums on them due to different values

we know that value of call and put is given by from a dealer perspective who is short on call and put,
call=premium1-max(S-K,0)..1
put=premium2-max(K-S,0)...2

for same underlying asset of price S and same exercise price,
from above equations 1 and 2 its clear that,

i) S>K= >call=premium1-S+K
put=premium2
=> call-put=premium1-S+K-premium2

ii) S<K= >call=premium1
put=premium2 -(K-S)
=> call-put=premium1-S+K-premium2


from put call parity, p+S=c+PV(K)=> c-p= S-PV(K)

from above , S-PV(K)=premium1-S+K-premium2 => premium1-premium2=2S-K-PV(K) which suggests the premiums are not equal. depending on maturity the values of call and put options premiums can differ.
if underlying stock pays dividend then replace S by Se^-dT and the answer should not change.
check if premiums of call & put are equal here: http://www.vfmdirect.com/info/option_calculator.html

thanks
 
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