It is easy to ascertain the optimal prices of calls during bull run with the help of delta and other option Greeks and does the same while ascertaining puts premiums during bear markets. But it would quite difficult when views remain on sideways and reduced volatility. In such cases, to decide the balance of call put options (it cannot be applied on American style options as they can be exercised on or before expiry), put call parity plays a crucial role.
Here the portfolio contains the option combination having the same expiration value with two different derivatives instruments of same underlying currency then they must have the same present value.
Else, arbitrager can go long on the undervalued portfolio and short the overvalued portfolio to make a risk free profit on expiration day.
Hence, considering the need to calculate the present value of the cash component using a suitable risk-free interest rate, we have calculated and illustrated the Put call parity of straddle:
We considered ATM options while calculating Put call parity of GBP straddle structure as shown in the figure.
C = S + p - Xe-r (T- t)
= 0.7425 + 597.90 - Euler (0.7426*2.71828) - 0.02*(7)
= 596.48
P = c - S + Xe-r (T- t)
= 566.86 - 0.7425 + Euler (0.7426*2.71828) - 0.02*(7)
= 567.99
Where,
S = Current Exchange Rate = 0.7425
X = Exercise price (strike) of option = 0.7426
C = Call Value = 566.86
P = Put price = 597.90
e = Euler's constant - approximately 2.71828 (exponential function on a financial calculator)
r = continuously compounded risk free interest rate = 2%
T-t = term to expiration measured in years = 7 days
T = Expiration date
t = Current value date
Note: Before jumping into a conclusion of above calculations, one has to be mindful of how the supply and demand impacts option prices and how all option values (at all the available strikes and expirations) on the same underlying security are related.
