We considered ATM options while calculating Put call parity of GBP straddle structure as shown in the figure.
This can only be applicable to European style of options as they will have to be exercised only at maturity unlike American options.
C = S + p - Xe-r (T- t)
= 1.5717 + 809.13 - Euler (1.5719*2.71828) - 0.02*(7)
= 806.2888
P = c - S + Xe-r (T- t)
= 801.40- 1.5717 + Euler (1.5719*2.71828) - 0.02*(7)
= 803.9611
Where,
S = Current Exchange Rate = 1.5717
X = Exercise price (strike) of option = 1.5719
C = Call Value = 801.40 as shown in the diagram
P = Put price = 809.13 as shown in the diagram
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: The straddle can't be a recommendation for all portfolios, we used it for computation purpose, 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.
