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Sagot :
Solution :
[tex]\text{Short forward = buy a put + short a call on the same stock}[/tex] with the same exercise price.
X = exercise price = 50
1). Position to be taken :
-- buy 10 numbers of Put options with strike price of $ 50 per unit.
--- short (sell) 10 numbers of Call option with strike price of $ 50 per unit.
2). Cost of synthetic short position = [tex]$10 \times (P-C)$[/tex],
where, P = price of 1 put ption
C = price of 1 call option
The Call - Put parity equation :
[tex]$\frac{C+X}{(1+r)^t}=S_0+P$[/tex]
Here, C = Call premium
X = strike price of call and Put
r = annual rate of interest
t = time in years
[tex]$S_0$[/tex] = initial price of underlying
P = Put premium
Therefore,
[tex]$P-C=PV(X)-S_0=\frac{X}{(1+r)^t}-S_0$[/tex]
Here, t = 1, [tex]S_0[/tex] = 48, X = 50
So the cost of the position is given as : [tex]$\frac{50}{(1+r)} -48$[/tex]
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