Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

You have been asked to create a synthetic short position in a forward contract that permits you to sell 10 units of the underlying one year from now at a price of $50 per unit. (1) Describe the positions you need to take in call and put options to achieve the synthetic short forward position. (2) If the underlying is selling for $48 today (i.e. So = 48), what is the cost of your synthetic short position?

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]

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.