Question

Suppose that a call option with a strike price of $48 expires in one year and has a current market price of ​$5.15. The market price of the underlying stock is ​$46.24​, and the​ risk-free rate is 1​%. Use​ put-call parity to calculate the price of a put option on the same underlying stock with a strike of ​$48 and an expiration of one year.

1. The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is

Answer 1

The price of put option by using following put-call parity equation

P = C –S0 + X* e^ (-r*t)

Where,

C = price of the call option = $5.15

P= price of the put option =?

S0 = spot price = $46.24

Strike price X= $48

The risk-free rate r= 1%

Time period t = 1 year

Now putting all the values in the put-call parity equation

P = $5.15 - $46.24 + $48 * e^ (-0.01*1)

Or P = $5.15 - $46.24 + $47.5224 = $6.4324

The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is $6.4324