Question

A stock priced at $61 has three-month calls and puts with an exercise price of $55 available. The calls have a premium of $5.28, and the puts cost $0.56. The risk-free rate is 1.1%. If the put options are mispriced, what is the profit per option assuming no transaction costs?

Answer 1

The Profit per option = $1.431

Step-by-step explanation:

Given that:

Current stock price S = $61

Exercise Strike price X = $55

Value of call option C = $5.28

Puts Costs = $0.56

risk-free rate = (1.1% × 3)/12

risk - free rate = 0.275%

If the put options are mispriced, what is the profit per option assuming no transaction costs

Present value of the strike price
`X = (X)/((1+r))`

`X = (55)/((1+(0.275)/(100)))`

`X = (55)/((1+0.00275))`

`X = (55)/((1.00275))`

X = $54.849

The formula that hold for the put option can be expressed as:

P = Present value of the strike price X + C - S

P = $(54.849 + 5.28 - 61)

P = $60.129 - $61

P = - $0.871

Thus, the put option = - $0.871

This implies that the Put option is out of cash since it is negative.

Now, The Profit per option = put costs - (- put option)

The Profit per option = 0.56 - ( - 0.871)

The Profit per option = $1.431