Question

1. Shares in Home Depot sell for $110. A call option with one year to maturity and a $110 strike price sells for $15. A put with the same terms sells for $5.

What is the risk free rate? 10%

What is the intrinsic and time value of the call?

I=0 T=$15

The answers are there but i need the steps on how to solve in order to prepare for an exam

Answer 1

What is the risk free rate?

By using following put-call parity equation

P – PV of X = C –S0

Where,

C = price of the call option = $15

P= price of the put option =$5

S0 = spot price or current share price = $110

Strike price X= $110

PV of X = X / (1+r) ^t

The risk-free rate r =?

Time period t= 1 year

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

$5 - $110/ (1+r) ^1 = $15 - $110

Or $110/ (1+r) = $5 - $15 + $110 = $100

Or (1+r) = $110/100 = 1.10

Or r = 0.10 or 10%

What is the intrinsic and time value of the call?

Intrinsic value of the call = strike price of the call option – current share price

= $110 - $110 = $0

Time value of the call = price of call option = $15