Question

The interest rate is 3% per year compounded monthly. Deere stock is trading at $169. A European put option expiring in eight months has a strike price of $160 and is trading at a premium of p=$18.50. No dividend payment is expected. A dealer quotes the otherwise identical call option at $27.23 bid, $27.73 ask. How much arbitrage profit can one make based on this information?

My professor's solution is this:

Using put-call parity adjusted for a known dividend, by writing a put, shorting a share and lending the PV of the strike. From the t=0 column of our arbitrage table, we find the profit as the sum of the cash flows of these four transactions, -27.73+18.50+169-160.00/1.020175878=$2.93.

My question is how was the 1.020175878 calculated?

Answer 1

Interest rate = 3% per year compounded monthly

Monthly interest rate(i) = 0.03/12 = 0.0025

Maturity of options (t) = 8 months

Thus, Time value factor for given inputs:

(?+1) =

=(1+0.0025)

=1.020175878

In given equation in question, this factor used to calculate the present value of strike price.

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.