Question

You are looking at options on Hedwig Corporation with 11 months until expiration and a strike price of $110. The risk free rate for 6 months is 2% and for 11 months is 3% (annualized with continuous compounding). You expect the firm to pay one dividend over the next 11 months: $4 per share, 6 months from today. The current stock price is $116.77. The price of the call option is $9.37 and the put option is $2.08. Use put-call parity to find the arbitrage trade given these prices and show the profit for each contract.

Answer 1

Put call parity formula with dividend

C+(D*e-r*t+X*e-r*t) = P+ S

Where C= call premium= $9.37, P = put premium = $2.08, S= stock price = $116.77

X= strike price = $110, D= dividend =$4 per share,

risk free rate for 6 month =2%,

risk free rate for 11 months =3%,

t= time to expiry = 6 months

As per Put call parity

Value of first portfolio = C+(D*e-r*t+X*e-r*t)

=9.37+(4*2.718^(-2%*0.5)+110*2.718^(-3%*11/12))

Value of first portfolio = $120.35

Value of second portfolio = 2.08 + 116.77 = $118.85

First portfolio is overpriced hence should be sold while second portfolio is under priced hence should be bought