Question 5

Consider the following information on put and call options on a stock:

Call price, c0=$5.40

Put price, p0=$8.60

Exercise price, X=$80

Days to option expiration =293

Current stock price, S0=$76.23

Risk-free rate, r=5 percent

A) Use put-call parity to calculate prices of the following

1. Synthetic call option

c0=p0+S0-X/(1+r)T

= $8.60+$76.23-$80/(1+0.05)293365

=7.9027

2. Synthetic put option

p0=c0-S0+X/(1+r)T

= $5.40-$76.23+$80/(1+0.05)293365

=6.0973

3. Synthetic bond

=p0+S0- c0

=$8.60+$76.23-$5.40

=$79.43

4. Synthetic underlying stock

=c0+X/(1+r)T-p0

= $5.40+$80/(1+0.05)293365-$8.60

=$73.73

2. For each of the synthetic instruments in part (a), identify any mispricing by comparing the actual price with the synthetic price.

3. Based on the mispricing in part (b), illustrate an arbitrage transaction using a synthetic call.