A barrel of oil is currently valued at $54.00. Its ATMF is $54.50. Given the following available
Question:
A barrel of oil is currently valued at $54.00. Its ATMF is $54.50. Given the following available derivatives, form the requested synthetic positions. Specify the traded positions you will take for each synthetic position. Also, for each synthetic position, calculate the (i) trading cost/premium, (ii) Delta, (iii) Gamma and (iv) Vega.
Derivative | Contract Price | Premium | Delta (for long position) | Gamma (for long position) | Vega (for long position) |
Forward | $54.50 | NA | 1.0000 | 0.0000 | 0.0000 |
54.00 | NA | 1.0000 | 0.0000 | 0.0000 | |
Call option | 54.50 | $3.04 | 0.5281 | 0.0522 | 0.1153 |
54.00 | 3.28 | 0.5540 | 0.0518 | 0.1145 | |
Put option | 54.50 | 3.04 | -0.4719 | 0.0522 | 0.1153 |
54.00 | 2.79 | -0.4460 | 0.0518 | 0.1145 |
1. Synthetic short forward
2. Synthetic long call
3. You notice that a traded call option on oil with a $54.50 strike price has a $2.87 premium. Given the premium you calculate for the call option in b., is there an option arbitrage opportunity? If so, what traded positions would you take to profit from this opportunity? If not, explain why not?
Fundamentals of corporate finance
ISBN: 978-0470876442
2nd Edition
Authors: Robert Parrino, David S. Kidwell, Thomas W. Bates