Chapter 5: Q16I (page 514)
a. A butterfly spread is the purchase of one call at exercise price X 1, the sale of two calls at exercise price X 2 , and the purchase of one call at exercise price X 3 . X 1 is less than X 2 , and X 2 is less than X 3 by equal amounts, and all calls have the same expiration date. Graph the payoff diagram to this strategy.
b. A vertical combination is the purchase of a call with exercise price X 2 and a put with exercise price X 1, with X 2 greater than X 1 . Graph the payoff to this strategy.
Short Answer
As below.
Step by step solution
Calculation of butterfly spread ‘a’
Position | ST < X1 | X1< ST < X2 | X2< ST < X3 | X3< ST |
Long call (X1) | 0 | ST - X1 | ST - X1 | ST - X1 |
Short call (X2) | 0 | 0 | -2(ST - X2) | -2(ST - X2) |
Long call (X3) | 0 | 0 | 0 | ST - X3 |
Total | 0 | ST - X1 | 2X2– X1 – S | (X2– X1) - (X3– X2)) = 0 |
Payoff diagram of ‘a’
Meaning of vertical strategy
In this strategy simultaneously sale and purchase of two opion is done which are of same type but with different strike price.
Calculation of vertical combination ‘b’
Position | ST < X1 | X1< ST < X2 | ST > X2 |
Long call (x2) | 0 | ST - X1 | ST - X2 |
Short call (x1) | X1 - ST | 0 | 0 |
Total | 0 | ST - X1 | ST - X2 |
Payoff diagram of ‘b’
Over 30 million students worldwide already upgrade their learning with Vaia!
