dstefan
03-22-2008, 01:20 PM
Chapter 1, Problem 16:
The bid and ask prices for a six months European call option with strike 40 on a non--dividend--paying stock with spot price 42 are $5 and $5.5, respectively. The bid and ask prices for a six months European put option with strike 40 on the same underlying asset are $2.75 and $3.25, respectively. Assume that the risk free rate is equal to 0. Is there an arbitrage opportunity present?
Solution:
For r=0, the Put-Call parity becomes P + S - C = K, which in this case can be written as C-P = 2.
Thus, an arbitrage occurs if C-P can be ``bought" for less than $2 (i.e., if a call option is bought and a put option is sold for less than $2), or if C-P can be ``sold" for more than $2 (i.e., if a call option can be sold and a put option can be bought for more than $2).
From the bid and ask prices, we find that the call can be bought for $5.5 and the put can be sold for $2.75. Therefore, C-P can be ``bought" for $2.75, which is more than $2, so no risk-free profit can be achieved this way.
Also, a call can be sold for $5 and a put can be bought for $3.25. Therefore, C-P can be ``sold" for $1.75, which is less than $2. Again, no risk-free profit can be achieved.
The bid and ask prices for a six months European call option with strike 40 on a non--dividend--paying stock with spot price 42 are $5 and $5.5, respectively. The bid and ask prices for a six months European put option with strike 40 on the same underlying asset are $2.75 and $3.25, respectively. Assume that the risk free rate is equal to 0. Is there an arbitrage opportunity present?
Solution:
For r=0, the Put-Call parity becomes P + S - C = K, which in this case can be written as C-P = 2.
Thus, an arbitrage occurs if C-P can be ``bought" for less than $2 (i.e., if a call option is bought and a put option is sold for less than $2), or if C-P can be ``sold" for more than $2 (i.e., if a call option can be sold and a put option can be bought for more than $2).
From the bid and ask prices, we find that the call can be bought for $5.5 and the put can be sold for $2.75. Therefore, C-P can be ``bought" for $2.75, which is more than $2, so no risk-free profit can be achieved this way.
Also, a call can be sold for $5 and a put can be bought for $3.25. Therefore, C-P can be ``sold" for $1.75, which is less than $2. Again, no risk-free profit can be achieved.