An American call option on a non-dividend-paying stock is currently trading in the CBOT market. The price of the underlying stock is $36, the option strike price is $30, and the option expiration date is in three months. The risk free interest rate is 8%
a. Calculate the upper and lower bounds for the price of this American call option --> Calculated as max (So - Ke^ -rT, 0)
b. Explain the arbitrage opportunities presented to an arbitrageur when this American call option is trading at $37 and when it is trading at $4. Calculate the risk-free profits that can be earned by an arbitrageur in both cases. (Note: calculate the risk-free profit also for both scenarios at maturity i.e. when ST is greater than $30 and when ST is lower than $30).
a.
S0: the current price of the underlying asset= $36
K: the exercised (strike) price =$30
T: the time to expiration of option =3 months
r: the risk-free interest rate= 8%
Upper bounds for this American call option, C <=S0
<=36
Lower bounds for this American call option, : C >= S0 - Ke -rT
>= 36-30*e -0.08*(3/12)
>=6.59
b.
When ST> $30,
When C=$37
C+ Ke -rT =37+30*e -0.08*(3/12) =66.4
When C=$4
C+ Ke -rT =4+30*e -0.08*(3/12) =33.40
Arbitrage opportunity exists with a risk-free profit of $33
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