Question

A stock is selling at $40, a 3-month put at $50 is selling for $11, a 3-month call at $50 is selling for $1, and the risk-free rate is 6%.How much, if anything, can be made on an arbitrage?

Answer 1

$0.745

Step-by-step explanation:

GIven that

Current stock price
`S_o` = $40

strike price X = $50

time to expiry of option = 3 - month

put price option
`P _o` = $11

call price option
`C_o` = $1

and the risk-free rate r = 6%

The amount that can be made on the arbitrage can be evaluated as a function of the Put-call parity.

i.e For parity ;

`C_o + (X * e^(-rt) ) = P_o + S_o`

`1 + (50 * e^(-(0.06 * 0.25) ) = 11 + 40`

`1 + (50 * 0.9851 ) = 51`

`1 + (49.255 ) = 51`

50.255 = 51

the difference in both values above illustrates that there is no parity taking place and the arbitrage estimation here = 51 - 50.255 = $0.745