Answer:
a) the rate of return on this position held until the expiration of the options is r = 0.05638
b) $5.52
c) C - P = $24.748
d)
- C - P = $4.748
- C - P = $24.748
- C - P = $44.748
- C - P = $64.748
Step-by-step explanation:
a) Assume that, we are buying the stock, selling the 815-strike call , and buying the 815 strike put, the rate of return on this position held until the expiration of the options can be determined as follows:
solving for the cost first; we have:
(- $800 + $75 - $45) = $770
After 1-year ; the compounded rate of return (r) can be expressed as:


Thus, the rate of return on this position held until the expiration of the options is r = 0.0564
b)
What is the arbitrage implied by your answer to (a)?
The return rate on this position shows more interest than the risk-free interest rate. However, there is need to borrow money at 5% (0.05) in order to purchase a large amount of the rate of return position of (a), resulting into a sure return of 0.64%. In essence, $770 is being borrowed from the bank to buy and secure one position; Therefore , after 1-year; the bank is being owed:
$
= $809.48
Thus, the arbitrage implied by the answer to (a) is:
$815 - $809.48 = $5.52
c) . What difference between the call and put prices would eliminate arbitrage? To eliminate arbitrage; it is crucial that the call and put prices should be on hold. This implies that:
C - P =

C - P =

C - P =

C - P = $24.748
d). What difference between the call and put prices eliminates arbitrage for strike prices of $780, $800, $820, and $840?
C - P =

where
is the spike prices
when
= $780
C - P =
C - P = $4.748
when
= $800
C - P =

C - P = $24.748
when
= $820
C - P =

C - P = $44.748
when
= $840
C - P =

C - P = $64.748