KCE stock is currently selling for $51.13 per share in the market. Six-month American put options on KCE with a strike price of $55 are available, and the risk-free rate of interest is 3.66%. Calculate the lower bound for the KCE American put options.
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A. B. C.C
To calculate the lower bound for the KCE American put options, we can use the concept of put-call parity. Put-call parity states that the difference between the price of a European call option and a European put option with the same strike price, underlying asset, and expiration date is equal to the difference between the current price of the underlying asset and the present value of the strike price.
The put-call parity formula is as follows:
C - P = S - PV(X)
Where: C = Price of the European call option P = Price of the European put option S = Current price of the underlying asset PV(X) = Present value of the strike price
In this case, we are dealing with American put options, but since they can be exercised early, their value must be at least as much as their European counterparts. Therefore, the lower bound for the American put options will be the same as the lower bound for the European put options.
Now let's plug in the given values into the put-call parity formula:
C - P = S - PV(X)
We are given: S = $51.13 (current price of KCE stock) X = $55 (strike price of the put options) r = 3.66% (risk-free rate of interest)
We need to calculate the present value of the strike price, PV(X).
PV(X) = X / (1 + r)^t
Where t is the time to expiration in years. In this case, the time to expiration is six months, which is equal to 0.5 years.
PV(X) = $55 / (1 + 0.0366)^0.5
PV(X) = $55 / (1.0366)^0.5
PV(X) ≈ $53.637
Now, let's substitute the values back into the put-call parity formula:
C - P = S - PV(X) P = C - S + PV(X)
We are given that the current price of the stock is $51.13, and the strike price is $55. The risk-free rate of interest is 3.66%.
P = C - S + PV(X) P = 0 - $51.13 + $53.637
P ≈ -$51.13 + $53.637 P ≈ $2.507
Since the put option price cannot be negative, the lower bound for the KCE American put options is $0. Therefore, none of the answer choices provided (A, B, C) are correct.
Please note that the calculation assumes no dividends or transaction costs and uses simplified assumptions. In practice, options pricing can be more complex and involve additional factors.