Explanation:
A synthetic call option can be created by taking a long position in a stock, a long position in a put option, and a short position in a zero-coupon bond. This combination of positions replicates the payoff of a long position in a call option. The underlying principle behind this strategy is the put-call parity, which is a fundamental concept in options pricing. The put-call parity states that the price of a call option (c) plus the present value of the strike price (X) discounted at the risk-free rate (r) for the time to maturity (T) is equal to the price of the stock (S) plus the price of a put option (p). Mathematically, this is represented as . Rearranging this equation to solve for the price of a call option, we get . This equation shows that a call option can be synthetically created by taking a long position in a stock, a long position in a put option, and a short position in a zero-coupon bond. This strategy allows an investor to replicate the payoff of a call option without actually owning the option.
Choice A is incorrect. While a long position in a stock and shorting a put option can replicate the payoff of a call option, shorting a zero-coupon bond would not contribute to this synthetic strategy. Shorting the bond would create an obligation to pay at maturity, which is not characteristic of a call option's payoff.
Choice B is incorrect. This choice involves both long and short positions in options (call and put respectively), which does not replicate the payoff of just one call option. Additionally, shorting a zero-coupon bond again introduces an obligation that does not align with the desired payoff.
Choice C is incorrect. Shorting a stock and going long on both put options and zero-coupon bonds do not mimic the characteristics of being long on call options. In fact, this combination could potentially lead to unlimited losses if the stock price increases significantly – something that doesn't align with the limited downside nature of a call option's payoff.
No comments yet.
Q.761 Jacob Clarke is an investment manager at one of the largest investment banks in Canada. Clarke has a wide variety of investment options to invest in. However, he is interested in constructing the payoff of a synthetically created long position in call options. Which of the following positions should he take to create the payoff of a synthetic call option?
A
Long a stock, short a put option, and short a zero-coupon bond.
B
Long a call option, short a put option, and short a zero-coupon bond.
C
Short a stock, long a put option, and long a zero-coupon bond.
D
Long a stock, long a put option, and short a zero-coupon bond.