Explanation:
In the Black-Scholes-Merton framework, both the call and put formulas use the same inputs: the current underlying price (S₀), the strike price (K), time to expiration (T), the risk-free rate (r), and volatility (σ). What differs is the payoff being priced, which leads to different replicating positions. A call can be replicated by a long position in the underlying combined with borrowing (a short position in a risk-free bond), while a put can be replicated by a short position in the underlying combined with lending (a long position in a risk-free zero-coupon bond). Therefore, the put formula is associated with a short underlying position and a long bond position; it does not assume nonconstant volatility or a higher risk-free rate.
(Book 4, Module 61.2, LO 61.d)
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Question 61
The Black-Scholes-Merton put option formula differs from the Black-Scholes-Merton call option formula in that the put option formula assumes:
A
a long position in the underlying security.
B
a short position in the underlying security and a long position in the bond.
C
a nonconstant return volatility of the underlying security price.
D
a long position in the bond and a higher risk-free rate.
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