不是很理解

问题如下：

A trader observes that a 1-year European call option is undervalued in the market. She decides to buy the call option and hedge it with replicating trades. The hedge ratio is h. The call values and stock values are described in the table below.

Within a single-period binomial framework, the trader should:

选项：

A.A.buy h = (c⁺ – c^–)/(S⁺ – S^–) units of the underlying and borrow the present value of (–hS^– + c^–).

B.B.buy h = (c⁺ + c^–)/(S⁺ + S^–) units of the underlying and borrow the present value of (–hS^– + c^–).

C.C.short sell h = (c⁺ – c^–)/(S⁺ – S^–) units of the underlying and lend the present value of (–hS^– + c^–).

解释：

A Correct because c = hS + PV(–hS^– +c^–) or, equivalently, c = hS + PV(–hS⁺ + c⁺). In words, going long a call option is equal to owning h shares of stock partially financed, where the financed amount is PV(–hS^– + c^–), or using the per period rate, (–hS^– + c^–)/(1 + r). Where at Time 1, there are only two possible outcomes and two resulting values of the under- lying, S⁺ (up occurs) and S⁻ (down occurs).

The hedge ratio is: h = (c⁺– c^–)/(S⁺ – S^–) ≥0

A simple rule for remembering this formula is that the hedge ratio is the value of the call if the underlying goes up minus the value of the call if the underlying goes down divided by the value of the underlying if it goes up minus the value of the underlying if it goes down. Further, Recall that by design, h is selected such that –hS^– + c^– = –hS⁺ + c⁺ or h = (c⁺ – c^–)/(S⁺ – S^–). Therefore, a call option can be replicated with (going long) the underlying and financing. Specifically, the call option is equivalent to a leveraged position in the underlying.

B Incorrect because the hedge ratio (h) is inaccurate. The accurate hedge ratio is h = (c⁺– c^–)/(S⁺ – S^–) ≥0, not h = (c⁺ + c^–)/(S⁺ + S^–).

A simple rule for remembering this formula is that the hedge ratio is the value of the call if the underlying goes up minus the value of the call if the underlying goes down divided by the value of the underlying if it goes up minus the value of the underlying if it goes down.

C Incorrect because short selling h units of the underlying is incorrect. Instead, c = hS + PV(–hS^– +c^–) or, equivalently, c = hS + PV(–hS⁺ + c⁺). In other words, long a call option is equal to owning h shares of stock partially financed, where the financed amount is PV(–hS^– + c^–), or using the per period rate, (–hS^– + c^–)/(1 + r).