Workplace reviews and discussion: 台新綜合證券股份有限公司

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A doctor named Calvin noticed, while attending a large charity concert, that the organizer had issued a structured warrant linked to an asset called “sports coins.” The doctor regularly studies financial engineering. During a break in the concert, he sat in the audience with a notebook and ballpoint pen, deriving the warrant’s theoretical value and hedging parameters, and planned to donate a fixed proportion of the warrant’s future returns to a rural medical fund.

The warrant’s core design is as follows:

The warrant is a European call warrant with no dividends.

Warrant maturity: T = 1 year

Current price of the underlying asset (sports coins): S0 = 120

Strike price: K = 110

Risk-free interest rate (continuously compounded): r = 3%

Annualized volatility: σ = 25%

Warrant conversion ratio: α = 0.2

In addition, the warrant includes a “donation clause”:

If the warrant is in the money at maturity, the warrant holder must immediately donate 10% of the warrant’s intrinsic value at maturity. However, this donation amount does not affect the underlying asset’s price or market dynamics, and a credit card may be used.

The doctor assumes that this donation clause can be treated as a linear reduction in the cash flow at maturity, and therefore expresses the warrant’s maturity payoff as:

Payoff = 0.9 × α × max(ST − K, 0)

Under the risk-neutral probability measure, the doctor writes the following pricing equation:

C = 0.9 × α [ S0 N(d1) − K e^(−rT) N(d2) ]

where

d1 = [ ln(S0 / K) + ( r + 0.5 σ^2 ) T ] / ( σ √T )

d2 = d1 − σ √T

After completing the pricing, the doctor further calculates the warrant’s first-order sensitivity to the price of sports coins (Delta) in his notebook and considers how to dynamically hedge it, ensuring that market fluctuations after the concert ends will not affect the final amount he can donate.

Which of the following options is closest to “the combination of the warrant’s theoretical price and Delta”?

A. Warrant price approximately 1.85, Delta approximately 0.09

B. Warrant price approximately 2.40, Delta approximately 0.12

C. Warrant price approximately 3.10, Delta approximately 0.18

D. Warrant price approximately 3.95, Delta approximately 0.22