Workplace reviews and discussion: 元大金融控股股份有限公司(元大金控) (元大證券) (元大銀行)

Circle, little circle, circle, come have tea

A doctor named Calvin, while attending a large charity concert, noticed that the organizer had issued a structured warrant linked to an asset called “Sports Coin.” The doctor regularly studies financial engineering. During a break at the concert, he sat in the audience and used a notebook and ballpoint pen to derive the warrant’s theoretical value and hedging parameters, planning to donate a fixed proportion of the warrant’s future proceeds to a rural healthcare 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 Coin): 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, the donation amount does not affect the underlying asset’s price or market dynamics; 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 Coin (Delta) in his notebook and considers how to dynamically hedge it, to ensure that market fluctuations after the concert ends do 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