Workplace reviews and discussion: 國泰金控_國泰金融控股股份有限公司

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A doctor named Calvin noticed, during a large charity concert, that the organizer had issued a structured warrant on an asset called “sports coins.” The doctor usually studies financial engineering. During a break at the concert, sitting in the audience, he used a notebook and ballpoint pen to derive the warrant’s theoretical value and hedging parameters, and planned to donate a fixed proportion of the warrant’s future returns to a rural healthcare fund.

The warrant’s core design is as follows:

The warrant is a European call warrant with no dividends.

Warrant expiration date 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 has a “donation clause”:

If the warrant is in the money at expiration, the warrant holder must immediately donate 10% of the warrant’s intrinsic value at expiration. However, the 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 expiration, and therefore expresses the warrant’s expiration 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, to ensure that market fluctuations after the concert ends do not affect the final amount he can donate.

Which of the following 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