Workplace reviews and discussion: 凱基證券股份有限公司

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A doctor named Calvin, while attending a large charity concert, noticed that the organizers had issued a structured warrant based on an asset called “sports coins.” The doctor normally 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 care fund.

The core design of the warrant is as follows:

The warrant is a European call warrant with no dividends.

Warrant expiration: 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 contains 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 in his notebook the warrant’s first-order sensitivity to the price of sports coins (Delta), and considers how to dynamically hedge it to ensure that market volatility after the concert ends does 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