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A doctor named Calvin noticed, while attending a large charity concert, that the organizer had issued a structured warrant based on an asset called “sports coins.” The doctor normally researches financial engineering. During a break in 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 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 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 includes 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 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 of 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
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HR is very unprofessional; I was burned several times from the interview process through to leaving the company.
The promotion system is opaque. It has a traditional Taiwanese corporate culture where connections can be used to place people in positions, and even interns can be parachuted in.