It is the days after the Supreme Court rules tariffs are illegal. Markets are rallying.

SPX = 6000

K = 5900

t = 3 months (0.25)

r = 4.5%

Implied Volatility = 25%

The value of the call option is closest to:

Question

It is the days after the Supreme Court rules tariffs are illegal. Markets are rallying.

SPX = 6000

K  = 5900

t = 3 months (0.25)

r = 4.5%

Implied Volatility = 25%

The value of the call option is closest to:

BlackTom AI · Accepted Answer

The question presents a Black-Scholes style call option pricing setup and asks for the option value given: S = 6000, K = 5900, T = 0.25 years, r = 4.5%, implied vol σ = 25%.

First, compute the key Black–Scholes components. The forward-related factors include: 
- ln(S/K) = ln(6000/5900) = ln(1.016949) ≈ 0.0168.
- The drift term under risk-neutral pricing is (r + 0.5 σ^2) T. Here, σ^2 = 0.25^2 = 0.0625, so 0.5 σ^2 = 0.03125. Then r + 0.5 σ^2 = 0.045 + 0.03125 = 0.07625. Multiplying by T = 0.25 gives ≈ 0.01906.
- The numerator for d1 is then ln(S/K) + (r + 0.5 σ^2) T ≈ 0.0168 + 0.01906 ≈ 0.03586.
- The denominator for d1 is σ√T = 0.25 × √0.25 = 0.25 × 0.5 = 0.125.
- Therefore d1 ≈ 0.03586 / 0.125 ≈ 0.287. 
- Then d2 = d1 − σ√T = 0.287 − 0.125 ≈ 0.162.

Next, look up standard normal probabilities (or approximate):
- N(d1) ≈ N(0.287) ≈ 0.613.
- N(d2) ≈ N(0.162) ≈ 0.564.

Compute the option value using the Black–Scholes formula for a European call:
C = S N(d1) − K e^{−rT} N(d2).
- rT = 0.045 × 0.25 = 0.01125, so e^{−rT} ≈ e^{−0.01125} ≈ 0.9888.
- K e^{−rT} ≈ 5900 × 0.9888 ≈ 5837.5.
- S N(d1) ≈ 6000 × 0.613 ≈ 3678.
- (K e^{−rT}) N(d2) ≈ 5837.5 × 0.564 ≈ 3290–3292.

Finally, C ≈ 3678 − 3292 ≈ 386. That places the call price in the mid-380s, around 385–386.

About the answer options: the provided data shows an answer of 385 but does not list any other choices. In a typical multiple-choice setup, you’d compare this computed value to the closest option. Since there are no alternative options shown here, the best-supported result from the calculation is approximately 385–386. If options were present, you’d select the one closest to this computed value.

In summary, the Black–Scholes valuation with the given inputs yields a call price around 385–386, which aligns with the given answer of 385. The key sources of approximation come from the normal CDF values for d1 and d2 and the small rounding in the exponential term; minor rounding differences could shift the value by a unit or two.

fin_412_120258_251367 Mid-term Test 2

It is the days after the Supreme Court rules tariffs are illegal. Markets are rallying. SPX = 6000 K = 5900 t = 3 months (0.25) r = 4.5% Implied Volatility = 25% The value of the call option is closest to:

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