Question

On Jan 19 2021, SPY (the ETF) closed at 378.64. The short-term interest rate is 0.25%. Assume no dividend payments before the February expiration. The minimum value of the February 2021, K = 375, What was the call option, on Jan 19 2021?

Answer 1

To calculate the value of the call option on Jan 19, 2021, we can use the Black-Scholes formula:

C = S*N(d1) - Ke^(-rt)*N(d2)

where:

C is the call option value
S is the spot price of the underlying asset (SPY ETF), which is 378.64
K is the strike price of the option, which is 375
r is the risk-free interest rate, which is 0.25%
t is the time to expiration of the option in years, which is (31 - 19)/365 = 0.0548
d1 = [ln(S/K) + (r + σ^2/2)t] / (σsqrt(t))
d2 = d1 - σ*sqrt(t)
N() is the cumulative standard normal distribution function
To calculate d1 and d2, we also need to know the volatility of the underlying asset. Let's assume the volatility is 20%.

Plugging in the values, we get:

d1 = [ln(378.64/375) + (0.0025 + 0.2^2/2)0.0548] / (0.2sqrt(0.0548)) = 0.5718
d2 = 0.5718 - 0.2*sqrt(0.0548) = 0.3981

Using a standard normal distribution table or calculator, we can find that N(d1) = 0.7152 and N(d2) = 0.6515.

Therefore, the value of the call option on Jan 19, 2021, is:

C = 378.640.7152 - 375e^(-0.0025*0.0548)*0.6515 = $7.71

So the call option with a strike price of $375 and an expiration date in February 2021 was worth $7.71 on Jan 19, 2021.

the call option with a strike price of $375