The SINDY index is currently at I = 10,100.European options on SINDY have a strike price K =$10,000 and mature in T = 90 days.The risk-free interest rate r = 5 percent per year.SINDY has a dividend yield $\delta$ = 2 percent per year and an implied volatility of $\sigma$= 20 percent per year.Then the Black-Scholes-Merton model gives a call option price of:

Question

Quizplus · Accepted Answer

Using the Black-Scholes-Merton model, we have:
d1 = (ln(S/K) + (r - δ + 0.5σ²)T) / (σ√T) = (ln(10100/10000) + (0.05 - 0.02 + 0.5×0.20²)×(90/365)) / (0.20√(90/365)) = 0.7657
d2 = d1 - σ√T = 0.5865
N(d1) = 0.7770
N(d2) = 0.7197
C = S×exp(-δT)×N(d1) - K×exp(-rT)×N(d2) = 10100×exp(-0.02×(90/365))×0.7770 - 10000×exp(-0.05×(90/365))×0.7197 = $487.03
Therefore, the answer is C: $487.03.

The SINDY Index Is Currently at I = 10,100 δ\deltaδ = 2 Percent Per Year and an Implied Volatility Of on SINDY

The SINDY Index Is Currently at I = 10,100 $\delta$ = 2 Percent Per Year and an Implied Volatility Of on SINDY