What is the Vanilla European Call option price for 1000 shares?

Quantitative Finance Level 2

This problem's question is: What is the Vanilla European Call option price for 1000 shares?

The parameters are: $\{\text{Vanilla},\text{European},\text{Call}\},\,\left\{\text{StrikePrice}\to 190\times 1000,\text{Expiration}\to \frac{91}{365}\right\},\,\{\text{InterestRate}\to 2.03\%,\text{Volatility}\to 28\%,\text{CurrentPrice}\to 195\times 1000,\text{Dividend}\to 1.5\%\}$

Round the answer to the nearest multiple of 500. Several web calculators were tried. Only one was in error and that one still gave the correct answer when rounded to the nearest multiple of 500. In fact, the error was less than 100. Using the call option value formula at the top of the Black-Scholes-Merton Brillliant Wiki page gave an answer matching the answer in the solution with about 12 initial digits the same and with the one mentioned exception, matched the rest to within a few cents so that rounding to the nearest even dollar would have hidden the differences. This could have been computer mathematics library differences or the difference between single and double precision arithmetic.

The answer is 13500.

1 solution

A Former Brilliant Member
Jun 12, 2019

Wolfram Mathematica 12:

$\text{FinancialDerivative}[\{\text{Vanilla},\text{European},\text{Call}\},\{\text{StrikePrice}\to 190\times 1000,\text{Expiration}\to \frac{91}{365}\},$

$\{\text{InterestRate}\to 2.03\%,\text{Volatility}\to 28\%,\text{CurrentPrice}\to 195\times 1000,\text{Dividend}\to 1.5\%\},\text{Rules}\}]$

$\{\text{Value}\to 13499.2488136309,$

$\text{Greeks}\to \{\text{Delta}\to 0.602296,\text{Gamma}\to 0.0000140752,\text{Rho}\to 25915.8,\text{Theta}\to -21328.2,\text{Vega}\to 37361.7\}\}$

Note well, the 1000 share lot quantity was built into the stock and strike prices so that the value of the call option is the total amount.

What is the Vanilla European Call option price for 1000 shares?

The answer is 13500.

1 solution

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