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| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | 5x 5x 5x 5x 7x 7x 5x 2x | import { standardNormalCdf } from "../utils/MathUtils.js";
/**
* Vanilla European option.
* The value of a European option and it's greeks can be calculated analytically using the Black-Scholes model (https://www.jstor.org/stable/1831029).
* This model was extended by Merton (https://www.jstor.org/stable/3003143) to allow for the inclusion of a continuous dividend yield.
*/
function blackScholesMerton(type, S, K, t, vol, r, q) {
const isCall = type === "call" ? 1 : -1;
const d1 =
(Math.log(S / K) + (r - q + vol ** 2 / 2) * t) / (vol * Math.sqrt(t));
const d2 =
(Math.log(S / K) + (r - q - vol ** 2 / 2) * t) / (vol * Math.sqrt(t));
return (
isCall * S * Math.exp(-q * t) * standardNormalCdf(isCall * d1) +
-isCall * K * Math.exp(-r * t) * standardNormalCdf(isCall * d2)
);
}
function price(option) {
const [S, K, t, vol, r, q] = [
option.initialSpotPrice,
option.strikePrice,
option.timeToMaturity,
option.volatility,
option.riskFreeRate,
option.dividendYield,
];
if (
option.style === "european" ||
(option.style === "american" && option.type === "call" && q === 0)
) {
return blackScholesMerton(option.type, S, K, t, vol, r, q);
}
return undefined; // There is no known analytical solution
}
export { price };
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