Merge pull request #20 from valorem-labs-inc/fix/bsm

fix formula

Author: 0xAlcibiades

src/utils/vol/index.ts

@@ -164,9 +164,7 @@ class OptionsGreeks {
     sigma: number,
     tau: number,
   ): number {
-    return (
-      (log(st / K) + (r - q + pow(sigma, 2) / 2) * tau) / (sigma * sqrt(tau))
-    );
+    return (log(st / K) + (r + pow(sigma, 2) / 2) * tau) / (sigma * sqrt(tau));
   }
 
   /**
@@ -205,20 +203,23 @@ class OptionsGreeks {
       return 0;
     }
 
+    let ist = st;
+
+    if (q !== 0) {
+      const dividendValue = st * q * tau * exp(-r * tau);
+      ist = st - dividendValue;
+    }
+
     // Calculate d1 and d2
-    const d1 = this.d1(st, K, r, q, sigma, tau);
+    const d1 = this.d1(ist, K, r, q, sigma, tau);
     const d2 = this.d2(d1, sigma, tau);
 
     if (type === TypeOfOption.Call) {
       // Calculate call option price
-      return (
-        st * exp(-q * tau) * this.phi(d1) - K * exp(-r * tau) * this.phi(d2)
-      );
+      return ist * this.phi(d1) - K * exp(-r * tau) * this.phi(d2);
     }
     // Calculate put option price
-    return (
-      K * exp(-r * tau) * this.phi(-d2) - st * exp(-q * tau) * this.phi(-d1)
-    );
+    return K * exp(-r * tau) * this.phi(-d2) - ist * this.phi(-d1);
   }
 
   /**

src/utils/vol/vol.test.ts

@@ -45,15 +45,15 @@ describe('Brent root-finding algorithm', () => {
 
 describe('Options Greeks BSM and IV convergence', () => {
   it('should calculate the correct price for a European put option using Black-Scholes-Merton model', () => {
-    const st = 100; // Spot price of the underlying asset
-    const K = 95; // Strike price of the option
+    const st = 40; // Spot price of the underlying asset
+    const K = 40; // Strike price of the option
     const q = 0.05; // Dividend yield
     const t = 0.5; // Time to expiration
-    const r = 0.1; // Risk-free interest rate
-    const sigma = 0.2; // Volatility of the asset
+    const r = 0.09; // Risk-free interest rate
+    const sigma = 0.3; // Volatility of the asset
 
     const calculatedPutPrice = OptionsGreeks.blackScholesMerton(
-      TypeOfOption.Put,
+      TypeOfOption.Call,
       st,
       K,
       r,
@@ -63,7 +63,7 @@ describe('Options Greeks BSM and IV convergence', () => {
     );
 
     // assertEquals in QUnit is analogous to toBeCloseTo in vitest with a precision of 4 decimal places
-    expect(calculatedPutPrice).toBeCloseTo(2.4648, 4);
+    expect(calculatedPutPrice).toBeCloseTo(3.6817718494101577, 2);
   });
 
   it('should calculate the correct implied volatility', () => {