Merge pull request #5 from samueledelia/3-autodiff-bs-greeks

Computed greeks leveraging automatic differentation

.gitignore

@@ -27,6 +27,10 @@ jaxfin/examples/requirements.txt
 test_report.xml
 test_report.html
 
+## Coverage results
+.coverage
+htmlcov/
+
 # Version file
 jaxfin.VERSION
 version.txt

jaxfin/price_engine/black/__init__.py

@@ -1,4 +1,6 @@
 """Option price computed with the Black'76 model"""
-from jaxfin.price_engine.black.black_model import black_price
+from jaxfin.price_engine.black.black_model import black_price, delta_black, gamma_black
 
 future_option_price = black_price
+future_option_delta = delta_black
+future_option_gamma = gamma_black

jaxfin/price_engine/black/black_model.py

@@ -3,6 +3,7 @@
 """
 import jax
 import jax.numpy as jnp
+from jax import grad, vmap
 
 from ..common import compute_undiscounted_call_prices
 from ..utils import cast_arrays
@@ -13,7 +14,7 @@ def black_price(
     strikes: jax.Array,
     expires: jax.Array,
     vols: jax.Array,
-    discount_rates: jax.Array = None,
+    discount_rates: jax.Array,
     dividend_rates: jax.Array = None,
     are_calls: jax.Array = None,
     dtype: jnp.dtype = None,
@@ -37,9 +38,6 @@ def black_price(
         [spots, strikes, expires, vols], dtype
     )
 
-    if discount_rates is None:
-        discount_rates = jnp.zeros(shape, dtype=dtype)
-
     if dividend_rates is None:
         dividend_rates = jnp.zeros(shape, dtype=dtype)
 
@@ -55,4 +53,118 @@ def black_price(
 
     undiscounted_forwards = forwards - strikes
     undiscouted_puts = undiscounted_calls - undiscounted_forwards
-    return discount_factors * jnp.where(are_calls, undiscounted_calls, undiscouted_puts)
+    return jnp.exp((-1 * discount_rates) * expires) * jnp.where(
+        are_calls, undiscounted_calls, undiscouted_puts
+    )
+
+
+def _delta_black(
+    spots: jax.Array,
+    strikes: jax.Array,
+    expires: jax.Array,
+    vols: jax.Array,
+    discount_rates: jax.Array,
+    dividend_rates: jax.Array,
+    are_calls: jax.Array = None,
+    dtype: jnp.dtype = None,
+) -> jax.Array:
+    """
+    Compute the option deltas for european options using the Black '76 model.
+
+    :param spots: (jax.Array): Array of current asset prices.
+    :param strikes: (jax.Array): Array of option strike prices.
+    :param expires: (jax.Array): Array of option expiration times.
+    :param vols: (jax.Array): Array of option volatility values.
+    :param discount_rates: (jax.Array): Array of risk-free interest rates. Defaults to None.
+    :param dividend_rates: (jax.Array): Array of dividend rates. Defaults to None.
+    :param are_calls: (jax.Array): Array of booleans indicating whether options are calls (True) or puts (False).
+    :param dtype: (jnp.dtype): Data type of the output. Defaults to None.
+    :return: (jax.Array): Array of computed option deltas.
+    """
+    return grad(black_price, argnums=0)(
+        spots, strikes, expires, vols, discount_rates, dividend_rates, are_calls, dtype
+    )
+
+
+def _gamma_black(
+    spots: jax.Array,
+    strikes: jax.Array,
+    expires: jax.Array,
+    vols: jax.Array,
+    discount_rates: jax.Array,
+    dividend_rates: jax.Array,
+    are_calls: jax.Array = None,
+    dtype: jnp.dtype = None,
+) -> jax.Array:
+    """
+    Compute the option gammas for european options using the Black '76 model.
+
+    :param spots: (jax.Array): Array of current asset prices.
+    :param strikes: (jax.Array): Array of option strike prices.
+    :param expires: (jax.Array): Array of option expiration times.
+    :param vols: (jax.Array): Array of option volatility values.
+    :param discount_rates: (jax.Array): Array of risk-free interest rates. Defaults to None.
+    :param dividend_rates: (jax.Array): Array of dividend rates. Defaults to None.
+    :param are_calls: (jax.Array): Array of booleans indicating whether options are calls (True) or puts (False).
+    :param dtype: (jnp.dtype): Data type of the output. Defaults to None.
+    :return: (jax.Array): Array of computed option gammas.
+    """
+    return grad(grad(black_price, argnums=0), argnums=0)(
+        spots, strikes, expires, vols, discount_rates, dividend_rates, are_calls, dtype
+    )
+
+
+def delta_black(
+    spots: jax.Array,
+    strikes: jax.Array,
+    expires: jax.Array,
+    vols: jax.Array,
+    discount_rates: jax.Array,
+    dividend_rates: jax.Array = None,
+    are_calls: jax.Array = None,
+    dtype: jnp.dtype = None,
+) -> jax.Array:
+    """
+    Compute the option deltas for european options using the Black '76 model. (vectorized)
+
+    :param spots: (jax.Array): Array of current asset prices.
+    :param strikes: (jax.Array): Array of option strike prices.
+    :param expires: (jax.Array): Array of option expiration times.
+    :param vols: (jax.Array): Array of option volatility values.
+    :param discount_rates: (jax.Array): Array of risk-free interest rates. Defaults to None.
+    :param dividend_rates: (jax.Array): Array of dividend rates. Defaults to None.
+    :param are_calls: (jax.Array): Array of booleans indicating whether options are calls (True) or puts (False).
+    :param dtype: (jnp.dtype): Data type of the output. Defaults to None.
+    :return: (jax.Array): Array of computed option deltas.
+    """
+    return vmap(_delta_black, in_axes=(0, 0, 0, 0, 0, 0, 0, None))(
+        spots, strikes, expires, vols, discount_rates, dividend_rates, are_calls, dtype
+    )
+
+
+def gamma_black(
+    spots: jax.Array,
+    strikes: jax.Array,
+    expires: jax.Array,
+    vols: jax.Array,
+    discount_rates: jax.Array,
+    dividend_rates: jax.Array = None,
+    are_calls: jax.Array = None,
+    dtype: jnp.dtype = None,
+) -> jax.Array:
+    """
+    Compute the option gammas for european options using the Black '76 model. (vectorized)
+
+    :param spots: (jax.Array): Array of current asset prices.
+    :param strikes: (jax.Array): Array of option strike prices.
+    :param expires: (jax.Array): Array of option expiration times.
+    :param vols: (jax.Array): Array of option volatility values.
+    :param discount_rates: (jax.Array): Array of risk-free interest rates. Defaults to None.
+    :param dividend_rates: (jax.Array): Array of dividend rates. Defaults to None.
+    :param are_calls: (jax.Array): Array of booleans indicating whether options are calls (True) or puts (False).
+    :param dtype: (jnp.dtype): Data type of the output. Defaults to None.
+    :return: (jax.Array): Array of computed option gammas.
+    """
+    return vmap(_gamma_black, in_axes=(0, 0, 0, 0, 0, 0, 0, None))(
+        spots, strikes, expires, vols, discount_rates, dividend_rates, are_calls, dtype
+    )

jaxfin/price_engine/black_scholes/__init__.py

@@ -3,8 +3,14 @@
     bs_price,
     delta_vanilla,
     gamma_vanilla,
+    rho_vanilla,
+    theta_vanilla,
+    vega_vanilla,
 )
 
 european_price = bs_price
 delta_european = delta_vanilla
 gamma_european = gamma_vanilla
+theta_european = theta_vanilla
+rho_european = rho_vanilla
+vega_european = vega_vanilla