Simulation Pricing

QFin.egg-info/PKG-INFO

@@ -0,0 +1,127 @@
+Metadata-Version: 2.1
+Name: QFin
+Version: 0.0.11
+Summary: A Python package for mathematical finance.
+Home-page: UNKNOWN
+Author: Roman Paolucci
+Author-email: <[email protected]>
+License: MIT
+Description: # Q-Fin
+        A mathematical finance Python library
+
+        # Time Value of Money
+
+        # Bond Pricing
+
+        # Option Pricing
+
+        ### <a href="https://medium.com/swlh/deriving-the-black-scholes-model-5e518c65d0bc"> Black-Scholes Pricing</a>
+        Theoretical options pricing for non-dividend paying stocks is available via the BlackScholesCall and BlackScholesPut classes.
+
+        ```Python
+        # 100 - initial underlying asset price
+        # .3 - asset underlying volatility
+        # 100 - option strike price
+        # 1 - time to maturity (annum)
+        # .01 - risk free rate of interest
+        euro_call = BlackScholesCall(100, .3, 100, 1, .01)
+        euro_put = BlackScholesPut(100, .3, 100, 1, .01)
+        ```
+
+        ```Python
+        print('Call price: ', euro_call.price)
+        print('Put price: ', euro_put.price)
+        ```
+
+        ```
+        Call price:  12.361726191532611
+        Put price:  11.366709566449416
+        ```
+
+        ### Option Greeks
+        First-order and some second-order partial derivatives of the Black-Scholes pricing model are available.
+
+        #### Delta
+        First-order partial derivative with respect to the underlying asset price.
+        ```Python
+        print('Call delta: ', euro_call.delta)
+        print('Put delta: ', euro_put.delta)
+        ```
+        ```
+        Call delta:  0.5596176923702425
+        Put delta:  -0.4403823076297575
+        ```
+
+        #### Gamma
+        Second-order partial derivative with respect to the underlying asset price.
+        ```Python
+        print('Call gamma: ', euro_call.gamma)
+        print('Put gamma: ', euro_put.gamma)
+        ```
+        ```
+        Call gamma:  0.018653923079008084
+        Put gamma:  0.018653923079008084
+        ```
+
+        #### Vega
+        First-order partial derivative with respect to the underlying asset volatility.
+        ```Python
+        print('Call vega: ', euro_call.vega)
+        print('Put vega: ', euro_put.vega)
+        ```
+        ```
+        Call vega:  39.447933090788894
+        Put vega:  39.447933090788894
+        ```
+
+        #### Theta
+        First-order partial derivative with respect to the time to maturity.
+        ```Python
+        print('Call theta: ', euro_call.theta)
+        print('Put theta: ', euro_put.theta)
+        ```
+        ```
+        Call theta:  -6.35319039407325
+        Put theta:  -5.363140560324083
+        ```
+
+        # Simulation Pricing
+
+        ### <a href="https://medium.com/swlh/python-for-pricing-exotics-3a2bfab5ff66"> Exotic Options </a>
+        Simulation pricing for exotic options is available under the assumptions associated with Geometric Brownian motion.
+
+        #### Binary Options
+        ```Python
+        # 100 - strike price
+        # 50 - binary option payout
+        # 1000 - number of simulated price paths
+        # .01 - risk free rate of interest
+        # 100 - initial underlying asset price
+        # 0 - underlying asset drift (mu)
+        # .3 - underlying asset volatility 
+        # 1/52 - time steps (dt)
+        # 1 - time to maturity (annum)
+        binary_call = MonteCarloBinaryCall(100, 50, 1000, .01, 100, 0, .3, 1/52, 1)
+        binary_put = MonteCarloBinaryPut(100, 50, 1000, .01, 100, 0, .3, 1/52, 1)
+        ```
+
+        ```Python
+        print(binary_call.price)
+        print(binary_put.price)
+        ```
+
+        ```
+        22.42462873441866
+        27.869902820039087
+        ```
+        # Futures Pricing
+
+Keywords: python,finance
+Platform: UNKNOWN
+Classifier: Development Status :: 1 - Planning
+Classifier: Intended Audience :: Developers
+Classifier: Programming Language :: Python :: 3
+Classifier: Operating System :: Unix
+Classifier: Operating System :: MacOS :: MacOS X
+Classifier: Operating System :: Microsoft :: Windows
+Description-Content-Type: text/markdown

QFin.egg-info/SOURCES.txt

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+README.md
+setup.py
+QFin/__init__.py
+QFin/bonds.py
+QFin/futures.py
+QFin/options.py
+QFin/simulations.py
+QFin/tvm.py
+QFin.egg-info/PKG-INFO
+QFin.egg-info/SOURCES.txt
+QFin.egg-info/dependency_links.txt
+QFin.egg-info/requires.txt
+QFin.egg-info/top_level.txt

QFin.egg-info/dependency_links.txt

@@ -0,0 +1 @@
+

QFin.egg-info/requires.txt

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+scipy
+numpy

QFin.egg-info/top_level.txt

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+QFin

__init__.py → QFin/__init__.py

@@ -1,5 +1,5 @@
 import tvm.*
 import bonds.*
 import options.*
-import exotics.*
-import 
+import simulations.*
+import futures.*

simulations.py → QFin/simulations.py

@@ -80,3 +80,15 @@ def simulate_price(self, strike, payout, n, r, S, mu, sigma, dt, T):
 
     def __init__(self, strike, payout, n, r, S, mu, sigma, dt, T):
         self.price = self.simulate_price(strike, payout, n, r, S, mu, sigma, dt, T)
+
+
+class MonteCarloBarrierCall:
+
+    def __init__(self):
+        pass
+
+
+class MonteCarloBarrierPut:
+
+    def __init__(self):
+        pass

build/lib/QFin/__init__.py

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+import tvm.*
+import bonds.*
+import options.*
+import simulations.*
+import futures.*

build/lib/QFin/options.py

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+import math
+from scipy.stats import norm
+
+
+class BlackScholesCall:
+
+    def call_delta(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.cdf(x1)
+        return z1
+
+    def call_gamma(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.cdf(x1)
+        z2 = z1/(asset_price*asset_volatility*math.sqrt(time_to_expiration))
+        return z2
+
+    def call_vega(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.pdf(x1)
+        z2 = asset_price*z1*math.sqrt(time_to_expiration)
+        return z2
+
+    def call_theta(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        n1 = -((asset_price*asset_volatility*norm.pdf(x1))/(2*math.sqrt(time_to_expiration)))
+        n2 = -(risk_free_rate*strike_price*math.exp(-risk_free_rate*time_to_expiration)*norm.cdf((x1 - (asset_volatility*math.sqrt(time_to_expiration)))))
+        return (n1 + n2)
+
+    def call_price(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.cdf(x1)
+        z1 = z1*asset_price
+        x2 = math.log(asset_price/(strike_price)) - .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x2 = x2/(asset_volatility*(time_to_expiration**.5))
+        z2 = norm.cdf(x2)
+        z2 = b*strike_price*z2
+        return z1 - z2
+
+    def __init__(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        self.asset_price = asset_price
+        self.asset_volatility = asset_volatility
+        self.strike_price = strike_price
+        self.time_to_expiration = time_to_expiration
+        self.risk_free_rate = risk_free_rate
+        self.price = self.call_price(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.delta = self.call_delta(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.gamma = self.call_gamma(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.vega = self.call_vega(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.theta = self.call_theta(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+
+
+class BlackScholesPut:
+
+    def put_delta(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.cdf(x1)
+        return z1 - 1
+
+    def put_gamma(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.cdf(x1)
+        z2 = z1/(asset_price*asset_volatility*math.sqrt(time_to_expiration))
+        return z2
+
+    def put_vega(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.pdf(x1)
+        z2 = asset_price*z1*math.sqrt(time_to_expiration)
+        return z2
+
+    def put_theta(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        x1 = math.log(asset_price/(strike_price)) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        n1 = -((asset_price*asset_volatility*norm.pdf(x1))/(2*math.sqrt(time_to_expiration)))
+        n2 = (risk_free_rate*strike_price*math.exp(-risk_free_rate*time_to_expiration)*norm.cdf(-(x1 - (asset_volatility*math.sqrt(time_to_expiration)))))
+        return (n1 + n2)
+
+    def put_price(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        b = math.exp(-risk_free_rate*time_to_expiration)
+        x1 = math.log((asset_price)/strike_price) + .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x1 = x1/(asset_volatility*(time_to_expiration**.5))
+        z1 = norm.cdf(x1)
+        z1 = b*strike_price*z1
+        x2 = math.log((asset_price)/strike_price) - .5*(asset_volatility*asset_volatility)*time_to_expiration
+        x2 = x2/(asset_volatility*(time_to_expiration**.5))
+        z2 = norm.cdf(x2)
+        z2 = asset_price*z2
+        return z1 - z2
+
+    def __init__(
+        self, asset_price, asset_volatility, strike_price,
+        time_to_expiration, risk_free_rate
+            ):
+        self.asset_price = asset_price
+        self.asset_volatility = asset_volatility
+        self.strike_price = strike_price
+        self.time_to_expiration = time_to_expiration
+        self.risk_free_rate = risk_free_rate
+        self.price = self.put_price(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.delta = self.put_delta(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.gamma = self.put_gamma(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.vega = self.put_vega(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)
+        self.theta = self.put_theta(asset_price, asset_volatility, strike_price, time_to_expiration, risk_free_rate)