Q-Fin

A mathematical finance Python library

Time Value of Money

Bond Pricing

Option Pricing

Black-Scholes Pricing

Theoretical options pricing for non-dividend paying stocks is available via the BlackScholesCall and BlackScholesPut classes.

# 100 - initial asset price
# .3 - asset 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)

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.

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.

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.

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.

print('Call theta: ', euro_call.theta)
print('Put theta: ', euro_put.theta)

Call theta:  -6.35319039407325
Put theta:  -5.363140560324083

Futures Pricing