mafipy.function module¶
function (mafipy.function)¶
Black Model¶
Basics¶
black_payers_swaption_value(init_swap_rate, ...) |
calculates value of payer’s swaptions under black model. |
black_receivers_swaption_value(...) |
calculates value of receiver’s swaptions under black model. |
black_payers_swaption_value_fprime_by_strike(...) |
First derivative of value of payer’s swaption with respect to strike under black model. |
black_payers_swaption_value_fhess_by_strike(...) |
Second derivative of value of payer’s swaption with respect to strike under black model. |
black_payers_swaption_value_third_by_strike(...) |
Third derivative of value of payer’s swaption with respect to strike under black model. |
Greeks¶
black_payers_swaption_delta(init_swap_rate, ...) |
calculates delta of payer’s swaptions under black model. |
black_payers_swaption_vega(init_swap_rate, ...) |
calculates vega of payer’s swaption under black model. |
black_payers_swaption_volga(init_swap_rate, ...) |
calculates volga of payer’s swaption under black model. |
black_payers_swaption_vega_fprime_by_strike(...) |
calculates derivative of vega with respect to strike under black model. |
Distribution¶
black_swaption_cdf(init_swap_rate, ...) |
calculates value of c.d.f. of black swaption. |
black_swaption_pdf(init_swap_rate, ...) |
calculates value of p.d.f. of black swaption. |
Black Scholes Model¶
Miscs¶
func_d1(underlying, strike, rate, maturity, vol) |
calculate \(d_{1}\) in black scholes formula. |
func_d2(underlying, strike, rate, maturity, vol) |
calculate \(d_{2}\) in black scholes formula. |
d_fprime_by_strike(underlying, strike, rate, ...) |
derivative of \(d_{1}\) with respect to \(K\) |
d_fhess_by_strike(underlying, strike, rate, ...) |
second derivative of \(d_{i}\ (i = 1, 2)\) with respect to \(K\), |
Basics¶
black_scholes_call_value(underlying, strike, ...) |
calculate call value in the case of today is not zero. |
black_scholes_put_value(underlying, strike, ...) |
evaluates value of put option using put-call parity so that |
black_scholes_call_value_fprime_by_strike(...) |
First derivative of value of call option with respect to strike under black scholes model. |
black_scholes_call_value_fhess_by_strike(...) |
Second derivative of value of call option with respect to strike under black scholes model. |
black_scholes_call_value_third_by_strike(...) |
Third derivative of value of call option with respect to strike under black scholes model. |
Greeks¶
black_scholes_call_delta(underlying, strike, ...) |
calculates black scholes delta. |
black_scholes_call_gamma(underlying, strike, ...) |
calculates black scholes gamma. |
black_scholes_call_vega(underlying, strike, ...) |
calculates black scholes vega. |
black_scholes_call_volga(underlying, strike, ...) |
black_scholes_call_volg |
black_scholes_call_theta(underlying, strike, ...) |
calculates black scholes theta. |
black_scholes_call_rho(underlying, strike, ...) |
calculates black scholes rho. |
black_scholes_call_vega_fprime_by_strike(...) |
calculates derivative of black scholes vega with respect to strike. |
Distribution¶
black_scholes_cdf(underlying, strike, rate, ...) |
calculates value of c.d.f. of black scholes model. |
black_scholes_pdf(underlying, strike, rate, ...) |
calculates value of p.d.f. of black scholes model. |
Local Volatility model¶
To be displayed.
Payoff functions¶
payoff_call(underlying, strike[, gearing]) |
Payoff of call option. |
payoff_call_fprime(underlying, strike[, gearing]) |
derivative of payoff of call option with respect to underlying. |
payoff_put(underlying, strike[, gearing]) |
Payoff of put option. |
payoff_put_fprime(underlying, strike[, gearing]) |
derivative of payoff of call option with respect to underlying. |
payoff_bull_spread(underlying, lower_strike, ...) |
Buy call option with lower_strike \(K_{\mathrm{lower}}\) and sell put option with upper_strike \(K_{\mathrm{upper}}\). |
payoff_bull_spread_fprime(underlying, ...[, ...]) |
calculate value of derivative of payoff of bull spread option |
payoff_straddle(underlying, strike[, gearing]) |
Buy call option and put option at same time with same strike. |
payoff_strangle(underlying, lower_strike, ...) |
Buy call option and put option at same time with different strike. |
payoff_butterfly_spread(underlying, ...[, ...]) |
Butterfly option consists of following options: |
payoff_risk_reversal(underlying, ...[, gearing]) |
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SABR model¶
Basics¶
sabr_payers_swaption_value(init_swap_rate, ...) |
calculate european payer’s swaption value. |
sabr_receivers_swaption_value(...) |
calculate european reciever’s swaption value. |
sabr_implied_vol_hagan(underlying, strike, ...) |
calculate implied volatility under SABR model. |
sabr_atm_implied_vol_hagan(underlying, ...) |
calculate implied volatility under SABR model at the money. |
Greeks¶
sabr_implied_vol_hagan_fprime_by_strike(...) |
first derivative of Hagan’s SABR implied volatility formula |
sabr_implied_vol_hagan_fhess_by_strike(...) |
second derivative of Hagan’s SABR implied volatility formula |
sabr_implied_vol_hagan_fprime_by_underlying(...) |
first derivative of Hagan’s SABR implied volatility formula |
sabr_implied_vol_hagan_fhess_by_underlying(...) |
second derivative of Hagan’s SABR implied volatility formula |
sabr_payers_swaption_delta(init_swap_rate, ...) |
calculate payer’s swaption delta under SABR model. |