# Black-Scholes pricing of european-exercise options with term structure arguments

### Description

Price an option according to the famous Black-Scholes formula, with the
optional addition of a jump-to-default intensity and discrete dividends. Volatility
and rates may be provided as constants or as 2+ parameter functions with
first argument `T`

corresponding to maturity and second argument `t`

corresponding to
model date.

### Usage

1 2 3 4 5 6 7 | ```
black_scholes_on_term_structures(callput, S0, K, time, const_volatility = 0.5,
const_short_rate = 0, const_default_intensity = 0,
discount_factor_fcn = function(T, t, ...) { exp(-const_short_rate * (T -
t)) }, survival_probability_fcn = function(T, t, ...) {
exp(-const_default_intensity * (T - t)) },
variance_cumulation_fcn = function(T, t) { const_volatility^2 * (T - t)
}, dividends = NULL, borrow_cost = 0, dividend_rate = 0)
``` |

### Arguments

`callput` |
1 for calls, -1 for puts |

`S0` |
initial underlying price |

`K` |
strike |

`time` |
Time from |

`const_volatility` |
A constant to use for volatility in case |

`const_short_rate` |
A constant to use for the instantaneous interest rate in case |

`const_default_intensity` |
A constant to use for the instantaneous default intensity in case |

`discount_factor_fcn` |
A function for computing present values to
time |

`survival_probability_fcn` |
A function for probability of survival, with
arguments |

`variance_cumulation_fcn` |
A function for computing total stock variance
occurring during this timestep, with arguments |

`dividends` |
A |

`borrow_cost` |
A continuous rate for stock borrow costs |

`dividend_rate` |
A continuous rate for dividends and other cashflows such as foreign interest rates |

### Details

Any term structures will be converted to equivalent constant arguments by calling
them with the arguments `(time, 0)`

.

### See Also

Other Equity Independent Default Intensity: `american_implied_volatility`

,
`american`

, `blackscholes`

,
`equivalent_bs_vola_to_jump`

,
`equivalent_jump_vola_to_bs`

,
`implied_volatilities_with_rates_struct`

,
`implied_volatilities`

,
`implied_volatility_with_term_struct`

,
`implied_volatility`

Other European Options: `blackscholes`

,
`implied_volatilities_with_rates_struct`

,
`implied_volatilities`

,
`implied_volatility_with_term_struct`

,
`implied_volatility`

### Examples

1 2 3 4 5 6 7 8 9 10 |

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