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# Tools for working with financial options

Tools for working with financial options

AUTHORS: - Brian Manion, 2013: initial version

`sage.finance.option.``black_scholes`(spot_price, strike_price, time_to_maturity, risk_free_rate, vol, opt_type)

  Calculates call/put price of European style options using Black-Scholes formula. See [S] for one of many standard references for this formula.

  INPUT:

  - `spot_price` – The current underlying asset price
  - `strike_price` – The strike of the option
  - `time_to_maturity` – The # of years until expiration
  - `risk_free_rate` – The risk-free interest-rate
  - `vol` – The volatility
  - `opt_type` – string; The type of option, either `'put'` for put option or `'call'` for call option

  OUTPUT:

  > The price of an option with the given parameters.

  EXAMPLES:

      sage: finance.black_scholes(42, 40, 0.5, 0.1, 0.2, 'call')       # abs tol 1e-10
      4.759422392871532
      sage: finance.black_scholes(42, 40, 0.5, 0.1, 0.2, 'put')        # abs tol 1e-10
      0.8085993729000958
      sage: finance.black_scholes(100, 95, 0.25, 0.1, 0.5, 'call')     # abs tol 1e-10
      13.695272738608132
      sage: finance.black_scholes(100, 95, 0.25, 0.1, 0.5, 'put')      # abs tol 1e-10
      6.349714381299734
      sage: finance.black_scholes(527.07, 520, 0.424563772, 0.0236734,0.15297,'whichever makes me more money')
      Traceback (most recent call last):
      ...
      ValueError: 'whichever makes me more money' is not a valid string

  REFERENCES:

  [S] | Shreve, S. Stochastic Calculus for Finance II: Continuous-Time Models. New York: Springer, 2004

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