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2. Margrabe's formula - Wikipedia

   en.wikipedia.org/wiki/Margrabe's_formula

   Applying the Black-Scholes formula with these values as the appropriate inputs, e.g. initial asset value S 1 (0)/S 2 (0), interest rate q 2, volatility σ, etc., gives us the price of the option under numeraire pricing. Since the resulting option price is in units of S 2, multiplying through by S 2 (0) will undo our change of numeraire, and ...

3. Black–Scholes model - Wikipedia

   en.wikipedia.org/wiki/Black–Scholes_model

   [12] [13] [14] Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model, and coined the term "Black–Scholes options pricing model". The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other ...

4. Black model - Wikipedia

   en.wikipedia.org/wiki/Black_model

   The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, interest rate cap and floors, and swaptions. It was first presented in a paper written by Fischer Black in 1976.

5. Black–Scholes equation - Wikipedia

   en.wikipedia.org/wiki/Black–Scholes_equation

   where (,) is the price of the option as a function of stock price S and time t, r is the risk-free interest rate, and is the volatility of the stock. The key financial insight behind the equation is that, under the model assumption of a frictionless market , one can perfectly hedge the option by buying and selling the underlying asset in just ...

6. Monte Carlo methods for option pricing - Wikipedia

   en.wikipedia.org/wiki/Monte_Carlo_methods_for...

   Here the price of the option is its discounted expected value; see risk neutrality and rational pricing. The technique applied then, is (1) to generate a large number of possible, but random , price paths for the underlying (or underlyings) via simulation , and (2) to then calculate the associated exercise value (i.e. "payoff") of the option ...

7. Black's approximation - Wikipedia

   en.wikipedia.org/wiki/Black's_approximation

   In finance, Black's approximation is an approximate method for computing the value of an American call option on a stock paying a single dividend. It was described by Fischer Black in 1975. [1] The Black–Scholes formula (hereinafter, "BS Formula") provides an explicit equation for the value of a call option on a non-dividend paying stock. In ...

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9. Finite difference methods for option pricing - Wikipedia

   en.wikipedia.org/wiki/Finite_difference_methods...

   In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations. The discrete difference equations may then be solved iteratively to calculate a price for the option. [4]