Sources
Help build the largest human-edited directory on the web.
Submit a site - Become an editor
Wikipedia. Licensed under the GNU Free Documentation License.
Are you an expert in this subject? Join the discussion and share your knowledge at Wikipedia.org.
Black model
From Wikipedia, the free encyclopedia
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 bond options, interest rate caps / floors, and swaptions. It was first presented in a paper written by Fischer Black in 1976.
Black's model can be generalized into a class of models known as log-normal forward models, also referred to as LIBOR Market Model.
Contents |
The Black formula is similar to the Black-Scholes formula for valuing stock options except that the spot price of the underlying is replaced by the forward price.
The Black formula for a call option on an underlying strike at K, expiring T years in the future is
- c = e − rT * [FN(d1) − KN(d2)]
where
- r is the risk-free interest rate
- F is the current forward price of the underlying for the option maturity
- σ is the volatility of the forward price.
- and N(.) is the standard cumulative Normal distribution function.
The put price is
- p = e − rT * [KN( − d2) − FN( − d1)]
The derivation of the pricing formulas in the model follows that of the Black-Scholes model almost exactly. The assumption that the spot price follows a log-normal process is replaced by the assumption that the forward price at maturity of the option is log-normally distributed. From there the derivation is identical and so the final formula is the same except that the spot price is replaced by the forward - the forward price represents the undiscounted expected future value.
- Options on Futures: quantnotes.com
- 'Greeks' Calculator using the Black model, Razvan Pascalau, Univ. of Alabama
- Black, Fischer (1976). The pricing of commodity contracts, Journal of Financial Economics, 3, 167-179.
- Garman, Mark B. and Steven W. Kohlhagen (1983). Foreign currency option values, Journal of International Money and Finance, 2, 231-237.
|
|
|
|---|---|
| Derivative (finance) | |
| Options |
Terms: Strike price · Expiration · Open interest · Pin risk Vanilla options: Option styles · Call · Put · Warrants · Fixed income · Employee stock option · FX Exotic options: Asian · Lookback · Barrier · Binary · Swaption · Mountain range Options strategies: Covered call · Naked put · Collar · Straddle · Strangle · Butterfly Options spreads: Bull spread · Bear spread · Calendar spread · Vertical spread · Debit spread · Credit spread Valuation of options: Moneyness · Option time value · Put-call parity · Black-Scholes · Black · Binomial · Simulation |
| Swaps | |
| Other derivatives | |