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Black Model Black’s vanilla option pricing model can be applied to a wide range of vanilla European options such as caps/floors, European swaptions, bond options, bond futures options and interest rate (IR) futures options. Black’s option pricing model, which is in a closed-form formula, can be applied to vanilla European type options under the Black-Scholes framework. Black’s option pricing formula has been widely applied in fixed income derivative market for years. A vanilla European call option can be defined by its payoff at maturity as where X is an underlying rate, T is the payoff reset time and K is the strike price. Accordingly, the payoff for a vanilla European put option is The matured payoffs is paid at a settlement time T' which is greater than or equal to T . Under the Black-Scholes framework, the key assumption is that, in the risk-neutral measure with respect to the zero bond price matured at T' , T is log-normally distributed with a single parameter X σ , the volatility of the underlying rate X . Black’s vanilla option pricing model can be applied to pricing a variety of instruments including caps/floors, European swaptions, bond options, bond futures options and IR futures options. In the case of caps/floors and European swaptions1, X is the forward term rate and forward swap rate, respectively. For European bond options, the rate X represents the bond price. For European bond futures options and European IR futures options, X stands for bond futures price and Euro-Dollar futures price, respectively. Black Model |