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As above, these methods can solve derivative pricing problems that have, in general, the same level of complexity as those problems solved by tree approaches, [1] but, given their relative complexity, are usually employed only when other approaches are inappropriate; an example here, being changing interest rates and / or time linked dividend policy.
More generally though, simulation is employed for path dependent exotic derivatives, such as Asian options. In other cases, the source of uncertainty may be at a remove. For example, for bond options [3] the underlying is a bond, but the source of uncertainty is the annualized interest rate (i.e. the short rate).
Binomial Lattice for equity, with CRR formulae Tree for an bond option returning the OAS (black vs red): the short rate is the top value; the development of the bond value shows pull-to-par clearly . In quantitative finance, a lattice model [1] is a numerical approach to the valuation of derivatives in situations requiring a discrete time model.
The first exit time (FET) is the minimum between: (i) the time in the future when the spot is expected to exit a barrier zone before maturity, and (ii) maturity, if the spot has not hit any of the barrier levels up to maturity.
Equity basket derivatives are futures, options or swaps where the underlying is a non-index basket of shares. They have similar characteristics to equity index derivatives, but are always traded OTC (over the counter, i.e. between established institutional investors), [ dubious – discuss ] as the basket definition is not standardized in the ...
The Greeks" measure the sensitivity of the value of a derivative product or a financial portfolio to changes in parameter values while holding the other parameters fixed. They are partial derivatives of the price with respect to the parameter values. One Greek, "gamma" (as well as others not listed here) is a partial derivative of another Greek ...
In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the parameters of the model.
Starting from a constant volatility approach, assume that the derivative's underlying asset price follows a standard model for geometric Brownian motion: = + where is the constant drift (i.e. expected return) of the security price , is the constant volatility, and is a standard Wiener process with zero mean and unit rate of variance.