has a net present value greater than zero (or any other value). See further under Corporate finance. In valuing an option on equity, the simulation generates several thousand possible (but random) price paths for the underlying share, with the associated exercise value (i.e. "payoff") of the option for each path. These payoffs are then averaged and discounted to today, and this result is the value of the option today. Note that whereas equity options are more commonly valued using other pricing models such as lattice based models, for path dependent exotic derivatives – such as Asian options – simulation is the valuation method most commonly employed; see Monte Carlo methods for option pricing for discussion as to further – and more complex – option modelling. To value fixed income instruments and interest rate derivatives the underlying source of uncertainty which is simulated is the short rate – the annualized interest rate at which an entity can borrow money for a given period of time; see Short-rate model. For example, for bonds, and bond options, under each possible evolution of interest rates we observe a different yield curve and a different resultant bond price. To determine the bond value, these bond prices are then averaged; to value the bond option, as for equity options, the corresponding exercise values are averaged and present valued. A similar approach is used in valuing swaps, swaptions, and convertible bonds. As for equity, for path dependent interest rate derivatives – such as CMOs – simulation is the primary technique employed; (Note that "to create realistic interest rate simulations" Multi-factor short-rate models are sometimes employed.) Monte Carlo Methods are used for portfolio evaluation. Here, for each sample, the correlated behaviour of the factors impacting the component instruments is simulated over time, the resultant value of each instrument is calculated, and the portfolio value is then observed. As for corporate finance, above, the various portfolio values are then combined in a histogram, and the statistical characteristics of the portfolio are observed, and the portfolio assessed as required. A similar approach is used in calculating value at risk, a better known application of simulation to portfolios. Structurers similarly use simulation to estimate the likely payout - and possibility of losses - of their bespoke structured note or other structured product, comprising several component securities. Monte Carlo Methods are used for personal financial planning. For instance, by simulating the overall