The Basic Models of Approximations
For most widely used financial models, there exist many kinds of assets which cannot be priced in closed-form, except for example for European options written on a single underlying asset. Other options can also computed in closed-form like lookback options (see ), but generally only for the standard model (i.e. the stock price process is a geometric Brownian motion). Thus efficient numerical procedures are needed, especially for options with path-dependent payoffs and other exotic options. In fact, these approximations are made for risk-neutral processes (it is assumed that the risk-neutral probability is a priori given or its choice is deduced from statistical analysis). Major approaches include binomial (or lattice) methods, Monte Carlo simulation, algorithms for solving partial differential equations, integral equations or variational inequalities.
KeywordsInterest Rate Stock Price Option Price Bond Price Geometric Brownian Motion
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