One what basis the pricing model can be differentiated for particular trade pricing. For exapmle why PDE or Binomial tree or MC or Analytical method will be consider for pricing any trade. Question may be sound little vague but trying to understand on the broader level. Thanks for the help.

  • $\begingroup$ Binomial trees and monte carlo methods are often used when no closed form solution for pricing a derivative exists or the closed form solution is too complicated. A partial differential equation, such as the Black-scholes equation is sometimes used to place restrictions on the no-arbitrage price of an asset. A stochastic differential equation models how the price of a security evolves over time. Financial economics is a very broad subject so you should be more specific about what you want to know. $\endgroup$ – nathanesau Jul 7 '15 at 6:10
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    $\begingroup$ Your question is a bit vague, but generally we use an analytical formula if there is such a formula. Unfortunately, most of the time we don't have it, but we might still use an analytical approximation formula. If there is no analytical approximation or you believe the approximation is insufficient, you should use one of the numerical methods. Monte-Carlo is simple but slow to converge. It's good for high-dimensional simulation but probably not the best way to simulate early exercise such as American option. Binomial tree would be a better alternative. $\endgroup$ – HelloWorld Jul 7 '15 at 7:56

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