In finance, there are two major applications of the Monte Carlo simulation: -- Generating stochastic paths for interest rates, exchange rates, and stock prices; -- Numerical valuation of derivative instruments; consider the risk-neutral pricing equati...
To apply the theoretical models, let us first see how to use interest rate trees to price and calibrate. As mentioned in Review 5, markovian property of short rate models is needed to implement recombining lattice. Usually, a short rate model can be w...
This topic is mainly about modeling of short rate which plays a central role in the theory and practice because zero coupon bonds can be priced as and so could discount factor. Assume there is only one source of uncertainty represented by a Brownian m...
After reviewing Ito lemma and SDE, it is time to have a look at the standard market model which are forward contracts, future contracts, options on bond, interest rate caps, floors, collars and swaptions. Forward contracts and future contracts are sim...
蒙特卡罗方法在金融数学中有很重要的作用, 比如可以方便的处理与路径相关的金 融衍生品定价, 它的基本原理是生成随机数, 进而生成多个随机路径, 假设这些路 径具有相同的概率, 于是根...