Feynman-Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations (PDEs) and stochastic processes. Suppose follows the stochastic process and if is defined as then satisfies , . The theo...
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...