In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise, though methods now exist for solving this problem.
In general the approach is to divide time between now and the option's expiration into N discrete periods. At the specific time n, the model has a finite number of outcomes at time n + 1 such that every possible change in the state of the world between n and n + 1 is captured in a branch. This process is iterated until every possible path between n = 0 and n = N is mapped. Probabilities are then estimated for every n to n + 1 path. The outcomes and probabilities flow backwards through the tree until a fair value of the option today is calculated.
For equity and commodities the application is as follows. The first step is to trace the evolution of the option's key underlying variable(s), starting with today's spot price, such that this process is consistent with its volatility; log-normal Brownian motion with constant volatility is usually assumed. The next step is to value the option recursively: stepping backwards from the final time-step, where we have exercise value at each node; and applying risk neutral valuation at each earlier node, where option value is the probability-weighted present value of the up- and down-nodes in the later time-step.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC. A European bond option is an option to buy or sell a bond at a certain date in future for a predetermined price. An American bond option is an option to buy or sell a bond on or before a certain date in future for a predetermined price. Generally, one buys a call option on the bond if one believes that interest rates will fall, causing an increase in bond prices.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition. IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates.
This course gives an introduction to the modeling of interest rates and credit risk. Such models are used for the valuation of interest rate securities with and without credit risk, the management and
The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mat
The objective of this course is to provide a detailed coverage of the standard models for the valuation and hedging of derivatives products such as European options, American options, forward contract
This course gives you an easy introduction to interest rates and related contracts. These include the LIBOR, bonds, forward rate agreements, swaps, interest rate futures, caps, floors, and swaptions.
Nonparametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these issues in the de ...
In this thesis we present three closed form approximation methods for portfolio valuation and risk management.The first chapter is titled ``Kernel methods for portfolio valuation and risk management'', and is a joint work with Damir Filipovi'c (SFI and EP ...
EPFL2023
Throughout history, the pace of knowledge and information sharing has evolved into an unthinkable speed and media. At the end of the XVII century, in Europe, the ideas that would shape the "Age of Enlightenment" were slowly being developed in coffeehouses, ...