chapter 21 Basic numerical procedures Flashcards
Risk-Neutral Valuation Principle
The risk-neutral valuation principle, explained in Chapters 13 and 15, assumes the world is risk neutral for valuation purposes. This involves assuming the expected return from all traded assets is the risk-free interest rate.
Discounting
Discounting is a calculation used in the risk-neutral valuation principle to value payoffs from derivatives. It involves calculating the expected values of payoffs and then discounting them at the risk-free interest rate.
Dividend-Paying Stock
When using the binomial model for a dividend-paying stock, the term “dividend” refers to the reduction in the stock price on the ex-dividend date.
Known Dividend Yield
A known dividend yield is an assumed continuous or discrete dividend yield for a stock. It can be used to value long-life stock options in the same way as options on a stock index.
Monte Carlo simulation
Monte Carlo simulation is an approach for valuing derivatives that uses random sampling of paths to obtain the expected payoff in a risk-neutral world.
Risk-neutral valuation
Risk-neutral valuation assumes that the world is risk-neutral, meaning that the expected return from all traded assets is the risk-free interest rate. This concept is used in Monte Carlo simulation to value derivatives.
Sample mean
The sample mean is calculated by taking the average of a set of sample values. In Monte Carlo simulation, the mean of the sample payoffs is calculated to estimate the expected payoff in a risk-neutral world.
Binomial Trees
Binomial trees assume stock price movements up or down in short time intervals, and are used to calculate derivative prices by working backward from the end of the tree. American options are valued by comparing immediate exercise value to the discounted expected value if held.
Monte Carlo Simulation
Monte Carlo simulation uses random sampling of paths in a risk-neutral world to estimate the expected payoff of a derivative, which is then discounted at the risk-free rate. It works forward from the beginning to the end of a derivative’s life and is efficient for complex European-style derivatives with multiple variables.
Finite Difference Methods
Finite difference methods convert differential equations to difference equations and work backward from the end of the life of a derivative to its beginning. The explicit method is similar to a trinomial tree, while the implicit method is more complex but more accurate.
Choosing a Valuation Method
The choice of valuation method depends on the derivative’s characteristics and the desired accuracy. Monte Carlo simulation works forward, is suitable for European-style derivatives, and becomes efficient with multiple variables. Tree approaches and finite difference methods work backward, can value American-style derivatives, but are less efficient with complex payoffs or multiple variables.
