Monte Carlo Pricing of American Options Using Nonparametric Regression

This paper provides an introduction to Monte Carlo algorithms for pricing American options written on multiple assets, with special emphasis on methods that can be applied in a multi-dimensional setting. Simulated paths can be used to estimate by nonparametric regression the continuation value of the option or the optimal exercise policy and the value functions can then be computed by backward induction. The flexibility of nonparametric regression allows to obtain accurate price estimates with remarkable speed. For illustrative purposes we price one- and two-dimensional American options.Option pricing, American options, Monte Carlo, nonparametric regression

Pricing Higher-Dimensional American Options Using The Stochastic Grid Method

This paper considers the problem of pricing options with early-exercise features whose payo depends on several sources of uncertainty. We propose a stochastic grid method for estimating the upper and lower bound values of high-dimensional American options. The method is a hybrid of the least squares method of Longsta and Schwartz (2001) [22], the stochastic mesh method of Broadie and Glasserman (2004) [11], and stratified state aggregation along the pay-off method of Barraquand and Martineau (1995) [3]. Numerical results are given for single asset Bermudan options, Bermudan max options, Bermudan options on the arithmetic mean of a collection of stocks

Numerical techniques for the American put

This dissertation considers an American put option written on a single underlying which does not pay dividends, for which no closed form solution exists. As a conse- quence, numerical techniques have been developed to estimate the value of the Amer- ican put option. These include analytical approximations, tree or lattice methods, ¯nite di®erence methods, Monte Carlo simulation and integral representations. We ¯rst present the mathematical descriptions underlying these numerical techniques. We then provide an examination of a selection of algorithms from each technique, including implementation details, possible enhancements and a description of the convergence behaviour. Finally, we compare the estimates and the execution times of each of the algorithms considered

The Usefulness of Funds Flow Statements: An Empirical Study of Hong Kong Banks' Loan Officers' Use of Published Company Accounts

Funds flow statements were part of the published accounts of most companies in most jurisdictions in the last two decades. In the USA and a few other countries, they have been replaced by cash flow statements. Before other countries, including the UK, follow the US lead, it is important to gather and assess evidence on the usefulness of the funds statement to see if the arguments for its replacement by the cash flow statement are well founded. In essence, the usefulness of the funds flow statement is a matter of its ability to enable its readers to make better, or possibly faster, judgments about a firm's changes in financial position than they would make in the absence of that statement. The research reported in this thesis addresses the usefulness of the funds statement to a group of users especially concerned with changes in the financial position of companies with whom members of the group do business. Banks employ loan officers and credit analysts to vet applications for new loans, and this group of people is therefore likely to appreciate information useful to them in assessing the ability of applicants to meet their actual and prospective financial obligations. Such a group based in Hong Kong would be exposed to accounts prepared under all kinds of different national formats and should not be unduly fixated on the format of any one nation. Such assumptions were the basis of the research. A factorial ANOVA research design was used with 116 Hong Kong bank loan officers in 15 sets to see if the provision of funds flow statements and cash flow statements in a variety of formats improved their speed or accuracy in answering simple calculation-based or judgment-based questions concerning the accounts. Order effects were controlled by shuffling question order. Accounts difficulty effects were controlled by providing the accounts in two matched sets of equivalent processing difficulty. Subject selection effects were controlled through random assignments of subjects to accounts sets. It was found that funds statements marginally improved accuracy but greatly increased processing time. Cash flow statements performed no better than funds flow statements in either respect. An information load explanation is discussed for these results

Computational Methods for Pricing and Hedging Derivatives

In this thesis, we propose three new computational methods to price financial derivatives and construct hedging strategies under several underlying asset price dynamics. First, we introduce a method to price and hedge European basket options under two displaced processes with jumps, which are capable of accommodating negative skewness and excess kurtosis. The new approach uses Hermite polynomial expansion of a standard normal variable to match the first m moments of the standardised basket return. It consists of Black-and-Scholes type formulae and its improvement on the existing methods is twofold: we consider more realistic asset price dynamics and we allow more flexible specifications for the basket. Additionally, we propose two methods for pricing and hedging American options: one quasi-analytic and one numerical method. The first approach aims to increase the accuracy of almost any existing quasi-analytic method for American options under the geometric Brownian motion dynamics. The new method relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches. An extensive scenario-based study shows that the new method improves the existing pricing and hedging formulae, for various maturity ranges, and, in particular, for long-maturity options where the existing methods perform worst. The second method combines Monte Carlo simulation with weighted least squares regressions to estimate the continuation value of American-style derivatives, in a similar framework to the one of the least squares Monte Carlo method proposed by Longstaff and Schwartz. We justify the introduction of the weighted least squares regressions by numerically and theoretically demonstrating that the regression estimators in the least squares Monte Carlo method are not the best linear unbiased estimators (BLUE) since there is evidence of heteroscedasticity in the regression errors. We find that the new method considerably reduces the upward bias in pricing that affects the least squares Monte Carlo algorithm. Finally, the superiority of our new two approaches for American options are also illustrated over real financial data by considering S&P 100 options and LEAPS®, traded from 15 February 2012 to 10 December 2014

Accountants\u27 index. Thirty-second supplement, January-December 1983, volume 2: M-Z

https://egrove.olemiss.edu/aicpa_accind/1042/thumbnail.jp

Accountants\u27 index. Thirty-second supplement, January-December 1983, volume 1: A-L

https://egrove.olemiss.edu/aicpa_accind/1041/thumbnail.jp

Accountants\u27 index. Twenty-eighth supplement, January-December 1979, volume 2: M-Z

https://egrove.olemiss.edu/aicpa_accind/1034/thumbnail.jp