Pricing of American call options using regression and numerical integration

Consider the American basket call option in the case where there are N underlying assets, the number of possible exercise times prior to maturity is finite, and the vector of N asset prices is modeled using a Levy process. A numerical method based on regression and numerical integration is proposed to estimate the price of the American option. In the proposed method, we first express the asset prices as nonlinear functions of N uncorrelated standard normal random variables. For a given set of time-t asset prices, we next determine the time-t continuation value by performing a numerical integration along the radial direction in the N-dimensional polar coordinate system for the N uncorrelated standard normal random variables, expressing the integrated value via a regression procedure as a function of the polar angles, and performing a numerical integration over the polar angles. The larger value of the continuation value and the time-t immediate exercise value will then be the option value. The time-t option values over the N-dimensional space may be represented by a quadratic function of the radial distance, with the coefficients of the quadratic function given by second degree polynomials in N-1 polar angles. Partitioning the maturity time T into k* intervals of length Δt, we obtain the time-(k-1)Δt option value from the time-kΔt option values for k= k*, k*-1,…, 1. The time-0 option value is then the price of the American option. It is found that the numerical results for the American option prices based on regression and numerical integration agree well with the simulation results, and exhibit a variation of the prices as we vary the non-normality of the underlying distributions of the assets. To assess the accuracy of the computed price we may use estimated standard error of the computed American option price. The standard error will help us gauge whether the number of selected points along the radial direction and the number of selected polar angles are large enough to achieve the required level of accuracy for the computed American option price

The Future of Malaysia Trade in One Belt One Road

The One Belt and One Road Initiative (OBOR) will open up more trade opportunities for Malaysia due to the two trade routes, namely, the land-based Silk Road Economic Belt and the seagoing 21st Century Maritime Silk Road. This paper empirically examines the short-term and long-term relationship between Malaysias trade balance, real exchange rates (RER), industry production index (IPI), Malaysias consumer price index (MCPI) and Chinas consumer price index (CCPI) for the period January 2000 to September 2017. The Malaysias trade balance is regarded as an explained variable while the MYR-RMB, IPI, MCPI and CCPI will be regarded as explanatory variables. The Autoregressive Distributed Lag (ARDL) cointegration test is employed to estimate the long-run relationship between China and Malaysia. Then the Error-Correction model and the error correction term would explain the speed of adjustment in restoring equilibrium in the dynamic model referred to in this paper. The finding shows that the exports in Malaysia would benefit from the real appreciation of MYR and Chinas inflation. The OBOR will open up more opportunities for Malaysia to generate trade mainly because it involves the belt and the maritime but diplomatic relationship and export constructive policy also important to improve Malaysia trade balance with Chin

Pricing of American call options using simulation and numerical analysis / Beh Woan Lin

Consider the American basket call option in the case where there are N underlying assets, the number of possible exercise times prior to maturity is finite, and the vector of asset prices is modeled using a Levy process. A numerical method based on regression and numerical integration is proposed to estimate the prices of the American options. In the proposed method, we make use of the distribution for the vector of asset prices at a given time t in the future to determine the “important” values of the vector of asset prices of which the option values should be determined. In determining the option values at time t, we first perform a numerical integration along the radial direction in the N-dimensional polar coordinate system. The value thus obtained is expressed via a regression procedure as a function of the polar angles, and another numerical integration is performed over the polar angles to obtain the continuation value. The larger value of the continuation value and the immediate exercise value will then be the option value. A method is also proposed to estimate the standard error of the computed American option price

The asymmetric responses of stock prices in US market

Machine learning and data analytics are so popular in making trading much more efficient by helping the investors to identify opportunities and reduce trading costs. Before applying suitable predictive modelling algorithms, it is crucial for investors or policymaker to understand the nature of the stock data properly. This paper investigates the dependency of macroeconomic factors against the stock markets in the United States using the nonlinear Autoregressive Distributed Lag (NARDL) approach. The analysis considered the Dow Jones Industrial Average Index, NASDAQ Composite Index, and S&P 500 Index. Macroeconomic factors in this country such as consumer price index, export, interest rates, money supply, real effective exchange rates, total reserves, and gold price are considered in this study. In the findings, the NARDL approach shows that the Dow Jones Industrial Average Index and S&P500 Index are having bi-directional positive asymmetric effects to each other in the short run. In short-run, increasing the consumer price index is found to have a negative effect on Dow Jones Industrial Average Index but with a positive effect on S&P500 Index. In conclusion, this study aids investors and other market participants in making a more efficient investment decision