The affine Heston model with correlated Gaussian interest rates for pricing hybrid derivatives

In this article we define a multi-factor equity–interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model and we use a Gaussian multi-factor short-rate process. By construction, the model fits in the framework of affine diffusion processes, allowing fast calibration to plain vanilla options. We also provide an efficient Monte Carlo simulation scheme.     

On the determination of an optimal sample size

Abstract

In works on sample survey theory and methods the sample size is usually regarded as determined by the sampling procedure and the total cost of the survey.     

A New Method for Identifying the Effects of Foreign Exchange Interventions

Central banks react even to intraday changes in the exchange rate; however, in most cases, intervention data are available only at a daily frequency. This temporal aggregation makes it difficult to identify the effects of interventions on the exchange rate. We apply the Bayesian Markov‐chain Monte Carlo (MCMC) approach to this endogeneity problem. We use “data augmentation” to obtain intraday intervention amounts and estimate the efficacy of interventions using the augmented data. Applying this new method to Japanese data, we find that an intervention of 1 trillion yen moves the yen/dollar rate by 1.8%, which is more than twice as much as the magnitude reported in previous studies applying ordinary least squares to daily observations. This shows the quantitative importance of the endogeneity problem due to temporal aggregation.     

The Risk Microstructure of Corporate Bonds: A Case Study from the German Corporate Bond Market

This article presents joint econometric analysis of interest rate risk, issuer‐specific risk (credit risk) and bond‐specific risk (liquidity risk) in a reduced‐form framework. We estimate issuer‐specific and bond‐specific risk from corporate bond data in the German market. We find that bond‐specific risk plays a crucial role in the pricing of corporate bonds. We observe substantial differences between different bonds with respect to the relative influence of issuer‐specific vs. bond‐specific spread on the level and the volatility of the total spread. Issuer‐specific risk exhibits strong autocorrelation and a strong impact of weekday effects, the level of the risk‐free term structure and the debt to value ratio. Moreover, we can observe some impact of the stock market volatility, the respective stock's return and the distance to default. For the bond‐specific risk we find strong autocorrelation, some impact of the stock market index, the stock market volatility, weekday effects and monthly effects as well as a very weak impact of the risk‐free term structure and the specific stock's return. Altogether, the determinants of the spread components vary strongly between different bonds/issuers.     

Can Warren Buffett forecast equity market corrections?

Warren Buffett suggested that the ratio of the market value of all publicly traded stocks to the Gross National Product could identify potential overvaluations and undervaluations in the US equity market when this ratio deviates above 120% or below 80%. We investigate whether this ratio is a statistically significant predictor of equity market corrections and rallies. We find that Buffett's decision rule does not deliver satisfactory forecasts. However, when we adopt a time-varying decision rule, the ratio becomes a statistically significant predictor of equity market corrections. The two time-varying decision rules are: (i) predict an equity market correction when the ratio exceeds a 95% one-tail confidence interval based on a normal distribution, and (ii) predict an equity market correction when the ratio exceeds a threshold computed using Cantelli's inequality. These new decision rules are robust to changes in the two key parameters: the confidence level and the forecasting horizon. This paper also shows that the MV/GNP ratio performs relatively well against the four most popular equity market correction models, but the ratio is not a particularly useful predictor of equity market rallies.     

Export Sophistication: A Dynamic Panel Data Approach

In this article, we analyze export sophistication based on a large panel dataset (2001–2015; 101 countries) and using various estimation algorithms. Using Monte Carlo simulations, we evaluate the bias properties of estimators and show that GMM-type estimators outperform instrumental-variable and fixed-effects estimators. Based on our analysis we document that GDP per capita and the size of the economy exhibit significant and positive effects on export sophistication; weak institutional quality exhibits negative effect. We also show that export sophistication is path-dependent and stable even during a major economic crisis, which is especially important for emerging and developing economies.     

Lognormal Approximation of Complex Path-Dependent Pension Scheme Payoffs

Abstract

This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation-based numerical experiments, and we point to several other potential practical applications of the paper's theoretical results.     

A STATE-SPACE PARTITIONING METHOD FOR PRICING HIGH-DIMENSIONAL AMERICAN-STYLE OPTIONS

The pricing of American-style options by simulation-based methods is an important but difficult task primarily due to the feature of early exercise, particularly for high-dimensional derivatives. In this paper, a bundling method based on quasi-Monte Carlo sequences is proposed to price high-dimensional American-style options. The proposed method substantially extends Tilley's bundling algorithm to higher-dimensional situations. By using low-discrepancy points, this approach partitions the state space and forms bundles. A dynamic programming algorithm is then applied to the bundles to estimate the continuation value of an American-style option. A convergence proof of the algorithm is provided. A variety of examples with up to 15 dimensions are investigated numerically and the algorithm is able to produce computationally efficient results with good accuracy.     

Design of limited-stop bus service with capacity constraint and stochastic travel time

This paper develops a mathematical model for the optimal stopping design of limited-stop bus service, which allows each bus vehicle to skip some stops. To better reflect the reality, this paper considers the vehicle capacity and stochastic travel time. Also, vehicles are all allowed to skip stops whereas any stop is not allowed to be skipped by two consecutive vehicles. A hybrid artificial bee colony (ABC) and Monte Carlo method is developed to solve the optimal stopping strategy. Finally, the model and solution method are validated by a numerical example, and a sensitivity analysis is performed on the passenger demand.     

A Monte-Carlo approach to estimating the effects of selected airport capacity options in London

The issue of future airport capacity in London is currently the subject of much political debate in the UK. Although realistic estimates of the effects of capacity enhancement may be desirable, such estimates are difficult. Through the use of Monte Carlo simulation, this paper quantifies and compares the relative capacity enhancements that may be afforded by the construction of a new hub airport in the Thames Estuary, additional runways at Heathrow, Gatwick and Stansted and changes to operating practices at Heathrow. The simulations show that a new hub airport would be the most effective way to increase capacity, although the reported financial and environmental costs of such a development indicate a comparatively poor rate of return. Proposed new runways at Heathrow, Gatwick and Stansted and the removal of runway alternation at Heathrow provide more modest increases in capacity.