Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.     

An expansion in the model space in the context of utility maximization

In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian), an explicit second-order expansion formula for the power investor’s value function—seen as a function of the underlying market price of risk process—is provided. This allows us to provide first-order approximations of the optimal primal and dual controls. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Chebyshev interpolation for parametric option pricing

Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real time. We concentrate on parametric option pricing (POP) as a generic instance of parametric conditional expectations and show that polynomial interpolation in the parameter space promises to considerably reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence and explicit error bounds. The method is most promising when the computation of the prices is most challenging. We therefore investigate its combination with Monte Carlo simulation and analyze the effect of (stochastic) approximations of the interpolation. For a wide and important range of problems, the Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo. We conclude with a numerical efficiency study.     

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.     

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the linear part of the drift being a generator of a \(C_{0}\)-semigroup) driven by an infinite-dimensional cylindrical Wiener process. In particular, we prove, under some sufficient conditions on the coefficients, the existence and uniqueness of solutions for these stochastic evolution equations in a class of Banach spaces satisfying the so-called \(H\)-condition. Moreover, we analyse the Markov property of the solutions.Secondly, we apply the abstract results obtained in the first part to prove the existence and uniqueness of solutions to the Heath–Jarrow–Morton–Musiela (HJMM) equations in weighted Lebesgue and Sobolev spaces.Finally, we study the ergodic properties of the solutions to the HJMM equations. In particular, we find a sufficient condition for the existence and uniqueness of invariant measures for the Markov semigroup associated to the HJMM equations (when the coefficients are time-independent) in the weighted Lebesgue spaces.Our paper is a modest contribution to the theory of financial models in which the short rate can be undefined.     

Public bicycle as a feeder mode to rail transit in China: The role of gender,age, income,trip purpose,and bicycle theft experience

A marriage between public bicycle and rail transit presents new opportunities for sustainable transportation in Chinese cities. To examine determinants of public bicycle usage for rail transit access, an intercept survey of feeder mode choice among rail transit users was conducted near rail stations in Nanjing, China. Mode choice models were estimated with five feeder mode alternatives, including car, bus, walk, private bike, and public bike. By differentiating between public and private bicycle modes in the mode choice models, the study reveals the effects of personal demographics, trip characteristics, and station environments on public bicycle usage for rail transit access. Results show that female, older, and low-income rail commuters are less likely to use public bicycle to access rail transit. Rail commuters with bicycle theft experience and making school- or work-related trips are more likely to use public bicycle to access rail transit. Land use variables are largely insignificant in this study except that density shows a positive relationship with walking to rail transit. The results on demographic differences raise equity concerns when it comes to investing in public bicycle systems. Policy implications are discussed for Chinese cities to equitably boost public bicycle integration with rail transit.     

Subsidiary-specific advantages for inter-regional expansion: The role of intermediate units

This paper explores the distinctive deployment of resources and capabilities by subsidiaries in order to develop an intermediate role within the MNC. Based on the regional management perspective, we focus on a specific intermediate role—the springboard subsidiary—that helps overcome the liability of inter-regional foreignness. Our results, which are based on a dataset covering 188 subsidiaries, show that the probability of taking on this role is contingent upon experiential knowledge about the target region, as well as a rich knowledge base derived from a wide range of activities and a broad geographical scope. Our findings also show that possession of slack resources does not necessarily mean that a subsidiary will take on this role, as such slack must be combined with experiential knowledge. This paper serves as a first step in helping MNCs plan resource allocation to handle inter-regional expansion.