Application of Homotopy Analysis Method to Option Pricing Under Lévy Processes

Option pricing under the Lévy process has been considered an important research direction in the field of financial engineering, where a closed-form expression for the standard European option is available due to the existence of analytically tractable characteristic function according to the Lévy–Khinchin representation. However, this approach cannot be applied to exotic derivatives (such as barrier options) directly, although a large volume of exotic derivatives are actively traded in the current options market. An alternative approach is to solve the corresponding partial integro-differential equation (PIDE) numerically, which is, in fact, time-consuming and is not computationally tractable in general. In this paper, we apply the so-called homotopy analysis method (HAM) to solve the corresponding PIDE in a semi analytic form, being obtained from the following three steps: (1) Apply the Fourier transform to convert the PIDE to an ordinal differential equitation (ODE), and construct a differential system of ODEs. (2) Solve the system of ODEs, where each differential equation is shown to have an analytical solution. (3) Express the option price using the sum of infinite series, where each term may be expressed analytically and derived by applying Steps (1) and (2) recursively. To illustrate our technique more precisely, we take the variance gamma model as an example and provide the semi-analytic form. Numerical examples demonstrate a fast convergence of our proposed method to the prices of European and down-and-out call options with a few number of terms. Note that this method is easy to implement and can be applied to other types of options under general Lévy processes.     

公私伙伴关系的定位与调适

供给主体单一会导致公共服务质量低下,应利用公私部门间各自优势,引入市场机制,理顺公共部门与私营部门间关系,构建政府、市场与社会三者间共同参与公共服务供给的新模式,以期提升公共服务供给水平。     

When and how US dollar shortages evolved into the full crisis? Evidence from the cross-currency swap market

This paper investigates when and how the US dollar shortages evolved into the full crisis in the cross-currency swap market between major European currencies and the US dollar during the turmoil of 2007-2009, using the dynamic factor model with regime-switching β coefficients of each swap price with respect to the latent common factor. The 1-year market entered the high-β crisis regime soon after the onset of the subprime problem in August 2007. The 10-year market entered that regime following the collapse of Bear Sterns in mid-March 2008. Financial credit spreads have significant predictive power for switches between high and low-β regimes.     

The causes of Japan's ‘lost decade’: The role of household consumption

In this paper, I analyze the causes of the prolonged slowdown of the Japanese economy in the 1990s and find that the stagnation of investment, especially private fixed investment, was the primary culprit. I then investigate the causes of the stagnation of household consumption during the 1990s and find that the stagnation of household disposable income, the decline in household wealth, and increased uncertainty about the future are among the contributing factors. Finally, I consider whether demand side factors or supply side factors were more important as causes of the prolonged slowdown of the Japanese economy in the 1990s and conclude that the former (especially misguided government policies) were probably more important.     

Inside the learning dynamism inducing the resonance between innovation and high-demand consumption: A case of Japan's high-functional mobile phones

Confronting the simultaneous global economic stagnation that has resulted in diminishing consumption, a new driver which can instill in customers an exciting story with their own initiative and thrills them with gratification of consumption is essential. Japan's mobile phone driven innovation may provide a constructive suggestion to this requirement.On the basis of an empirical analysis focusing on the learning dynamism for innovative products in Japan's digital industry, this paper demonstrates the foregoing hypothetical anticipation. Based on measurement of dynamic learning coefficients for seven leading innovative products centered on mobile phones, the Granger causal test, Chow forecast test and wavelet analysis were conducted, and the significant role of mobile phones in leveraging broad dissemination, learning and absorption of core technologies essential to the advancement of digital industry was identified. Furthermore, significant role of demanding customers in inducing resonance between mobile phones learning and that of innovative products was demonstrated.     

Footloose Capital and Comparative Advantage

We investigate the effect of country size differentials and Ricardian technology differences on firms’ location decisions using a two‐country, two‐good (homogeneous agricultural good and differentiated manufacturing products), two‐factor (labour and footloose capital) simple new economic geography model. We found that manufacturing firms may agglomerate in a country where the manufacturing sector has a comparative disadvantage. In addition, when country size differentials and Ricardian technology differences exist between two countries, the key factor influencing firms’ location decisions changes according to the level of trade liberalization, from being market size‐dependent to becoming technology‐dependent.     

A possible explanation of the ‘Exchange Rate Disconnect Puzzle’: a common solution to three macroeconomic puzzles?

Meese and Rogoff (1983) and subsequent studies find that economic fundamentals are apparently not able to explain exchange rate movements, but we argue that this so-called ‘Exchange Rate Disconnect Puzzle’ arose because researchers such as Meese and Rogoff (1983) did not use the right fundamentals and because they did not allow for the forward-looking nature of exchange rate determination. Further, because they apparently were not aware that financial markets by themselves could not equalize interest rates across countries, they did not properly appreciate that the exchange rate is strongly influenced by agents’ expectations of aggregated differences in local returns. Thus, we believe that the same underlying explanation provided by Ford (2015) and Ford and Horioka (2016a, 2016b) for the Feldstein-Horioka (1980) Puzzle and the PPP Puzzle – namely that financial markets alone cannot achieve net transfers of financial capital and cannot equalize real interest rates across countries – also helps explain why previous attempts to connect changes in the exchange rate to economic fundamentals have not been successful and so can also be said to contribute to solving the Exchange Rate Disconnect Puzzle.     

Determining the optimal scheme of zoned effluent charges for the control of air pollution

A minimum costly zoned effluent charge program for the control of air pollution is considered paying attention to the general situation where polluters' cost functions of treating pollutant are unknown to the policy authority, and an iterative procedure by which the authority can attain a set of optimal charges is presented. The algorithm consists of steps of estimating the unknown treatment cost functions by observing polluter behavior and steps of revising charges based on the estimated cost functions. In the latter steps, a newly developed solution procedure for the zoned charge programming problem is involved. Simulated use of the algorithm indicates that the iterative charge revision procedure proposed in this paper can effectively provide the optimal scheme of zoned effluent charges.     

Market Share Instability and the Dynamics of Competition: a Panel Data Analysis of Japanese Manufacturing Industries

This paper explores market share instability as a measure of market mobility. Using a newly constructed panel data set, we examine the determinants of the market share instability of leading firms in Japanese manufacturing industries. The findings suggest that there is a significant relationship between concentration and market share instability, and the market shares of leading firms are more stable in highly concentrated industries. We also provide evidence that industry growth has a significantly positive effect on market share instability.