"An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates"

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on the third order asymptotic expansion scheme; we do not model a foreign exchange rate's variance such as in Heston[1993], but its volatility that follows a general time-inhomogeneous Markovian process, and we allow the correlations among all the factors, that is domestic and foreign interest rates, a spot foreign exchange rate and its volatility. Finally, we provide numerical examples and apply the pricing formula to the calibration of volatility surfaces in the JPY/USD option market.

"Asymptotic Expansion Approaches in Finance: Applications to Currency Options"

This chapter presents a basic of the methodology so-called an asymptotic expansion approach, and applies this method to approximation of prices of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. The scheme enables us to derive closed-form approximation formulas for pricing currency options even with high flexibility of the underlying model; we do not model a foreign exchange rate's variance such as in Heston [27], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. At the end of this chapter some numerical examples are provided and the pricing formula is applied to the calibration of volatility surfaces in the JPY/USD option market.

Relationship between labor-income risk and average return: empirical evidence from the Japanese stock market

In Japan, as in the United States, stocks that are more sensitive to changes in the monthly growth rate of labor income earn a higher return on average. Whereas the stock-index beta can only explain 2 percent of the cross-sectional variation in the average return on stock portfolios, the stock-index beta and the labor-beta together explain 75 percent of the variation. We find that the labor-beta drives out the size effect but not the book-to-market-price effect that is documented in the literature. We explore the extent to which these results are an artifact of seasonal patterns in labor-income growth rates as well as asset returns. In Japan, the book-to-market-price characteristic can be adequately captured by a particular factor-beta, as suggested by Fama and French (1993). This is in contrast to the findings reported by Daniel and Titman (1997) for the United States.Labor supply ; Stock - Prices ; Japan

Pricing Currency Options with a Market Model of Interest Rates under Jump-Diffusion Stochastic Volatility Processes of Spot Exchange Rates

This paper proposes a pricing method of currency options with a market model of interest rates. Using a simple approximation and a Fourier transform method, we derive a formula of the option pricing under jump-diffusion stochastic volatility processes of spot exchange rates. As an application, we apply the formula to the calibration of volatility smiles in the JPY/USD currency option market. Moreover, using the approximate prices as a control variate, we achieve substantial variance reduction in Monte Carlo simulation.

"Pricing Currency Options with a Market Model of Interest Rates under Jump-Diffusion Stochastic Volatility Processes of Spot Exchange Rates"

This paper proposes a pricing method of currency options with a market model of interest rates. Using a simple approximation and a Fourier transform method, we derive a formula of the option pricing under jump-diffusion stochastic volatility processes of spot exchange rates. As an application, we apply the formula to the calibration of volatility smiles in the JPY/USD currency option market. Moreover, using the approximate prices as a control variate, we achieve substantial variance reduction in Monte Carlo simulation.

A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options ( Revised in April 2008, January 2009 and April 2010; forthcoming in "International Journal of Theoretical and Applied Finance". )

This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for the valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates. Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained. Moreover, the hybrid scheme develops Fourier transform method with an asymptotic expansion to utilize closed-form characteristic functions obtainable in parts of a model. Our scheme also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of closed-form characteristic functions. Finally, a series of numerical examples shows the validity of our scheme.

"Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options"

This paper develops a Fourier transform method with an asymptotic expansion approach for option pricing. The method is applied to European currency options with a libor market model of interest rates and jump-diffusion stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas of the characteristic functions of log-prices of the underlying assets and the prices of currency options based on a third order asymptotic expansion scheme; we use a jump- diffusion model with a mean-reverting stochastic variance process such as in Heston [1993] / Bates [1996] and log-normal market models for domestic and foreign interest rates. Finally, the validity of our method is confirmed through numerical examples.

Asymptotic Expansion Approaches in Finance: Applications to Currency Options

This chapter presents a basic of the methodology so-called an asymptotic expansion approach, and applies this method to approximation of prices of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. The scheme enables us to derive closed-form approximation formulas for pricing currency options even with high flexibility of the underlying model; we do not model a foreign exchange rate's variance such as in Heston [27], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. At the end of this chapter some numerical examples are provided and the pricing formula is applied to the calibration of volatility surfaces in the JPY/USD option market.

Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options ( Revised in December 2008; subsequently published in "International Journal of Theoretical and Applied Finance", Vol.11-4,pp.381-401. )

This paper develops a Fourier transform method with an asymptotic expansion approach for option pricing.The method is applied to European currency options with a libor market model of interest rates and jump-diffusion stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas of the characteristic functions of log-prices of the underlying assets and the prices of currency options based on a third order asymptotic expansion scheme; we use a jump-diffusion model with a mean-reverting stochastic variance process such as in Heston[1993]/Bates[1996] and log-normal market models for domestic and foreign interest rates. Finally, the validity of our method is confirmed through numerical examples.

On-line Electrochemical Oxidation of Cr(III) for the Determination of Total Cr by Flow Injection–Solid Phase Spectrophotometry

A novel on-line oxidation method of ultra-trace Cr(III) dissolved in natural water has been developed using a flow electrolysis cell. This method was successfully applied to the determination of the total Cr concentration by flow injection–solid phase spectrophotometry using diphenylcarbazide as a coloring agent. With the applied potential of 1.35 V (vs. Ag/AgCl) and the flow rate of 0.80 cm3 min–1, Cr(III) was quantitatively oxidized to Cr(VI) at room temperature. The total Cr concentration of sub-μg dm–3 in 3 – 4 samples could be determined within 1 h using an aqueous sample volume of 7.1 cm3. The analytical values of the total Cr concentration in natural water were in good agreement with those obtained by ICP-MS. The detection limit of the proposed method was 0.014 μg dm–3 (3σ, n = 7). This method could be applied to the specific determination of Cr(III) and Cr(VI) in river water samples