The Expected Return and Exercise Time of Merton-style Real Options

We analyse the rate of return and expected exercise time of Merton-style options (1973) employed in many real option situations where the possibility of exercise is both perpetual and American in nature. Using risk-neutral and risk-adjusted pricing techniques, Merton-style options are shown to have an expected return that is a constant percentage of the option value and independent of the proximity to the critical exercise boundary. Merton options thus remain at the same point on the Security Market Line, unlike European options whose position and rate of return change dynamically. We also present formulae for the expected time and discounted times to exercise and analyse the dependency of these variables on volatility.     

Discrete-time bond and option pricing for jump-diffusion processes

This paper provides a methodology for numerically pricing generalized interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite-differencing approach to deal with partial differential-difference equations derived in a jump-diffusion setting. Numerical illustrations compare jump-diffusion and pure-diffusion models.I am especially grateful to Darrell Duffie, who provided me immensely valuable input on the paper. I would also like to thank Dilip Madan and Rangarajan Sundaram for alleviating my confusion with helpful comments.     

Testing for constant hedge ratios in commodity markets: a multivariate GARCH approach

We develop a new multivariate generalized ARCH (GARCH) parameterization suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity (ARCH). The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time to maturity effects.     

The New Growth Enterprise Board

As a serious snowstorm hit most of southern China,some heart-warming news on the capital markets came from the National Work Conference on Securities and Futures Supervision held on January 16th and 17th.According to Shang Fulin,Chairman of the China Securities Regulatory Commission（CSRC）, securities regulators hope to open a new stock market in the first half of the year aimed at high-growth enterprises.＂The Growth Enterprise Board has a chance to be launched after China＇s first two sessions,＂ said Chen Siwei, Vice- Chairman of the Standing Committee of the National People＇s Congress （NPC） on January 19th, ＂Preparations for the Growth Enterprise Board have been completed, and we are just waiting for the go-ahead.＂     

American and European options in multi-factor jump-diffusion models,near expiry

We derive a general formula for the time decay θ for out-of-the-money European options on stocks and bonds at expiry, in terms of the density of jumps F(x,dy) and the payoff g ₊: −θ(x)=∫ g(x+y)₊ F(x,dy). Explicit formulas are derived for the standard put and call options, exchange options in stochastic volatility and local volatility models, and options on bonds in ATSMs. Using these formulas, we show that in the presence of jumps, the limit of the no-exercise region for the American option with the payoff (−g)₊ as time to expiry τ tends to 0 may be larger than in the pure Gaussian case. In particular, for many families of non-Gaussian processes used in empirical studies of financial markets, the early exercise boundary for the American put without dividends is separated from the strike price by a nonvanishing margin on the interval [0,T), where T is the maturity date.      

Long term spread option valuation and hedging

This paper investigates the valuation and hedging of spread options on two commodity prices which in the long run are in dynamic equilibrium (i.e., cointegrated). The spread exhibits properties different from its two underlying commodity prices and should therefore be modelled directly. This approach offers significant advantages relative to the traditional two price methods since the correlation between two asset returns is notoriously hard to model. In this paper, we propose a two factor model for the spot spread and develop pricing and hedging formulae for options on spot and futures spreads. Two examples of spreads in energy markets – the crack spread between heating oil and WTI crude oil and the location spread between Brent blend and WTI crude oil – are analyzed to illustrate the results.     

美国老年呆痴病人及家庭照料者服务方案评介

在老年人所患的疾病之中 ,老年呆痴病患者给其家人带来的压力和负担可以说是最独特和巨大的 ,这种家庭的压力及负担同时也给社会带来很多问题。介绍了美国老年呆痴病人及其家庭照料者在照料病人过程中所承受的压力情况 ,述说了美国为老年呆痴病人所设立的相关服务机构和所实行的措施方案。     

An Improved Approach to Computing Implied Volatility

A well‐known problem in finance is the absence of a closed form solution for volatility in common option pricing models. Several approaches have been developed to provide closed form approximations to volatility. This paper examines Chance's (1993, 1996) model, Corrado and Miller's (1996) model and Bharadia, Christofides and Salkin's (1996) model for approximating implied volatility. We develop a simplified extension of Chance's model that has greater accuracy than previous models. Our tests indicate dramatically improved results.     

Is Volatility Risk for the British Pound Priced in U.S. Options Markets?

This paper estimates the premium for volatility risk for European currency options written on British pounds. The average annualized premium for volatility risk is neither statistically different from zero nor invariant to the option's moneyness. However, the risk premium is positively and nonproportionaly related to the level of volatility, except for out‐of‐the‐money options. Finding a zero premium for volatility risk does not undermine the assumption of a zero‐price volatility risk in many extant stochastic‐volatility option pricing models and the option pricing formulas in those models.