Reversible stopping (“switching”) implies super contact

This note shows that the second derivative of the value function exists (across a stopping threshold, short “super contact”) if reversibly stopping and entering involves no cost, called “switching”. This holds for discrete (real option) as well as for continuous stochastic control problems and proves particularly suitable in real option set ups since it provides the lacking boundary condition. However, super contact does not hold in dynamic games. A simple example documents the applicability of this condition. This paper was written during my visit of the University of Technology, Sydney (UTS) and I am grateful for the hospitality of and the stimulus at the School of Finance and Economics, in particular to Carl Chiarella. I also acknowledge many helpful discussions with Thomas Dangl on related issues, valuable suggestions from a referee and last but not least encouragement by Josef Kallrath     

An optimal insurance strategy for an individual under an intertemporal equilibrium

In this paper, we discuss how a risk-averse individual under an intertemporal equilibrium chooses his/her optimal insurance strategy to maximize his/her expected utility of terminal wealth. It is shown that the individual’s optimal insurance strategy actually is equivalent to buying a put option, which is written on his/her holding asset with a proper strike price. Since the cost of avoiding risk can be seen as a risk measure, the put option premium can be considered as a reasonable risk measure. Jarrow [Jarrow, R., 2002. Put option premiums and coherent risk measures. Math. Finance 12, 135-142] drew this conclusion with an axiomatic approach, and we verify it by solving the individual’s optimal insurance problem.     

具限制投资组合和交易费用的博弈未定权益的保值

博弈期权是由kifer(2000)提出的,但就其本质而言,仍是美式期权的一种,只是增加了卖方中止合约的权利.本文主要对连续市场模型中具交易费用和限制投资组合的博弈未定权益的保值问题进行了研究,给出了买卖双方的保值价格和一个无套利区间.     

基于傅里叶级数展开式的有效期权定价方法

A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L~vy models are also given to compare these new methods with the Fang and Oosterlee＇s method and other methods.     

The Pietra term structures of financial assets

This paper explores an elemental connection between call options-the most commonly tradable financial derivatives, implied volatility term structures-critical “market information” emanating from call-option prices, and the Pietra index-a quantitative economic measure of societal egalitarianism. Our study: (i) unveils an intrinsic “Pietra structure” of call-option prices; (ii) introduces the notion of the “Pietra term structures” of financial assets; (iii) describes the probabilistic meaning of the Pietra term structures; (iv) establishes an explicit nonlinear one-to-one mapping between the Pietra term structures and the implied volatility term structures of financial assets. The results presented in this paper provide a deep insight into the econophysics of call options and implied volatility term structures.     

Developing real option game models

By mixing concepts from both game theoretic analysis and real options theory, an investment decision in a competitive market can be seen as a “game” between firms, as firms implicitly take into account other firms’ reactions to their own investment actions. We review two decades of real option game models, suggesting which critical problems have been “solved” by considering game theory, and which significant problems have not been yet adequately addressed. We provide some insights on the plausible empirical applications, or shortfalls in applications to date, and suggest some promising avenues for future research.     

基于跳-分形模型的美式看涨期权定价

假设股票变化过程服从跳一分形布朗运动,根据风险中性定价原理对股票发生跳跃次数的收益求条件期望现值推导出M次离散支付红利的美式看涨期权解析定价方程,并使用外推加速法求出当M趋于无穷时方程的二重、三重正态积分多项式表达,依此计算连续支付红利美式看涨期权价值.数值模拟表明通常仅需二重正态积分多项式能产生精确价值,而在极实值状态下则需三重正态积分多项式才能满足,结合两种多项式可以编出有效数字程序评价支付红利的美式看涨期权.     

Sharing risk through concession contracts

In this paper we model concession contracts between a public and a private party, under dynamic uncertainty arising both from the volatility of the cash flow generated by the project and by the strategic behaviour of the two parties. Under these conditions we derive three notions of equilibrium price and apply the model to a case study for one of the most important concession contracts in Italy.     

A boundary element method to price time-dependent double barrier options

In this paper we propose a new method for pricing double-barrier options with moving barriers under the Black-Scholes and the CEV models. First of all, by applying a variational technique typical of the boundary element method, we derive an integral representation of the double-barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. Second, we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained. Several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate, even if the barriers are not differentiable functions. Moreover the numerical method presented in this paper performs significantly better than the finite difference approach.     

Application of the Singularity-Separating Method to American Exotic Option Pricing

This paper is devoted to numerical methods for American barrier and lookback options, which are important examples of American exotic options. Since the singularity-separating method is adopted, accurate numerical results can be obtained very fast.