Implicit Bayesian Inference Using Option Prices

Abstract. A Bayesian approach to option pricing is presented in which posterior inference about the underlying returns process is conducted implicitly via observed option prices. A range of models allowing for conditional leptokurtosis, skewness and time‐varying volatility in returns are considered, with posterior parameter distributions and model probabilities backed out from the option prices. Models are ranked according to several criteria, including out‐of‐sample predictive and hedging performance. The methodology accommodates heteroscedasticity and autocorrelation in the option pricing errors, as well as regime shifts across contract groups. The method is applied to intraday option price data on the S&P500 stock index for 1995. While the results provide support for models that accommodate leptokurtosis and skewness, no one model dominates when all criteria are considered.     

分数跳-扩散下外汇期权定价

用保险精算方法,在股票价格服从分数跳-扩散过程,且无风险利率、波动率和期望收益率为时间的非随机函数,给出了外汇期权定价公式.     

在分数Brown运动环境下具有红利支付期权定价的鞅分析

本文在分数Brown运动环境下,利用基础资产价格逼近过程的鞅性,推导分析了具有红利支付时期期权定价方程.     

高校足球选项课实施“合作讨论”教学法的实验

通过教学实验的方法,将"合作讨论"教学法和传统教学法运用于高校足球选项课的技术教学中的效应问题进行实验对比。结果表明:"合作讨论"教学法与传统教学法相比,课堂教学的互动更加频繁,有利于教学资源的整合,教学效果显著;能够更加有效地提高学生的运动技能水平,发展学生身体素质,而且在改善学生的心境状态,提高学生的学习兴趣和团队合作能力等方面效果更明显。     

多阶段复合期权模型在新药研发中的应用研究

考虑到新药研发周期长和高度的不确定性的特点,在实物期权理论的基础上建立了多阶段复合期权的评价模型,针对二阶段定价模型的不足,提出了各阶段波动率不同的三阶段定价模型,并得到其封闭解。最后用改进的三阶段变波动率复合期权模型来评估一个新药研发项目的价值,计算结果表明模型具有较好的实用性。     

A tree approach to options pricing under regime-switching jump diffusion models

A simple, efficient tree is developed to price options in a very general regime-switching jump diffusion model. Under this model, the switching rates of the switching process depend on the underlying stock price process. Sufficient conditions that guarantee the positivity of branch probabilities are provided. Using the regime-switching tree, we approximate Heston's stochastic volatility model with an additional jump component. Finally, we illustrate the effectiveness of the tree method by several numerical examples.     

Valuation of European continuous-installment options

This paper is concerned with the valuation of European continuous-installment options where the aim is to determine the initial premium given a constant installment payment plan. The distinctive feature of this pricing problem is the determination, along with the initial premium, of an optimal stopping boundary since the option holder has the right to stop making installment payments at any time before maturity. Given that the initial premium function of this option is governed by an inhomogeneous Black-Scholes partial differential equation, we can obtain two alternative characterizations of the European continuous-installment option pricing problem, for which no closed-form solution is available. First, we formulate the pricing problem as a free boundary problem and using the integral representation method, we derive integral expressions for both the initial premium and the optimal stopping boundary. Next, we use the linear complementarity formulation of the pricing problem for determining the initial premium and the early stopping curve implicitly with a finite difference scheme. Finally, the pricing problem is posed as an optimal stopping problem and then implemented by a Monte Carlo approach.     

Pricing fuzzy vulnerable options and risk management

The assumption of unrealistic “identical rationality” in classic option pricing theory is released in this article to amend Klein’s [Klein, P. (1996). Pricing Black–Scholes options with correlated credit risk. Journal of Banking Finance, 1211–1129] vulnerable option pricing formula. Through this formula, default risk and liquidity risk are both well-explained when the investment behaviors and market expectations of the participants are heterogeneous. The numerical results show that when the investing decisions of each market participant come from their individual rationality and use their own subjective price to trade, the option price becomes a boundary. The upper boundary becomes an absolutely safe line and the lower boundary becomes an absolutely unsafe line for investors who want to invest in some financial securities with default risk. The proposed model suggests a more realistic pricing mechanism for the issuers and traders who want to value options with default risk.