Volatility and jump risk in option returns

We examine the importance of volatility and jump risk in the time-series prediction of S&P 500 index option returns. The empirical analysis provides a different result between call and put option returns. Both volatility and jump risk are important predictors of put option returns. In contrast, only volatility risk is consistently significant in the prediction of call option returns over the sample period. The empirical results support the theory that there is option risk premium associated with volatility and jump risk, and reflect the asymmetry property of S&P 500 index distribution.     

Option trading and the cross-listed stock returns: Evidence from Chinese A–H shares

We empirically investigate the effects of option trading on the cross-listed stock returns. Using dual-listed stocks in mainland China (A) and Hong Kong (H) stock exchanges, we show that option order imbalance (OI) positively and significantly predicts daily stock returns for both markets, controlling for risk factors and firm characteristics. Informed trading rather than price pressure better explain the predictability. High OI stocks have higher trading volume and present lottery-like properties. Three important events significantly affect the predictive power of OI, consistent with the improved market quality and the episode of speculative trading. Robustness checks support the main findings.     

An analytical perturbative solution to the Merton–Garman model using symmetries

In this paper, we introduce an analytical perturbative solution to the Merton–Garman model. It is obtained by doing perturbation theory around the exact analytical solution of a model which possesses a two-dimensional Galilean symmetry. We compare our perturbative solution of the Merton–Garman model to Monte Carlo simulations and find that our solutions perform surprisingly well for a wide range of parameters. We also show how to use symmetries to build option pricing models. Our results demonstrate that the concept of symmetry is important in mathematical finance.     

Computational aspects of robust optimized certainty equivalents and option pricing

Accounting for model uncertainty in risk management and option pricing leads to infinite‐dimensional optimization problems that are both analytically and numerically intractable. In this article, we study when this hurdle can be overcome for the so‐called optimized certainty equivalent (OCE) risk measure—including the average value‐at‐risk as a special case. First, we focus on the case where the uncertainty is modeled by a nonlinear expectation that penalizes distributions that are “far” in terms of optimal‐transport distance (e.g. Wasserstein distance) from a given baseline distribution. It turns out that the computation of the robust OCE reduces to a finite‐dimensional problem, which in some cases can even be solved explicitly. This principle also applies to the shortfall risk measure as well as for the pricing of European options. Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions. Finally, we give conditions on the latter set under which the robust average value‐at‐risk is a tail risk measure.     

Improved method for static replication under the CEV model

This paper studies the hedging performance of static replication approach proposed by Derman, Ergener, and Kani (DEK, 1995) for continuous barrier options under the constant elasticity of variance (CEV) model of Cox (1975) and Cox and Ross (1976), and then focuses on how to improve the DEK method. Given the time-varying volatility feature of the CEV model, I show that the DEK static hedging portfolio exhibits serious mismatches of the theta values on the barrier, particularly when one of the component options of the portfolio is around the neighborhood of expiration, which primarily explains why static portfolio values are greater than zero on the barrier except at the matching points. The DEK method (hereafter, the improved DEK method) is improved by re-forming a static replication portfolio consisting of plain vanilla options and cash-or-nothing binary options with different maturities to match both the value-matching condition and the theta-matching condition on the barrier. The numerical analyses indicate that under the CEV model, the improved DEK method significantly reduces replication errors for an up-and-out call option.     

On Stochastic Approximation and Credibility

Stochastic approximation is a powerful tool for sequential estimation of zero points of a function. This methodology is defined and is shown to be related to a broad class of credibility formulae derived for the Exponential Dispersion Family (EDF). We further consider a Location Dispersion Family (LDF) which is rich enough and for which no simple credibility formula exists. For this case, a Generalized Sequential Credibility Formula is suggested and an optimal stepwise gain sequence is derived.     

Pricing and integration of credit default swap index tranches

This paper first designs an efficient procedure to value Credit Default Swap Index tranches using an intensity-based model. The tranche spreads are effectively explained by a three-factor version of this model, both before and during the financial crisis of 2008. We then construct tradable tranche portfolios to track the intensity factors and compare the pricing of the tranches with equities and their derivatives. Our results show that the senior tranche spreads do not offer returns in excess of the common risk compensations in the equity and derivatives markets, while the junior tranche is not spanned by these standard factors.     

基于实物期权的三阶段投资策略分析

研究了三阶段投资项目中,投资比例对项目总价值的影响和关键因素对投资阈值的影响问题。描述了复合实物期权的基本思想,参照Ottoo的研究思路,调整了投资时刻与投资比例的前提假设,分析了三阶段的投资比例的问题,并进行了数值计算,对关键因素进行了敏感性分析,得出了三阶段最佳投资策略。     

Pricing chained dynamic fund protection

In this paper, we propose a new kind of dynamic fund protection (DFP). In contrast to the usual DFP, our newly developed DFP has two protection levels and protection is activated only when the value of underlying asset reaches upper protection levels. This kind of product has a structure similar to that of the chained barrier option proposed by Jun and Ku (2012). In this context, we name our newly designed equity-linked product as chained dynamic fund protection (CDFP). Buying CDFP can be advantageous for both vendors and investors compared to buy usual DFP. Relatively small downside risk for CDFP is beneficial for vendors. Also for investors, the price they cost for protection of CDFP is cheaper than that of usual DFP. Furthermore, investors can handle the price of protection by adjusting the level of upper protection as they desired. In this paper, we derive a closed-form formula for CDFP using reflection principle under Black–Scholes framework. Furthermore, we represent numerical results for values of CDFP according to various parameters.