Pricing Vulnerable Options Under a Markov-Modulated Regime Switching Model

In this article, we consider the pricing of vulnerable European options when the dynamic of the risky assets are governed by Markov-modulated Geometric Brownian Motions. The regime switching Esscher transform is employed to determine an equivalent martingale measure. In particular, we also provide analytical pricing formulas of vulnerable European options under a Markov-modulated jump-diffusion model.     

Risk-minimizing pricing and hedging foreign currency options under regime-switching jump-diffusion models

This article mainly investigates risk-minimizing European currency option pricing and hedging strategy when the spot foreign exchange rate is driven by a Markov-modulated jump-diffusion model. We suppose the domestic and foreign money market floating interest rates, the drift, and the volatility of the exchange rate dynamics all depend on the state of the economy, which is modeled by a continuous-time hidden Markov chain. The model considered in this article will provide market practitioners with flexibility in characterizing the dynamics of the spot foreign exchange rate. Using the minimal martingale measure, we obtain a system of coupled partial-differential-integral equations satisfied by the currency option price and find the corresponding hedging strategies and the residual risk. According to simulation of currency option prices in the special case of double exponential jump-diffusion regime-switching model, we further discuss and show the effects of the parameters on the prices.     

Analysis of a jump-diffusion option pricing model with serially correlated jump sizes

This paper extends the classical jump-diffusion option pricing model to incorporate serially correlated jump sizes which have been documented in recent empirical studies. We model the series of jump sizes by an autoregressive process and provide an analysis on the underlying stock return process. Based on this analysis, the European option price and the hedging parameters under the extended model are derived analytically. Through numerical examples, we investigate how the autocorrelation of jump sizes influences stock returns, option prices and hedging parameters, and demonstrate its effects on hedging portfolios and implied volatility smiles. A calibration example based on real market data is provided to show the advantage of incorporating the autocorrelation of jump sizes.     

Pricing and hedging equity-indexed annuities via local risk-minimization

Lin et al. (2009) employed the Esscher transform method to price equity-indexed annuities (EIAs) when the dynamic of the market value of a reference asset was driven by a generalized geometric Brownian motion model with regime-switching. Some rare events (release of an unexpected economic figure, major political changes or even a natural disaster in a major economy) can lead to brusque variations in asset prices, and hence we sometimes need to consider jump models. This paper extends the model and analysis in Lin et al. (2009). Specifically, we assume that the financial market has a regime-switching jump-diffusion model, under which we price the point-to-point, the Asian-end, the high water mark and the annual reset EIAs by exploiting the local risk-minimization approach. The effects of the model parameters on the EIAs pricing are illustrated through numerical experiments. Meanwhile, we present the locally risk-minimizing hedging strategies for EIAs.     

连续贝塔、非连续贝塔与股票风险溢酬

本文利用高频数据将传统的CAPM贝塔分解为连续贝塔和非连续贝塔（跳跃贝塔和隔夜贝塔），并在此基础上进一步考虑正向市场和负向市场的非对称性，将跳跃贝塔又细分为正向跳跃贝塔和负向跳跃贝塔，以探讨不同类型系统性风险的特征差异及其所对应的风险溢酬。实证结果表明，个股对市场发生的非连续变动比连续变动更加敏感，投资者对市场发生的负向跳跃比正向跳跃反应更加强烈；中国股票市场上的系统性非连续风险溢酬（跳跃风险溢酬和隔夜风险溢酬）显著为正，但系统性连续风险并没有得到定价；其中，跳跃风险溢酬则主要来源于对系统性负向跳跃风险的补偿，而正向跳跃风险对股票横截面收益率没有显著的影响。     

Pricing options with credit risk in a reduced form model

This article investigates the valuation of European option with credit risk in a reduced form model. We assume that the interest rate follows the Vasicek model and the intensity of default is driven by a jump diffusion process. We obtain the closed form formula for the price of the option and provide some numerical illustrations of the results obtained.     

Uniform asymptotics for random time ruin probability with subexponential claims and constant interest rate

Consider the probability of random time ruin in the renewal risk model with the general nonnegative and non decreasing premium process and constant interest rate. We obtain a uniform asymptotic formula for random time τ and subexponential distribution.     

The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier

In this paper, we investigate the price for the zero-coupon defaultable bond under a structural form credit risk with regime switching. We model the value of a firm and the default threshold by two dependent regime-switching jump-diffusion processes, in which the Markov chain represents the states of an economy. The price is associated with the Laplace transform of the first passage time and the expected discounted ratio of the firm value to the default threshold at default. Closed-form results used for calculating the price are derived when the jump sizes follow a regime-switching double exponential distribution. We present some numerical results for the price of the zero-coupon defaultable bond via Gaver-Stehfest algorithm.     

Exchange option pricing in jump-diffusion models based on esscher transform

In the real world, we introduce a dynamic model about the risky asset which is governed by Brownian motion, stationary compound Poisson process and its compensation process. By choosing Esscher transform parameters, we obtain a risk-neural measure Q under which the discounted value of the risky underlying asset is a martingale. Then, we give the pricing formulas of Exchange option by change of numeraire. At last, we analyze the option pricing formula and provide numerical illustrations by introducing BBY stock and SBUX stock.     

The finite-time ruin probability in two non-standard renewal risk models with constant interest rate and dependent subexponential claims

This paper considers an ordinary renewal risk model and a compound renewal risk model with constant interest rate, subexponential claims and a general premium process. We derive some asymptotic results on the finite-time ruin probabilities.     

中国短期利率跳跃行为的实证研究

内容提要：通过在Vasicek模型中引入跳跃强度与宏观经济变量相关的跳跃成分,本文建立了一个更具一般性的跳跃－扩散动态利率期限结构模型,并对该模型的五种不同形式进行了实证比较与分析。借助于新模型和比较结果,本文对中国短期利率的跳跃行为进行了实证研究。结果表明：（1）短期利率不仅存在均值回复和扩散行为,还存在显著的跳跃行为;（2）短期利率的跳跃强度存在显著的正向水平效应和宏观经济效应 ,但水平效应比宏观经济效应更显著;（3）跳跃行为、跳跃强度的水平效应以及宏观经济效应在刻画利率动态行为时都是必要的,现有的跳跃－扩散模型不足以描述中国短期利率的动态行为特征;（4）随着跳跃、跳跃强度的宏观经济效应和水平效应的逐步引入,模型的拟合优度和预测能力逐步显著提高。     

The credibility premiums based on estimated moment-generating function

Traditionally, experience ratemaking is in principle based on the idea of Bühlmann’s credibility theory that, except for net premiums, was rarely applied to other premium calculation principles. This article uses Bühlmann’s credibility procedure to estimate moment-generating functions (MGFs) of risks and then deduces estimates of moments of those risks. For the premium calculation principles that can be expressed as functions of certain moments or more directly of the MGFs, this article develops a new type of experience ratemaking methods by means of the estimated MGFs and discusses their consistency and asymptotic normality. Numerical simulation shows that, under the Esscher and exponential premium principles, the new credibility estimates are better than existing credibilityestimates in the literature.     

The Variance Risk Premium: Components,Term Structures,and Stock Return Predictability

This article examines the properties of the variance risk premium (VRP). We propose a flexible asset pricing model that captures co-jumps in prices and volatility, and self-exciting jump clustering. We estimate the model on equity returns and variance swap rates at different horizons. The total VRP is negative and has a downward-sloping term structure, while its jump component displays an upward-sloping term structure. The abrupt and persistent response of the short-term jump VRP to extreme events makes this specific premium a proxy for investors’ fear of a market crash. Furthermore, the use of the VRP level and slope, and of its components, helps improve the short-run predictability of equity excess returns.     

Jump-diffusion models of German stock returns

This paper discusses the statistical properties of jump-diffusion processes and reports on parameter estimates for the DAX stock index and 48 German stocks with traded options. It is found that a Poisson-type jump-diffusion process can explain the high levels of kurtosis and skewness of observed return distributions of German stocks. Furthermore, we demonstrate that the return dynamics of the DAX include a statistically significant jump component except for a few sample subperiods. This finding is seen to be inconsistent with asset pricing models assuming that the jump component of the stock's return is unsystematic and diversifiable in the market portfolio.     

议价能力对审计定价的影响——基于双边随机边界模型的分析

审计收费中的最终价格确定是审计双方博弈的结果。使用双边随机边界模型分析框架分析审计收费中的定价,以及审计双方议价能力对审计定价的影响。结果发现:事务所的议价能力使得审计收费比理论均衡价格高出大约24.02%,上市公司的议价能力使得审计收费比理论均衡价格低了大约17.29%,两者的最终博弈结果使得中国审计收费比均衡价格高大约6.73%,中国事务所审计收费存在一定的高收费现象,事务所对大规模企业有收费溢价,2006年后,国际四大事务所存在高收费溢价现象。     

Omega model for a jump–diffusion process with a two-step premium rate

In this paper, a jump–diffusion Omega model with a two-step premium rate is studied. In this model, the surplus process is a perturbation of a compound Poisson process by a Brown motion. Firstly, using the strong Markov property, the integro-differential equations for the Gerber–Shiu expected discounted penalty function and the bankruptcy probability are derived. Secondly, for a constant bankruptcy rate function, the renewal equations satisfied by the Gerber–Shiu expected discounted penalty function are obtained, and by iteration, the closed-form solutions of the function are also given. Further, the explicit solutions of the Gerber–Shiu expected discounted penalty function are obtained when the individual claim size is subject to exponential distribution. Finally, a numerical example is presented to illustrate some properties of the model.     

Estimating the Parameters of Stochastic Volatility Models Using Option Price Data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.     

Static Hedging of Geometric Average Asian Options with Standard Options

In this article, we first establish a theorem that represents the price of an Asian option in terms of standard European options with a shorter term and different strikes. Then using Gauss–Hermite numerical integration, we discretize our theorem so as to use Monte Carlo simulation to examine the error of the static hedging under the Black–Scholes model and the Merton jump-diffusion model. For ease of comparison, we also provide the error of the dynamic hedging. The numerical results show that the static hedging strategy performs better than the dynamic one under both models.     

Optimal investment and life insurance strategies in a mixed jump-diffusion framework

Abstract

This article investigates an optimal investment and life insurance strategies in a mixed jump-diffusion framework. The individual life insurance policyholder who has CRRA preferences. The market consists of riskless asset, a zero-coupon bond, a stock and life insurance. The instantaneous interest rate is modeled as the O-U model, while a zero-coupon bond with credit risk follows a BSDE and a risky asset be driven by MJD-fBm model. The problem is solved by the mixed jump diffusion fractional HJB SDE which satisfied the admissible strategy, then the closed form solution and optimal strategies are derived and the simulation of the various parameters are also given.