Exchange options for catastrophe risk management

In this paper, we investigate the pricing issue and catastrophe risk management of exchange options. Exchange options allow the holder to exchange its stocks for another at maturity and can be seen as an extended version of catastrophe equity put options with another traded asset price as strike prices. Since option holders have to issue new shares to exercise the option, we illustrate the differences between option prices calculated using pre-exercise and post-exercise share prices. The effects of default risk on option prices and risk management are also considered. Finally, risk management analysis shows that exchange options can effectively hedge catastrophe risk.     

Pricing of vulnerable exchange options with early counterparty credit risk

The exchange option is one of the most popular options in the over-the-counter (OTC) market, which enables the holder of two underlying assets to exchange one with another. In OTC markets, with the increasing apprehension of credit default risk in the case of option pricing since the global financial crisis, it has become necessary to consider the counterparty credit risk while evaluating the option price. In this study, we combine the vulnerable exchange option and early counterparty default risk to obtain the closed-form formula for the vulnerable exchange option with early counterparty credit risk by using the method of dimension reduction, Mellin transform, and the method of images. Moreover, we examine the pricing accuracy of the option value by comparing our closed-form solution with the formula derived by the Monte-Carlo simulation.     

Valuation of double trigger catastrophe options with counterparty risk

This study presents a novel catastrophe option pricing model that considers counterparty risk. Asset prices are modeled through a jump-diffusion process which is correlated to counterparty loss process and collateral assets. Because of the long term of catastrophe options, this study also examines the model in the stochastic interest rate environment. The numerical results indicate that counterparty risk significantly affects the value of options. Recently, numerous serious financial events have demonstrated the importance of counterparty risk when valuing financial products.     

Valuing spread options with counterparty risk and jump risk

In this paper, we investigate spread options with counterparty risk in a jump-diffusion model. Due to the fact that there is no closed-form formula of spread options with counterparty risk, we obtain analytical expressions of lower and upper bounds by employing the measure-change technique. Finally, we numerically check the accuracy of the bounds and analyze the impacts of counterparty risk and jump risk on spread option prices.     

Joint dynamic modeling and option pricing in incomplete derivative-security market

In this study, we evaluate the option prices on two assets under stochastic interest rates when the stochastic process that underlying asset prices follow is depending on a correlated bivariate Markov-modulated geometric Brownian motion model with jump risks. More specifically, we conduct the joint dynamic modeling by identifying two independent compound Poisson processes with the log-normal jump sizes to describe both individual jumps and systematic cojumps. Facilitating the cojumping behavior this way with the time-inhomogeneity of the volatility, option pricing expressions are readily obtainable since the Gerber–Siu’s approach is employed to determine a pricing kernel. The empirical results and numerical illustrations are provided to show the impact of cojumps and stochastic volatilities on option prices.     

European quanto option pricing in presence of liquidity risk

In this paper, we study the pricing problems of the European quanto options in which the underlying foreign asset is in imperfectly liquid markets. First, we assume that the dynamics of the underlying foreign asset price are affected by market liquidity and propose a liquidity-adjusted quanto model. This allows for the effects of market liquidity on European quanto option pricing. And then we derive the analytical pricing formulas for four different types of European quanto options. Finally, we empirically investigate the pricing performance of our proposed model with a European quanto construction involving the SSE 50 ETF, as the underlying asset, and the CNY/HKD exchange rate. Empirical results demonstrate that the pricing accuracy of the proposed model is markedly superior to that of the Black-Scholes quanto model. In other words, allowing for liquidity risk in the framework of European quanto option pricing can make markedly improvements in fitting the real market data. Particularly, the improvement rate is high for medium-term and out-of-the-money options. Moreover, these results are robust for different liquidity measures.     

Calibration of stochastic volatility models: A Tikhonov regularization approach

We aim to calibrate stochastic volatility models from option prices. We develop a Tikhonov regularization approach with an efficient numerical algorithm to recover the risk neutral drift term of the volatility (or variance) process. In contrast to most existing literature, we do not assume that the drift term has any special structure. As such, our algorithm applies to calibration of general stochastic volatility models. An extensive numerical analysis is presented to demonstrate the efficiency of our approach. Interestingly, our empirical study reveals that the risk neutral variance processes recovered from market prices of options on S&P 500 index and EUR/USD exchange rate are indeed linearly mean-reverting.     

The market for crash risk

This paper examines the equilibrium when stock market crashes can occur and investors have heterogeneous attitudes towards crash risk. The less crash averse insure the more crash averse through options markets that dynamically complete the economy. The resulting equilibrium is compared with various option pricing anomalies: the tendency of stock index options to overpredict volatility and jump risk, the Jackwerth [Recovering risk aversion from option prices and realized returns. Review of Financial Studies 13, 433–451] implicit pricing kernel puzzle, and the stochastic evolution of option prices. Crash aversion is compatible with some static option pricing puzzles, while heterogeneity partially explains dynamic puzzles. Heterogeneity also magnifies substantially the stock market impact of adverse news about fundamentals.     

存货购销中最优期权合约交易量研究

在分析利用期权合约规避价格波动风险的原理的基础上,分别给出存货购销两个环节中可以运用的期权策略,然后利用均值方差模型计算使投资组合达到效用最大化时所对应的最优期权合约交易量及其对经营利润的影响,研究发现：在存货采购环节,企业可以通过购入看涨期权、购入看涨期权同时售出看跌期权两种策略控制采购价格波动的风险,在存货销售环节,企业可以通过购入看跌期权、同时购入看跌期权并售出看涨期权两种策略来稳定销售利润;从最优期权合约交易量及其对企业经营利润的影响来看,期权工具在控制存货采购价格、稳定销售利润中可以发挥良好作用。     

Analytically pricing variance and volatility swaps under a Markov-modulated model with liquidity risks

This paper determines strike prices of discretely sampled variance/volatility swaps taking into account stochastic liquidity risks and the switching of economic conditions. We adopt nonlinear regime switching volatility to reflect how asset prices are affected by economic cycles, and market prices of assets are discounted according to the level of market liquidity. We then establish a risk-neutral measure under regime switching Esscher transform, so that analytical valuation of variance/volatility swaps can be completed based on the closed-form forward characteristic function. The limiting behavior of discretely sampled variance/volatility swaps is also considered through the investigation of pricing continuously sampled variance/volatility swaps. Finally, based on the results from numerical implementation, we confirm that the new model is very flexible in reflecting different influence associated with common real market observations.     

公司流动性价值的复合实物期权定价法研究

公司流动性是指公司或企业持有的流动性资产,它除了账面价值外,还含有某种潜在价值。对公司流动性价值进行科学的评估,对于投资者、公司管理者等各方都非常重要。采用实物期权理论对公司流动性进行定价,是目前公司金融理论的前沿课题。本文首次揭示了公司流动性的复合实物期权性质,并用复合实物期权模型进行了定价的尝试,为公司财务管理决策提供了一种量化的工具。     

Do interest rate options contain information about excess returns?

There is strong empirical evidence that long-term interest rates contain a time-varying risk premium. Options may contain valuable information about this risk premium because their prices are sensitive to the underlying interest rates. We use the joint time series of swap rates and interest rate option prices to estimate dynamic term structure models. The risk premiums that we estimate using option prices are better able to predict excess returns for long-term swaps over short-term swaps. Moreover, in contrast to the previous literature, the most successful models for predicting excess returns have risk factors with stochastic volatility. We also show that the stochastic volatility models we estimate using option prices match the failure of the expectations hypothesis.     

Applications of the Likelihood Theory in Finance: Modelling and Pricing

This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their meaning can be translated to the world of mathematical finance and vice versa. A lot of similarities can be expressed in terms of LeCam’s theory for statistical experiments which is the theory of the behaviour of likelihood processes. For positive prices the arbitrage free financial assets fit into statistical experiments. It is shown that they are given by filtered likelihood ratio processes. From the statistical point of view, martingale measures, completeness, and pricing formulas are revisited. The pricing formulas for various options are connected with the power functions of tests. For instance the Black–Scholes price of a European option is related to Neyman–Pearson tests and it has an interpretation as Bayes risk. Under contiguity the convergence of financial experiments and option prices are obtained. In particular, the approximation of Itô type price processes by discrete models and the convergence of associated option prices is studied. The result relies on the central limit theorem for statistical experiments, which is well known in statistics in connection with local asymptotic normal (LAN) families. As application certain continuous time option prices can be approximated by related discrete time pricing formulas.     

Catastrophe equity put options with floating strike prices

In this study, we extend the results in Cox et al. (2004) by considering floating strike prices, which are affected by accumulated losses. We employ a compound Poisson process to describe catastrophe losses and adopt a mean-reverting square root process to capture the volatility of the underlying stock. In the numerical section, we first compare the differences in the prices of the options with fixed and floating strike prices. In addition, we illustrate the variance of the portfolios consisting of the stock and options with alternative kinds of strike prices by holding the total cost of the options constant. Variance-optimal portfolios are also investigated. Interestingly, numerical results show that the portfolios consisting of the stock and options with floating strike prices have lower variances in all cases, even when we hold the total option costs constant.     

Valuation of options on the maximum of two prices with default risk under GARCH models

In this paper, we work under GARCH models to value options on the maximum or the minimum of two prices. In addition, we consider not only two underlying asset prices but also geometric average ones. Further, default risk is also incorporated in a reduced-form model. In the proposed framework, closed-form pricing formulae of options on the maximum with or without default risk are derived and then used to perform numerical examples.     

Pricing basket spread options with default risk under Heston–Nandi GARCH models

In this paper, we investigate basket spread options under the Heston–Nandi GARCH model. Moreover, we adopt the reduced-form model to capture default risk, which is correlated with all underlying assets. Because of the nonexistence of the analytical fair values, we obtain a closed-form approximated pricing formula of basket spread options with default risk. Finally, we examine the accuracy of approximations and then use the proposed formulae to illustrate the effect of the number of the underlying assets and default risk as well.     

Non-transferable non-hedgeable executive stock option pricing

To value non-transferable non-hedgeable (NTNH) contingent claims and price executive stock options (ESOs), we use a replication argument to translate portfolios with NTNH derivatives into portfolios of primary assets (only) with stochastic portfolio constraints. By identifying stochastic discount factors and finding subjective prices of NTNH European and American ESOs, for block and continuous partial exercise, we derive executives׳ optimal exercise policies, and use these to find objective prices/costs of ESOs to firms. Through numerical simulations, we obtain policy implications regarding ESOs׳ incentivizing efficiency. For the first time, we demonstrate that, unlike under block exercise, subjective prices under continuous partial exercise may be higher than objective ones. Moreover, volatility regimes and executives׳ “other wealth” are important in ESO pricing, and are thus essential to empirical executive compensation studies.     

State Prices of Conditional Quantiles: New Evidence on Time Variation in the Pricing Kernel

We develop a set of statistics to represent the option‐implied stochastic discount factor and we apply them to S&P 500 returns between 1990 and 2012. Our statistics, which we call state prices of conditional quantiles (SPOCQ), estimate the market's willingness to pay for insurance against outcomes in various quantiles of the return distribution. By estimating state prices at conditional quantiles, we separate variation in the shape of the pricing kernel from variation in the probability of a particular event. Thus, without imposing strong assumptions about the distribution of returns, we obtain a novel view of pricing‐kernel dynamics. We document six features of SPOCQ for the S&P 500. Most notably, and in contrast to recent studies, we find that the price of downside risk decreases when volatility increases. Under a standard asset pricing model, this result implies that most changes in volatility stem from fluctuations in idiosyncratic risk. Consistent with this interpretation, no known systematic risk factors such as consumer sentiment, liquidity or macroeconomic risk can account for the negative relationship between the price of downside risk and volatility. Copyright © 2016 John Wiley & Sons, Ltd.     

Cross-hedging minimum return guarantees: Basis and liquidity risks

We reveal pitfalls in the hedging of insurance contracts with a minimum return guarantee on the underlying investment, e.g. an external mutual fund. We analyze basis risk entailed by hedging the guarantee with a dynamic portfolio of proxy assets for the funds. We also take account of liquidity risk which arises since the insurer may need to advance funds for performing the hedge. Based on a least-squares Monte Carlo simulation, we study the economic implications of basis and liquidity risks. We demonstrate that both risks may be surprisingly high and show how the design of the contract and the hedging strategy may help to alleviate them.     

基于期权调整持续期的银行资产负债组合优化模型

提出了基于期权调整持续期的银行资产负债隐含期权风险控制原理,结合持续期缺口的控制和法律、法规约束等控制银行的利率风险与流动性风险。以贷款利息收益最大为目标,以线性规划为工具,建立了基于期权调整持续期的银行资产负债组合优化模型。本文的创新与特色一是提出了基于期权调整持续期的银行资产负债组合优化原理,避免了资产与负债中的隐含期权给银行带来提前偿付风险。二是将利率结构对称原理和数量结构对称原理引入资产负债组合优化中,控制了银行经营中的流动性风险与利率风险,保护银行股东权益的安全,保证了银行资产配给的合法性与合规性。