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.     

Option pricing and replication with transaction costs and dividends

This paper derives optimal perfect hedging portfolios in the presence of transaction costs within the binomial model of stock returns, for a market maker that establishes bid and ask prices for American call options on stocks paying dividends prior to expiration. It is shown that, while the option holder's optimal exercise policy at the ex-dividend date varies according to the stock price, there are intervals of values for such a price where the optimal policy would depend on the holder's preferences. Nonetheless, the perfect hedging assumption still allows the derivation of optimal hedging portfolios for both long and short positions of a market maker on the option.     

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.     

Pricing vulnerable options with stochastic liquidity risk

In this paper, we consider vulnerable options with stochastic liquidity risk. We employ liquidity-adjusted pricing models to describe the underlying stock price and option issuer’s assets. In addition, the correlation between these assets is stochastic, depending on the market liquidity measures. In the proposed framework, we derive closed forms of vulnerable European options with stochastic liquidity risk and then use them to illustrate the effects of stochastic liquidity risk on vulnerable option prices. Numerical results show that the effects of liquidity risk on the prices of out-of-the-money options or the options with a short maturity are not negligible.     

Intensity-based framework and penalty formulation of optimal stopping problems

Financial derivatives commonly contain premature termination clauses, which are embedded rights held by the holder or writer. Well known examples of these stopping rights include the early exercise right in American options, the callable right in callable securities and the prepayment right in mortgage loans. In this paper, we show how to model the mortgagor's prepayment in mortgage loans and the issuer's call in the American warrant as an event risk using the intensity based approach, where the propensity of prepayment or calling is modeled by the intensity of a Poisson process. We illustrate that the corresponding pricing formulation resembles the penalty approximation approach commonly used in the solution of the linear complementarity formulation of an optimal stopping problem. We obtain several theoretical results on the prepayment strategies of mortgage loans and calling policies of American warrants. We also propose robust second order accurate numerical schemes for solving the penalty formulation of an optimal stopping problem.     

Chicago board call options as predictors of common stock price changes

The intent in this study is to determine, using response surface methodology, whether call option prices can be relied upon to predict future rises in common stock prices. If call option prices are bid up by insiders prior to the time that new information becomes available to stock traders, recognition of this price action could form the basis of a stock trading strategy yielding returns superior to buy and hold. Evidence of such an advantage would be inconsistent with the efficient market hypothesis.     

关于在中国上市公司实行雇员股票期权会计的思考

基于委托—代理理论研究的深入,雇员股票期权被作为一种对代理人的长期激励机制,在业界广泛采用,而关于雇员股票期权会计的研究,尚不成熟。从雇员股票会计的定义入手,结合我国新颁布的会计准则,给出了在我国实行雇员股票期权会计的新框架:确认、计量、记录及其报告,以作参考。     

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.     

The pricing of callable preferred stock

In this study, the authors use both the Black/Scholes European option model and the Barone-Adesi/Whaley American option model to estimate call option values implicit in seasoned callable preferred stock issues. Consistent with the finding that call features increase bond yields, a significant relationship is found between estimated option values and discounts of these securities’ market prices from their estimated income values. However, the size of the discount is only a fraction of what would be predicted by the American option model. Specifically, the market does not appear to take the “early exercise premium” into account. Furthermore, this discount seems to be isolated to in-the-money call features that have evolved to their final call price. Thus, incorporation of a call feature into a security’s indentures, with a deferment period and an initial premium call price, appears to represent a pure gain for the issuing corporation.     

Probability of multiple crossings and pricing of double barrier options

This paper derives pricing formulas of standard double barrier option, generalized window double barrier option and chained option. Our method is based on probabilitic approach. We derive the probability of multiple crossings of curved barriers for Brownian motion with drift, by repeatedly applying the Girsanov theorem and the reflection principle. The price of a standard double barrier option is presented as an infinite sum that converges very rapidly. Although the price formula of standard double barrier option is the same with Kunitomo and Ikeda (1992), our method gives an intuitive interpretation for each term in the infinite series. From the intuitive interpretation we present the way how to approximate the infinite sum in the pricing formula and an error bound for the given approximation. Guillaume (2003) and Jun and Ku (2013) assumed that barriers are constant to price barrier options. We extend constant barriers of window double barrier option and chained option to curved barriers. By employing multiple crossing probabilities and previous skills we derive closed formula for prices of 16 types of the generalized chained option. Based on our analytic formulas we compute Greeks of chained options directly.     

Backdating executive stock options—An ex ante valuation

When backdating executive stock options (ESOs), the exercise price is set in favor of the recipient executive. Relative to a non-backdated benchmark, we find an (ex ante) upper bound for the cost of backdating to shrink from 10% to about 3.7%, as a consequence of the regime change represented by the Sarbanes-Oxley act (SOX).We frame the backdating behavior as a (compound) exotic option, considering both simple and extended models of the underlying ESO—in the latter case we draw on the analytical ESO models of Sircar and Xiong (2007). Post-SOX, we use a Longstaff-Schwartz inspired least squares Monte Carlo approach.     

The valuation of American barrier options using the decomposition technique

In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call ‘symmetry’ relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options. Our implementation of the obtained solution indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and efficiency. In particular, the method is free of the difficulty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.     

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。     

Is the nonlinear hedge of options more effective?—Evidence from the SSE 50 ETF options in China

The linear hedging of the options ignores the characteristic of the nonlinear change of option prices with the underlying asset. This paper establishes the nonlinear hedging strategy followed the study by Hull and White (2017) to investigate the effectiveness on the Shanghai Stock Exchange (SSE) 50 ETF options. The results show that the nonlinear hedge of the Chinese option market is less effective than the U.S option market because of the short history and the lower activity of the Chinese option market. The effect of nonlinear hedging strategy is better than the linear hedging strategy for calls in China. But for puts, the effect of the nonlinear hedging strategy is not as significant as it for calls. The difference in the trading volume between calls and puts and the high short-selling cost in the Chinese market are the main factors leading to the difference in hedge effectiveness. This paper suggests that the stock exchange could reduce margin standard of 50 ETF securities lending, promote a more flexible shorting mechanism, and accelerate the process of index options listed, so as to achieve hedging the risk of options more directly and efficiently.     

Pricing executive stock options under employment shocks

We obtain explicit expressions for the subjective, objective and market value of perpetual executive stock options (ESOs) under exogenous employment shocks driven by an independent Poisson process. Previously, we obtain the executive's optimal exercise policy from the subjective valuation that is necessary for the objective one, or fair value. The perpetual ESO is compared with the true finite maturity ESO finding that the approximation is reasonably good. To illustrate the usefulness of the objective valuation for accounting purposes, we analyze the statistical distribution of the fair value when there is uncertainty about the employment shock intensity. Finally, the role of ESOs in the design of executives’ incentives is also discussed.     

Optimal capital accumulation under price uncertainty and costly reversibility

We consider the optimal capital accumulation policy of a competitive firm operating in the presence of decreasing returns to scale, price uncertainty, and costly reversibility of investment. We characterize the optimal accumulation policy and derive the value of the firm by focusing on the marginal investment decision and solving the associated optimal timing problem characterizing the option value of the associated opportunity to either disinvest or acquire a marginal unit of capacity. We also characterize the required exercise premia associated with the optimal policies and demonstrate that hysteresis prevails within this class of accumulation problems as well.     

Risk, uncertainty, and option exercise

Many economic decisions can be described as an option exercise or optimal stopping problem under uncertainty. Motivated by experimental evidence such as the Ellsberg Paradox, we follow Knight (1921) and distinguish risk from uncertainty. To capture this distinction, we adopt the multiple-priors utility model. We show that the impact of ambiguity on the option exercise decision depends on the relative degrees of ambiguity about continuation payoffs and termination payoffs. Consequently, ambiguity may accelerate or delay option exercise. We apply our results to investment and exit problems, and show that the myopic NPV rule can be optimal for an agent having an extremely high degree of ambiguity aversion.     

Optimal corporate hedging using options with basis and production risk

We investigate the optimal hedging strategy for a firm using options, where the role of production and basis risk are considered. Contrary to the existing literature, we find that the exercise price which minimizes the shortfall of the hedged portfolio is primarily affected by the amount of cash spent on the hedging. Also, we decompose the effect of production and basis risk showing that the former affects hedging effectiveness while the latter drives the choice of the optimal contract. Fitting the model parameters to match a financial turmoil scenario confirms that suboptimal option moneyness leads to a non-negligible economic loss.     

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.