Hedging and pricing early-exercise options with complex fourier series expansion

We introduce a new numerical method called the complex Fourier series (CFS) method proposed by Chan (2017) to price options with an early-exercise feature—American, Bermudan and discretely monitored barrier options—under exponential Lévy asset dynamics. This new method allows us to quickly and accurately compute the values of early-exercise options and their Greeks. We also provide an error analysis to demonstrate that, in many cases, we can achieve an exponential convergence rate in the pricing method as long as we choose the correct truncated computational interval. Our numerical analysis indicates that the CFS method is computationally more comparable or favourable than the methods currently available. Finally, the superiority of the CFS method is illustrated with real financial data by considering Standard & Poor’s depositary receipts (SPDR) exchange-traded fund (ETF) on the S&P 500® index options, which are American options traded from November 2017 to February 2018 and from 30 January 2019 to 21 June 2019.     

CEO career horizon,corporate governance,and real options: The role of economic short‐termism

Research Summary: Combining studies on real options theory and economic short‐termism, we propose that, depending on CEOs’ career horizons, CEOs have heterogeneous interests in strategic flexibility, and thus, have different incentives to make real options investments. We argue that compared to CEOs with longer career horizons, CEOs with shorter career horizons will be less inclined to make real options investments because they may not fully reap the rewards during their tenure. In addition, we argue that long‐term incentives and institutional ownership will mitigate the relationship between CEOs’ career horizons and real options investments. U.S. public firms as an empirical setting produced consistent evidence for our predictions. Our study is the first to theoretically explain and empirically show that a CEO's self‐seeking behavior will impact real options investments. Managerial Summary: This article helps to explain how a CEO's self seeking‐behavior may shape a firm's real option investment, which could result in different level of strategic flexibility. We argue that CEOs with short career horizons have less time to exercise their firms’ real options, which should lower the investments in the firms’ real options portfolios relative to CEOs with long career horizons. We study a sample of U.S. public firms and find strong evidence that a CEO's expected tenure in the firm is positively related to the real options investments at the firm level. We find that this agency issue can be mitigated by adopting appropriate corporate governance mechanisms such as long‐term incentives and institutional investors.     

Irreversible investment,ambiguity and equity default swaps

We study the impact of ambiguity on the pricing and timing of the option to invest. There is a funding gap to undertake the investment, which is covered by entering into an equity-for-guarantee swap. Our model predicts that the more ambiguity-averse the agents, the less the option value, the later the investment and the higher the guarantee cost and the leverage. If the entrepreneur is more ambiguity-averse than the insurer, the investment threshold slightly rises as the perceived ambiguity increases, and on the contrary, if the entrepreneur is less ambiguity-averse than the insurer, the investment threshold increases sharply as the perceived ambiguity rises.     

The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework

We consider a modeling setup where the volatility index (VIX) dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed‐form expansions and sharp error bounds for VIX futures, options, and implied volatilities. In particular, we derive exact asymptotic results for VIX‐implied volatilities, and their sensitivities, in the joint limit of short time‐to‐maturity and small log‐moneyness. The expansions obtained are explicit based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol‐of‐vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has previously been adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications.     

Do firms lease to hedge? CEO risk-taking and operating lease intensity

Operating leases are used extensively for financing, but their ability to separate ownership and use also creates hedging opportunities. We investigate whether firms recognize such opportunities by examining the relation between chief executive officer (CEO) risk-taking incentives and the use of operating leases. Consistent with firms using operating leases to hedge, we find higher CEO risk-taking incentives lower operating lease intensity. To address endogeneity, we use the adoption of Statement of Financial Accounting Standards 123R as an exogenous shock to option compensation, dynamic panel generalized method of moments, simultaneous equations, and change regressions. Our results are robust to placebo and alternative tests.     

Financing Technological Innovation: Evidence from Patent-Intensive Firms

ABSTRACT

Equityholders of firms with high debt loads have an incentive to underinvest, a distortion that can be most costly for firms with attractive growth options. Using a novel patent-based measure of a firm's growth options, we find that firms issue more equity and shy away from debt financing when they have larger investment opportunities sets. The results are more pronounced among firms in patent-intensive industries. The findings suggest the existence of conflicts of interest between debtholders and equityholders. Our results are consistent with the use of conservative debt policies by technology-intensive firms to mitigate the debt overhang associated with their future growth options.     

Extendible stock loan

In this paper, the model of extendible stock loan with forbearance is proposed. The loan is extendible, so as to prevent immediate losses or to prevent subsequent price drop; while the forbearance is granted only when the pledged share’s value is above threshold, so as to mitigate the risk-taking behavior induced by the extension. The non-synchronization of the liquidation of insolvent stock loans also alleviates the downward leverage spiral in a market downturn. Numerical analysis shows that fair extendible stock loan rates increase with the forbearance level as well as extension period, and loan rates are quite sensitive to the change of asset volatility and debt ratio. For lenders waiving the interest rates during extension period, their burden grows with extension rapidly when they grant looser forbearance and when asset volatility or loan-to-value is higher. Some suggestions are made accordingly. First, lenders offering uniform extendible loan rate can let borrowers choose between looser forbearance with shorter extension, or tighter forbearance with longer extension. Second, if the loan rate is priced fairly, lower margin requirement can only be accomplished with tighter forbearance. More looser forbearance worth higher rates.     

Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm

In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete‐ and continuous‐time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete‐time case the WSM algorithm leads to semitractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by with being the dimension of the underlying Markov chain. Furthermore, we study the WSM approach in the context of continuous‐time optimal stopping problems and derive the corresponding complexity bounds. Although we cannot prove semitractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example.     

Expanding airport capacity of cities under uncertainty: Strategies to mitigate congestion

Airport capacity constraints are increasingly challenging the growth of air traffic. At the same time, decision-making about airport capacity investments is extremely complex, involving trade-offs. This paper’s objective is to optimise a privately owned airport system’s capacity investment decision in a city under demand uncertainty. Next to the investment size, our real options model incorporates the timing of the investment, as well as the cost of congestion. The results reveal that the larger a city’s initial airport capacity, the smaller its investment will relatively be and the lower the occupancy rate threshold at which investment will take place. We also show that, in case of a higher demand growth combined with more demand uncertainty, the city will benefit from a significantly larger investment, but made later at a higher occupancy rate. In this case, cities with a small initial capacity will sometimes even more than double current capacity. Higher airport charges and an increase in non-aeronautical revenues both lead to a later investment in more capacity, due to the increased project attractiveness. An increase in congestion costs results in a larger investment made earlier, in order to eliminate delays. Airport operational cost and capacity holding cost increases both lead to smaller investments.     

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.