A direct solution method for pricing options in regime‐switching models

Pricing financial or real options with arbitrary payoffs in regime‐switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime‐switching models. In this article, we reduce an optimal stopping problem with an arbitrary value function in a two‐regime environment to a pair of optimal stopping problems without regime switching. We then propose a method for finding optimal stopping rules using the techniques available for nonswitching problems. In contrast to other methods, our systematic solution procedure is more direct as we first obtain the explicit form of the value functions. In the end, we discuss an option pricing problem, which may not be dealt with by the conventional methods, demonstrating the simplicity of our approach.     

Analytical valuation of Asian options with counterparty risk under stochastic volatility models

In this paper, we consider Asian options with counterparty risk under stochastic volatility models. We propose a simple way to construct stochastic volatility models through the market factor channel. In the proposed framework, we obtain an explicit pricing formula of Asian options with counterparty risk and illustrate the effects of systematic risk on Asian option prices. Specially, the U-shaped and inverted U-shaped curves appear when we keep the total risk of the underlying asset and the issuer's assets unchanged, respectively.     

Pricing European-type,early-exercise and discrete barrier options using an algorithm for the convolution of Legendre series

This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend, An algorithm for the convolution of Legendre series. SIAM J. Sci. Comput., 2014, 36, A1207–A1220), to pricing European-type, early-exercise and discrete-monitored barrier options under a Lévy process. The paper employs Chebfun (cf. Trefethen et al., Chebfun Guide, 2014 (Pafnuty Publications: Oxford), Available online at: http://www.chebfun.org/) in computational finance and provides a quadrature-free approach by applying the Chebyshev series in financial modelling. A significant advantage of using the CONLeg method is to formulate option pricing and option Greek curves rather than individual prices/values. Moreover, the CONLeg method can yield high accuracy in option pricing when the risk-free smooth probability density function (PDF) is smooth/non-smooth. Finally, we show that our method can accurately price options deep in/out of the money and with very long/short maturities. Compared with existing techniques, the CONLeg method performs either favourably or comparably in numerical experiments.     

Real options or disaster risk? Distinguishing uncertainty effects on investment

ABSTRACT

Motivated by the fact that uncertainty shocks are a countercyclical phenomenon, this article takes a deeper look at the nature of uncertainty shocks in times of crisis and its effect on the real economy. We distinguish between volatility and disaster risk shocks and specify the consequences of these shock specifications on investment decisions. We first analyse the different impact of both shocks within a real options framework. Our theoretical results show that the effects of the two shocks are different, especially concerning disinvestment and the mid-term investment response. Second, we perform structural vector autoregression (SVAR) estimations on different country data sets. The SVAR estimations confirm our theoretical hypothesis: countries more prone to states of disaster do not show the usual real option pattern of investment to an uncertainty shock.     

What Does the CAPM Say About Operating Leverage?

We examine the issue of operating leverage and firm value. Johnstone (2020), in this issue, questions existing results which indicate that higher operating leverage results in lower firm value. We agree with Johnstone (2020) that this result is to be questioned and present a number of arguments which indicate that operating leverage is irrelevant to the valuation of the firm in the context of the CAPM model.     

Pricing VIX options with volatility clustering

We investigate the valuation of volatility index (VIX) options by developing a model with a self-exciting Hawkes process that allows for clustering in the VIX. In the proposed framework, we find semianalytical expressions for the characteristic function and forward characteristic function, and then we solve the pricing problem of standard-start and forward-start options via the fast Fourier transform. The empirical results provide evidence to support the significance of accounting for volatility clustering when pricing VIX options.     

Stock options,restricted stock,salary, or bonus? Managing CEO compensation to maximize organizational performance

CEO pay has gone through remarkable changes over the past two decades. The most striking new features have been the increased use of stock options in the early 2000s, and of restricted stock since then. Both forms of stock-based compensation are intended to resolve the agency problem that occurs when CEOs do not act in the best interests of stockholders, but each has its advantages and limitations. In this instalment of Organizational Performance, we discuss the history of their use and similarities and differences between the two, and argue that both are often overused. Bonuses based on strategic goals, on the other hand, may be underused. We conclude with a contextual approach to guide boards of directors in making choices among the forms of CEO compensation—stock options, restricted stock, salary, and bonus—to incentivize CEOs to work toward maximizing organizational performance. Briefly, stock options are most appropriate for growth firms, and restricted stock for stable firms. Both forms of stock-based compensation are more appropriate for new than for long-tenured CEOs.     

A smiling bear in the equity options market and the cross-section of stock returns

We propose a measure for the convexity of an option-implied volatility curve, IV convexity, as a forward-looking measure of risk-neutral tail-risk contribution to the perceived variance of underlying equity returns. Using equity options data for individual US-listed stocks during 2000–2013, we find that the average realized return differential between the lowest and highest IV convexity quintile portfolios exceeds 1% per month, which is both economically and statistically significant on a risk-adjusted basis. Our empirical findings indicate the contribution of informed options trading to price discovery in terms of the realization of tail-risk aversion in the stock market.     

Singular Fourier–Padé series expansion of European option prices

We apply a new numerical method, the singular Fourier–Padé (SFP) method invented by Driscoll and Fornberg [Numer. Algorithms, 2001, 26, 77–92; The Gibbs Phenomenon in Various Representations and Applications, 2011], to price European-type options in Lévy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecewise continuous (non-smooth) probability density functions. When techniques such as fast Fourier transforms and Fourier series are applied to price and hedge options with non-smooth probability density functions, they cause the Gibbs phenomenon; accordingly, the techniques converge slowly for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. Moreover, we show that our method requires a small number of terms to yield fast error convergence, and it is able to accurately price any European-type option deep in/out of the money and with very long/short maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This new method performs favourably in numerical experiments compared with existing techniques.