Review of Derivatives Research最新文献

This paper examines the risk incentives of traditional and non-traditional call options in the context of a levered firm where managers under-invest due to risk aversion. Our results contrast with those presented in the literature inasmuch as lookback calls do not always induce higher risk taking than regular calls, and managers always prefer a combination of regular calls and shares of stock in their compensation package as opposed to only company shares. We also show that Asian options outperform both plain-vanilla and other nonstandard options in inducing higher risk taking and, thereby, are a superior remedy for alleviating the agency costs of deviating from the optimal volatility level. Finally, we shed new insights that better clarify the incorrect arguments found in the literature regarding the delta of regular and lookback calls.

I propose an affine model of short rates that incorporates a random walk with stochastic drift. This framework enables my model to capture the behavior of monetary authorities in the short rate market, allowing for minor deviations while reacting strongly to deviations large enough to threaten production. Importantly, my model facilitates the derivation of closed-form bond prices, thereby providing an analytical solution for bond-option prices. I compare my model with nine standard short rate models found in the literature. Among these, five are single-factor models and four are multifactor models. Remarkably, my model outperforms all competing short rate models, including the constant elasticity of volatility, stochastic mean, and stochastic volatility models. Moreover, it yields interest rate forecasts consistent with common term structure priors and surpasses the performance of the naive random walk model. Additionally, my stochastic mean model can explain the unspanned risks documented in the literature.

We propose a general structural model for valuing risky corporate debt securities within a two-dimensional framework. The state variables in our model include the firm’s asset value, described as a geometric Brownian motion stochastic process, and the short-term interest rate, following a mean-reverting Ornstein–Uhlenbeck stochastic process. Our model accommodates flexible debt structure, multiple seniority classes, tax benefits, bankruptcy costs, and a stochastic endogenous default barrier. The proposed methodology relies on a two-dimensional dynamic program coupled with finite elements where key transition parameters are computed in closed form, and effective approximations using local interpolations are made during backward recursion. Our design incorporates space discretization without imposing time discretization, which is advantageous, particularly in the valuation of corporate bonds where exercise opportunities are often distant. Our methodology distinguishes itself by assuming a numerical error, setting it apart from statistical methods. Together, the above features establish dynamic programming coupled with finite elements as a competitive valuation approach as compared to its counterparts in the existing literature. We use parallel computing to enhance the efficiency of our methodology. We conduct a numerical and and an empirical investigation, both of which show consistency with several empirical evidence documented in the literature.

The martingale theory of bubbles enables testing for asset price bubbles by analyzing option prices. As recently shown by Piiroinen et al. (Asset price bubbles: an option-based indicator, 2018), the SABR model is a strict local martingale when its parameterization implies a positive correlation between stock and option prices. We operationalize this theoretical result and analyze stock price bubbles in 2576 stocks over 26 years. Martingale defect conditions are absorbed quickly by options markets, but identify high proportions in significant and permanent changes in distribution of price returns, option trading activity, short interest in the underlying, and institutional ownership. These results confirm many common assumptions about stock price bubbles. These bubbles are temporally clustered, and tend to occur in periods of positive market development. Martingale defects are rare in market corrections, which indicates that they are a result of overoptimistic speculation.

Abstract

Much of the work on the valuation of levered (and unlevered) warrants assumes that the volatility of the underlying state variable is constant. This paper extends the literature on warrant pricing to a more general assumption for the state variable process, the so-called constant elasticity of variance (CEV) process. The CEV model is well-known for its ability to capture some empirical observations found in the financial economics literature, namely the asymmetry between equity returns and volatility and the implied volatility skew. Using the CEV process, we are able to reduce pricing bias as the volatility becomes a function of the underlying state variable. We price European-style call warrants without restrictions on the debt maturity. When warrants have the same maturity as debt, it is possible to obtain closed-form solutions for warrants prices. When the maturity of warrants is different from the maturity of debt, prices can be computed numerically through very efficient and simple to implement valuation methodologies.

Most empirical studies show that three factors are sufficient to explain all the relevant uncertainties inherent in option prices. In this paper, we consider a three-factor CIR model exhibiting unspanned stochastic volatility (USV), which means that it is impossible to fully hedge volatility risk with portfolios of bonds or swaps. The incompleteness of bond markets is necessary for the existence of USV. Restrictions on the model parameters are needed for incompleteness. We provide necessary and sufficient conditions for a three-factor CIR model that generates incomplete bond markets. Bond prices are exponential affine functions of only the two term-structure factors, independent of the unspanned factor. With our three-factor CIR model exhibiting USV, we derive the dynamic form of bond futures prices. By introducing the exponential solution of a transform and using the Fourier inversion theorem, we obtain a closed-form solution for the European zero-coupon option prices. The pricing method is efficient for taking into account the existence of unspanned stochastic volatility.

In order to estimate volatility-dependent probability weighting functions, we obtain risk neutral and physical densities from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) stochastic volatility and jumps model. Across volatility levels, we find pronounced inverse S-shapes, i.e. small probabilities are overweighted, and probability weighting almost monotonically increases in volatility, indicating higher skewness preferences and crash aversion in volatile market environments. Moreover, by estimating probabilistic risk attitudes, equivalent to the share of risk aversion related to probability weighting, we shed further light on the pricing kernel puzzle. While pricing kernels estimated from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) model display the typical U-shape as documented in the literature, pricing kernels—net of probability weighting—are strictly monotonically decreasing and thus in line with economic theory. Equivalently, we find risk aversion to be positive across wealth levels. Our results are robust to alternative maturities, wealth percentiles, alternative functional forms, a nonparametric empirical setting and variations of the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) coefficient estimates.