Static hedging and pricing American options

This paper utilizes the static hedge portfolio (SHP) approach of Derman et al. [Derman, E., Ergener, D., Kani, I., 1995. Static options replication. Journal of Derivatives 2, 78–95] and Carr et al. [Carr, P., Ellis, K., Gupta, V., 1998. Static hedging of exotic options. Journal of Finance 53, 1165–1190] to price and hedge American options under the Black-Scholes (1973) model and the constant elasticity of variance (CEV) model of Cox [Cox, J., 1975. Notes on option pricing I: Constant elasticity of variance diffusion. Working Paper, Stanford University]. The static hedge portfolio of an American option is formulated by applying the value-matching and smooth-pasting conditions on the early exercise boundary. The results indicate that the numerical efficiency of our static hedge portfolio approach is comparable to some recent advanced numerical methods such as Broadie and Detemple [Broadie, M., Detemple, J., 1996. American option valuation: New bounds, approximations, and a comparison of existing methods. Review of Financial Studies 9, 1211–1250] binomial Black-Scholes method with Richardson extrapolation (BBSR). The accuracy of the SHP method for the calculation of deltas and gammas is especially notable. Moreover, when the stock price changes, the recalculation of the prices and hedge ratios of the American options under the SHP method is quick because there is no need to solve the static hedge portfolio again. Finally, our static hedging approach also provides an intuitive derivation of the early exercise boundary near expiration.     

“Extended Black” term structure models

This paper examines “Extended Black” term structure models (EBTSM), which are multi-factor extensions of the one-factor Black model (Black, F., 1995. Interest rates as options. Journal of Finance 50, 1371-1376). EBTSM are not affected by the admissibility restrictions that plague canonical affine models. EBTSM encompass quadratic models, but unlike in quadratic models bond yields are sufficient statistics to infer the latent factors driving the short interest rate. EBTSM are amenable to econometric estimation despite the need to solve bond pricing equations through finite difference numerical methods. Estimation through the Iterated Extended Kalman filter reveals that a two-factor EBTSM fit well the observed cross section and time series of Japanese Government bond yields. A three-factor EBTSM is also proposed.     

No-arbitrage conditions for storable commodities and the modeling of futures term structures

One distinguishable feature of storable commodities is that they relate to two markets: cash market and storage market. This paper proves that, if no arbitrage exists in the storage-cash dual markets, the commodity convenience yield has to be non-negative. However, classical reduced-form models for futures term structures could allow serious arbitrages due to the high volatility of the convenience yield. To avoid negative convenience yield, this paper proposes a semi-affine arbitrage-free model, which prices futures analytically and fits futures term structures reasonably well. Importantly, our model prices commodity-related contingent claims (such as calendar spread options) quite differently with classical models.     

A generalization of reset options pricing formulae with stochastic interest rates

A generalization of reset call options with predetermined dates is derived in the case of time-dependent volatility and time-dependent interest rate by applying martingale method and change of nume?aire or change of probability measure. An analytical pricing formula for the reset call option is also obtained when the interest rate follows an extended Vasicek’s model. Numerical results show that the correlated coefficient between the stock price and interest rate is almost unacted on the price of reset call option with short maturity and Monte Carlo method is inefficient. Monte Carlo method should be only used if there is no closed-formed solution for option pricing.     

The term structure of illiquidity premia

We investigate the term structure of bond market illiquidity premia and show that the term structure varies greatly over time. Short and long end are strictly separated suggesting that different economic factors drive different parts of the term structure. We propose a stylized theoretical model which implies that current trading needs of investors determine the short end. The long-term risk of being forced to liquidate bond positions determines the long end. Empirical evidence supports these predictions. While short-term liquidation risk captured by asset market volatilities drives the short end, the long end depends on the long-term economic outlook.     

Empirical evaluation of asset pricing models: Arbitrage and pricing errors in contingent claims

Hansen and Jagannathan (1997) have developed two measures of pricing errors for asset-pricing models: the maximum pricing error in all static portfolios of the test assets and the maximum pricing error in all contingent claims of the assets. In this paper, we develop simulation-based Bayesian inference for these measures. While the literature reports that the time-varying extensions substantially reduce pricing errors of classic models on the standard test assets, our analysis shows that the reduction is much smaller based on the second measure. Those time-varying models have large pricing errors on the contingent claims of the test assets because their stochastic discount factors are often negative and admit arbitrage opportunities.     

Asymmetric effect of basis on dynamic futures hedging: Empirical evidence from commodity markets

The dynamic minimum variance hedge ratios (MVHRs) have been commonly estimated using the Bivariate GARCH model that overlooks the basis effect on the time-varying variance–covariance of spot and futures returns. This paper proposes an alternative specification of the BGARCH model in which the effect is incorporated for estimating MVHRs. Empirical investigation in commodity markets suggests that the basis effect is asymmetric, i.e., the positive basis has greater impact than the negative basis on the variance and covariance structure. Both in-sample and out-of-sample comparisons of the MVHR performance reveal that the model with the asymmetric effect provides greater risk reduction than the conventional models, illustrating importance of the asymmetric effect when modeling the joint dynamics of spot and futures returns and hence estimating hedging strategies.     

Inference in asset pricing models with a low-variance factor

This paper concerns with the effects of including a low-variance factor in an asset pricing model. When a low-variance factor is present, the commonly applied Fama–MacBeth two-pass regression procedure is very likely to yield misleading results. Local asymptotic analysis and simulation evidence indicate that the risk premiums corresponding to all factors are very likely to be unreliably estimated. Moreover, t- and F-statistics are less likely to detect whether the risk premiums are significantly different from zero. We recommend Kleibergen’s (2009)FAR statistic when there is a low-variance factor included in an asset pricing model.     

Tactical allocation in commodity futures markets: Combining momentum and term structure signals

This paper examines the combined role of momentum and term structure signals for the design of profitable trading strategies in commodity futures markets. With significant annualized alphas of 10.14% and 12.66%, respectively, the momentum and term structure strategies appear profitable when implemented individually. With an abnormal return of 21.02%, our double-sort strategy that exploits both momentum and term structure signals clearly outperforms the single-sort strategies. This double-sort strategy can additionally be utilized as a portfolio diversification tool. The abnormal performance of the combined portfolios cannot be explained by a lack of liquidity, data mining or transaction costs.     

An FFT-network for Lévy option pricing

This paper develops a simple network approach to American exotic option valuation under Lévy processes using the fast Fourier transform (FFT). The forward shooting grid (FSG) technique of the lattice approach is then generalized to expand the FFT-network to accommodate path-dependent variables. This network pricing approach is applicable to all Lévy processes for which the characteristic function is readily available. In other words, the log-value of the underlying asset can follow finite-activity or infinite-activity Lévy processes. With the powerful computation of FFT, the proposed network has a negligible additional computational burden compared to the binomial tree approach. The early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach. Numerical examples using American-style barrier, lookback, and Asian options demonstrate that the FFT-network is accurate and efficient.     

Common asset pricing factors in volatilities and returns in futures markets

Factor-based asset pricing models have been used to explain the common predictable variation in excess asset returns. This paper combines means with volatilities of returns in several futures markets to explain their common predictable variation. Using a latent variables methodology, tests do not reject a single factor model with a common time-varying factor loading. The single common factor accounts for up to 53% of the predictable variation in the volatilities and up to 14% of the predictable variation in the means. S&P500 futures volatility predicted by the factor model is highly correlated with volatility implied in S&P500 futures options. But both the factor and implied volatilities are significant in predicting future volatility. In derivatives pricing, both implied volatility from options and factors extracted from asset pricing models should be employed.     

Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models

This paper demonstrates how to value American interest rate options under the jump-extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie et al., 2000) and lognormal jumps (see Johannes, 2004) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.     

Evaluation of linear asset pricing models by implied portfolio performance

We present a theoretical perspective that motivates the use of the Generalized Least Squares R-Square, prominently advocated by Lewellen et al. [Lewellen, J., Nagel, S., Shanken, J., forthcoming. A skeptical appraisal of asset-pricing tests. Journal of Financial Economics], as an evaluation measure for multivariate linear asset pricing models. Adapting results from Shanken [Shanken, J., 1985. Multivariate tests of the zero-beta CAPM. Journal of Financial Economics 14, 327–348] and Kandel and Stambaugh [Kandel, S., Stambaugh, R.F., 1995. Portfolio inefficiency and the cross-section of expected returns. Journal of Finance 50, 157–184], we provide various interpretations and a graphical account in mean-variance space of this measure, facilitating a better understanding of its properties. We furthermore relate it to another leading evaluation metric, the HJ-distance of Hansen and Jagannathan [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 557–590]. Additionally, we present a comparison between these evaluation measures using mean-variance mathematics in risk-return space, and we provide a simple formula for calculating both model evaluation measures that involves only the parameters of the mean-variance asset and factor frontiers.     

Capturing the risk premium of commodity futures: The role of hedging pressure

We construct long–short factor mimicking portfolios that capture the hedging pressure risk premium of commodity futures. We consider single sorts based on the open interests of hedgers or speculators, as well as double sorts based on both positions. The long–short hedging pressure portfolios are priced cross-sectionally and present Sharpe ratios that systematically exceed those of long-only benchmarks. Further tests show that the hedging pressure risk premiums rise with the volatility of commodity futures markets and that the predictive power of hedging pressure over cross-sectional commodity futures returns is different from the previously documented forecasting power of past returns and the slope of the term structure.     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

Asset pricing with Second-Order Esscher Transforms

The purpose of the paper is to introduce, in a discrete-time no-arbitrage pricing context, a bridge between the historical and the risk-neutral state vector dynamics which is wider than the one implied by a classical exponential-affine stochastic discount factor (SDF) and to preserve, at the same time, the tractability and flexibility of the associated asset pricing model. This goal is achieved by introducing the notion of exponential-quadratic SDF or, equivalently, the notion of Second-Order Esscher Transform. The log-pricing kernel is specified as a quadratic function of the factor and the associated sources of risk are priced by means of possibly non-linear stochastic first-order and second-order risk-correction coefficients. Focusing on security market models, this approach is developed in the multivariate conditionally Gaussian framework and its usefulness is testified by the specification and calibration of what we name the Second-Order GARCH Option Pricing Model. The associated European Call option pricing formula generates a rich family of implied volatility smiles and skews able to match the typically observed ones.     

Noise, equity prices, and hedging: A new approach

The existence of noise trading in equity markets has possible economic implications for arbitrage, and asset pricing. In terms of pricing, noise trading can lead to excess volatility which has been shown to influence the value of options and futures. Furthermore, option research shows that modeling volatility leads to improved hedging performance. To this end, we derive a general hedging model for equity index futures in the presence of noise trading. Our analysis shows how the level and dynamics of noise trading should influence a hedger's behavior. Finally, we empirically test our model using the NASDAQ-100 index futures and FTSE 100 index futures over the period of January 1998 to May 2003.     

Pricing and static hedging of American-style options under the jump to default extended CEV model

This paper prices (and hedges) American-style options through the static hedge approach (SHP) proposed by Chung and Shih (2009) and extends the literature in two directions. First, the SHP approach is generalized to the jump to default extended CEV (JDCEV) model of Carr and Linetsky (2006), and plain-vanilla American-style options on defaultable equity are priced. The robustness and efficiency of the proposed pricing solutions are compared with the optimal stopping approach offered by Nunes (2009), under both the JDCEV framework and the nested constant elasticity of variance (CEV) model of Cox (1975), using different elasticity parameter values. Second, the early exercise boundary near expiration is derived under the JDCEV model.     

Pinning in the S&P 500 futures

We show that Standard & Poor's (S&P) 500 futures are pulled toward the at-the-money strike price on days when serial options on the S&P 500 futures expire (pinning) and are pushed away from the cost-of-carry adjusted at-the-money strike price right before the expiration of options on the S&P 500 index (anti-cross-pinning). These effects are driven by the interplay of market makers' rebalancing of delta hedges due to the time decay of those hedges as well as in response to reselling (and early exercise) of in-the-money options by individual investors. The associated shift in notional futures value is at least $115 million per expiration day.