Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence

American options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2009) from 1983 to 2006 are identified as potentially profitable trades. Call bid prices more frequently violate their upper bound than put bid prices do, while violations of the lower bounds by ask prices are infrequent. In out‐of‐sample tests of stochastic dominance, the writing of options that violate the upper bound increases the expected utility of any risk‐averse investor holding the market and cash, net of transaction costs and bid‐ask spreads. The results are economically significant and robust.     

Shedding light on a dark matter: Jump diffusion and option-implied investor preferences

We compare equilibrium jump diffusion option prices with endogenously determined stochastic dominance (SD) option bounds. We use model parameters from earlier studies and find that most equilibrium model prices consistent with SD bounds yield economically meaningless results. Further, the implied distributions of the SD bounds exhibit a tail risk comparable to that of the underlying return data, thus shedding light on the dark matter of the inconsistency of physical and risk-neutral tail probabilities. Since the SD bound assumptions are weaker, we conclude that these bounds should either replace or be used to verify the equilibrium model results.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

Option Bounds with Finite Revision Opportunities

This article generalizes the single-period linear-programming bounds on option prices by allowing for a finite number of revision opportunities. It is shown that, in an incomplete market, the bounds on option prices can be derived using a modified binomial option-pricing model. Tighter bounds are developed under more restrictive assumptions on probabilities and risk aversion. For this case the upper bounds are shown to coincide with the upper bounds derived by Perrakis, while the lower bounds are shown to be tighter.     

Option Pricing Bounds and the Elasticity of the Pricing Kernel

In this paper we use power functions as pricing kernels to derive option-pricing bounds. We derive option pricing bounds given the bounds of the elasticity of the true pricing kernel. The bounds of the elasticity of the true pricing kernel are closely related to the bounds of the representative investor's coefficient of relative risk aversion. This methodology produces a tighter upper call option bound than traditional approaches. As a special case we show how to use the Black–Scholes formula to obtain option pricing bounds under the assumption of lognormality.     

General closed-form basket option pricing bounds

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms; hence, they do not suffer from the curse of dimensionality and can be applied also to high-dimensional problems where most existing methods fail. In particular, we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate.     

Non-parametric method for European option bounds

There is much research whose efforts have been devoted to discovering the distributional defects in the Black–Scholes model, which are known to cause severe biases. However, with a free specification for the distribution, one can only find upper and lower bounds for option prices. In this paper, we derive a new non-parametric lower bound and provide an alternative interpretation of Ritchken’s (J Finance 40:1219–1233, 1985) upper bound to the price of the European option. In a series of numerical examples, our new lower bound is substantially tighter than previous lower bounds. This is prevalent especially for out of the money options where the previous lower bounds perform badly. Moreover, we present how our bounds can be derived from histograms which are completely non-parametric in an empirical study. We discover violations in our lower bound and show that those violations present arbitrage profits. In particular, our empirical results show that out of the money calls are substantially overpriced (violate the lower bound).     

Stochastic Dominance Bounds on American Option Prices in Markets with Frictions

We derive equilibrium restrictions on the range of the transactionprices of American options on the stock market index and indexfutures. Trading over the lifetime of the options is accountedfor, in contrast to earlier single-period results. The boundson the reservation purchase price of American puts and the reservationwrite price of American calls are tight. We allow the marketto be incomplete and imperfect due to the presence of proportionaltransaction costs in trading the underlying security and dueto bid-ask spreads in option prices. The bounds may be derivedfor any given probability distribution of the return of theunderlying security and admit price jumps and stochastic volatility.We assume that at least some of the traders maximize a time-separable utility function. The bounds are derived by applyingthe weak notion of stochastic dominance and are independentof a trader's particular utility function and initial portfolioposition.     

Universal bounds for asset prices in heterogeneous economies

We establish universal bounds for asset prices in heterogeneous complete market economies with scale invariant preferences. Namely, for each agent in the economy we consider an artificial homogeneous economy populated solely by this agent, and calculate the “homogeneous” price of an asset in each of these economies. Dumas (Rev. Financ. Stud. 2, 157–188, [1989]) conjectured that the risk free rate in a heterogeneous economy must lie in the interval determined by the minimal and maximal of the “homogeneous” risk free rates. We show that the answer depends on the risk aversions of the agents in the economy: the upper bound holds when all risk aversions are smaller than one, and the lower bound holds when all risk aversions are larger than one. The bounds almost never hold simultaneously. Furthermore, we prove these bounds for arbitrary assets.      

Option Bounds and the Pricing of the Volatility Smile

This paper presents a new approach forthe estimation of the risk-neutral probability distribution impliedby observed option prices in the presence of a non-horizontalvolatility smile. This approach is based on theoretical considerationsderived from option pricing in incomplete markets. Instead ofa single distribution, a pair of risk-neutral distributions areestimated, that bracket the option prices defined by the volatilitybid/ask midpoint. These distributions define upper and lowerbounds on option prices that are consistent with the observableoption parameters and are the tightest ones possible, in thesense of minimizing the distance between the option upper andlower bounds. The application of the new approach to a sampleof observations on the S&P 500 option market showsthat the bounds produces are quite tight, and also that theirderivation is robust to the presence of violations of arbitragerelations in option quotes, which cause many other methods tofail.     

A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk.As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. The q-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q.JEL Classification: D52, G13     

风险喜好型零售商主导的双渠道定价策略研究(英文)

针对由一个风险喜好的零售商和一个风险规避的供应商组成的两层双渠道供应链,本文研究了当零售商在供应链中占主导地位情况下,双渠道中参与者的风险偏好程度和需求方差变化对其定价决策的影响。研究表明,随着零售商风险喜好程度的增加,零售渠道最优定价会减小;当零售商风险喜好达到一定程度时,随着需求方差的增长零售渠道最优定价才会提高。最后用一个算例验证了结论。     

Binomial option pricing with stochastic parameters: A beta distribution approach

This research extends the binomial option-pricing model of Cox, Ross, and Rubinstein (1979) and Rendleman and Barter (1979) to the case where the up and down percentage changes of stock prices are stochastic. Assuming stochastic parameters in the discrete-time binomial option pricing is analogous to assuming stochastic volatility in the continuous-time option pricing. By assuming that the up and down parameters are independent random variables following beta distributions, we are able to derive a closed-form solution to this stochastic discrete-time option pricing. We also derive an upper and a lower bounds of the option price.     

Tight bounds on American option prices

In contrast to the constant exercise boundary assumed by Broadie and Detemple (1996) [Broadie, M., Detemple, J., 1996. American option valuation: New bounds, approximations, and comparison of existing methods. Review of Financial Studies 9, 1211–1250], we use an exponential function to approximate the early exercise boundary. Then, we obtain lower bounds for American option prices and the optimal exercise boundary which improve the bounds of Broadie and Detemple (1996). With the tight lower bound for the optimal exercise boundary, we further derive a tight upper bound for the American option price using the early exercise premium integral of Kim (1990) [Kim, I.J., 1990. The analytic valuation of American options. Review of Financial Studies 3, 547–572]. The numerical results show that our lower and upper bounds are very tight and can improve the pricing errors of the lower bound and upper bound of Broadie and Detemple (1996) by 83.0% and 87.5%, respectively. The tightness of our upper bounds is comparable to some best accurate/efficient methods in the literature for pricing American options. Moreover, the results also indicate that the hedge ratios (deltas and gammas) of our bounds are close to the accurate values of American options.     

Disasters Implied by Equity Index Options

We use equity index options to quantify the distribution of consumption growth disasters. The challenge lies in connecting the risk‐neutral distribution of equity returns implied by options to the true distribution of consumption growth. First, we compare pricing kernels constructed from macro‐finance and option‐pricing models. Second, we compare option prices derived from a macro‐finance model to those we observe. Third, we compare the distribution of consumption growth derived from option prices using a macro‐finance model to estimates based on macroeconomic data. All three perspectives suggest that options imply smaller probabilities of extreme outcomes than have been estimated from macroeconomic data.     

The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile

Value-at-risk (VaR) has become the standard criterion for assessing risk in the financial industry. Given the widespread usage of VaR, it becomes increasingly important to study the effects of VaR based risk management on the prices of stocks and options. We solve a continuous-time asset pricing model, based on Lucas (1978) and Basak and Shapiro (2001), to investigate these effects. We find that the presence of risk managers tends to reduce market volatility, as intended. However, in some cases VaR risk management undesirably raises the probability of extreme losses. Finally, we demonstrate that option prices in an economy with VaR risk managers display a volatility smile.     

Binomial Option Pricing Biases and Inconsistent Implied Volatilities

We evaluate the binomial option pricing methodology (OPM) by examining simulated portfolio strategies. A key aspect of our study involves sampling from the empirical distribution of observed equity returns. Using a Monte Carlo simulation, we generate equity prices under known volatility and return parameters. We price American–style put options on the equity and evaluate the risk–adjusted performance of various strategies that require writing put options with different maturities and moneyness characteristics. The performance of these strategies is compared to an alternative strategy of investing in the underlying equity. The relative performance of the strategies allows us to identify biases in the binomial OPM leading to the well–known volatility smile . By adjusting option prices so as to rule out dominated option strategies in a mean–variance context, we are able to reduce the pricing errors of the OPM with respect to option prices obtained from the LIFFE. Our results suggest that a simple recalibration of inputs may improve binomial OPM performance.     

Cross-sectional tests of deterministic volatility functions

We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a corresponding panel of American style options. We find that the implied binomial tree model performs no better than an ad-hoc procedure of smoothing Black–Scholes implied volatilities across strike prices and maturities. Our cross-sectional results complement the time-series findings of Dumas et al. [J. Finance 53 (1998) 2059].     

Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities

In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst Value-at-Risk of the total risk. Using the idea of complete mixability, we provide a new lower bound for any given marginal distributions and give a necessary and sufficient condition for the sharpness of this new bound. For the sum of dependent risks with an identical distribution, which has either a monotone density or a tail-monotone density, the explicit values of the worst Value-at-Risk and bounds on the distribution of the total risk are obtained. Some examples are given to illustrate the new results.