Option Pricing Using Variance Gamma Markov Chains

This paper proposes a Markov Chain between homogeneous Lévy processesas a candidate class of processes for the statistical and risk neutral dynamicsof financial asset prices. The method is illustrated using the variance gammaprocess. Closed forms for the characteristic function are developed and thisrenders feasible, series and option prices respectively. It is observed inthe statistical and risk neutral process is fit to data on time period of4 to 6 months in a state while this reduces to month for indices. Risk neutrallythere is generally a low probability of a move to a state with higher moments.In some cases this is reversed.     

On the estimation of location parameters in the multivariate one sample and two sample problems

Summary In this paper we consider the problem of estimating the vectors of location parameters in the multivariate one sample and two sample problems. These estimators are obtained through the use of the multivariate rank order statistics such as theWilcoxon or the normal scores statistic considered by the authors inPuri, Sen [1966] andSen, Puri [1967] for the corresponding testing problems. The distribution of these estimators is shown to be symmetric with respect to the parameters being estimated. These estimators are translation invariant, robust and asymptotically normal. Their asymptotic relative efficiencies with respect to the estimators based on the vector of means and medians are discussed by applying the criterion ofWilks generalized variance [Anderson, p. 166]. In particular, it is shown that the estimators based on the multivariate normal scores statistics are asymptotically as efficient as the ones based on the method of least squares when the parent distributions are normal. Research sponsored by National Science Foundation Grant No. GP-12462, and by Research Grant, GM-12868 from the N.I.H., Public Health Service.     

Returns of claims on the upside and the viability of U-shaped pricing kernels

When the pricing kernel is U-shaped, then expected returns of claims with payout on the upside are negative for strikes beyond a threshold, determined by the slope of the U-shaped kernel in its increasing region, and have negative partial derivative with respect to strike in the increasing region of the kernel. Using returns of (i) S&P 500 index calls, (ii) calls on major international equity indexes, (iii) digital calls, (iv) upside variance contracts, and (v) a theoretical construct that we denote as kernel call, we find broad support for the implications of U-shaped pricing kernels. A possible theoretical reconciliation of our empirical findings is explored through a model that accommodates heterogeneity in beliefs about return outcomes and short-selling.     

Demand for fish in Asia: a cross‐country analysis*

Fish demand patterns in nine Asian countries were investigated using a multistage budgeting framework allowing a disaggregated approach to analysing fish consumption. This paper highlights the heterogeneity of fisheries products in terms of species, sources and cultural responses of consumers, factors that are important in fish demand under the Asian setting. Specifically, fish demand by income groups were compared to determine how the low‐ and high‐income households respond to price and income changes. Results showed that the estimated price and income elasticities of all fish types included in the study were relatively more elastic among the poorer households.     

Asset pricing theory for two price economies

We show that nonlinearly discounted nonlinear martingales are related to no arbitrage in two price economies as linearly discounted martingales were related to no arbitrage in economies satisfying the law of one price. Furthermore, assuming risk acceptability requires a positive physical expectation, we demonstrate that expected rates of return on ask prices should be dominated by expected rates of return on bid prices. A preliminary investigation conducted here, supports this hypothesis. In general we observe that asset pricing theory in two price economies leads to asset pricing inequalities. A model incorporating both nonlinear discounting and nonlinear martingales is developed for the valuation of contingent claims in two price economies. Examples illustrate the interactions present between the severity of measure changes and their associated discount rates. As a consequence arbitrage free two price economies can involve unique discount curves and measure changes that are however specific to both the product being priced and the trade direction. Furthermore the developed valuation operators call into question the current practice of Debt Valuation Adjustments.     

ENDOGENOUS TRANSFER PRICES,TARIFFS, AND A HOST COUNTRY DUOPOLY

This article examines the impact of transfer-price effects on the interaction between a multinational firm and a domestic duopolist in the presence of resale-price restraints. The transfer-price effects have a direct impact on the strength of the strategic relationship between the multinational firm and the domestic firm. The transfer-price effect may give rise to an "anti-protective" tariff increase, wherein an increase in the tariff rate increases optimal host-country sales of the multinational firm and reduces the optimal sales level of the domestic firm. These results are valid with Cournot quantity-competition as well as a Stackleberg duopoly with either firm as the leader.     

Risk premia in option markets

Risk premia are related to price probability ratios or for continuous time pure jump processes the ratios of jump arrival rates under the pricing and physical measures. The variance gamma model is employed to synthesize densities with risk premia seen as the ratio of the three parameters. The premia are shown to be mean reverting, predictable, focused on crashes at shorter horizons and rallies at the longer horizon. Predicted premia may be used to adjust physical parameters to develop option prices based on time series data.     

Adapted hedging

Exponentials of squared returns in Gaussian densities, with their consequently thin tails, are replaced by the absolute return to form Laplacian and exponentially tilted Laplacian densities at unit time. Scaling provides densities at other maturities. Stochastic processes with these marginals are identified. In addition to a specific local volatility model the densities are consistent with the difference of compound exponential processes taken at log time and scaled by the square root of time. The underlying process has a single parameter, the constant variance rate of the process. Delta hedging using Laplacian and Asymmetric Laplacian implied volatilities are developed and compared with Black Merton Scholes implied volatility hedging.The hedging strategies are implemented for stylized businesses represented by dynamic volatility indexes. The Laplacian hedge is seen to be smoother for the skew trade. It also performs better through the financial crisis for the sale of strangles. The Laplacian and Gaussian models are then synthesized as special cases of a model allowing for other powers between unity and the square. Numerous hedging strategies may be run using different powers and biases in the probability of an up move. Adapted strategies that select the best performer on past quarterly data can dominate fixed strategies. Adapted hedging strategies can effectively reduce drawdowns in the marked to market value of businesses trading options.