Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den

We introduce a general binomial model for asset prices based on the concept of random maps. The asymptotic stationary distribution for such model is studied using techniques from dynamical systems. In particular, we present a technique to construct a general binomial model with a predetermined stationary distribution. This technique is independent of the chosen distribution making our model potentially useful in financial applications. We brie y explore the suitability of our construction as an implied binomial tree.

Application of the American Real Flexible Switch Options Methodology A Generalized Approach

The paper deals with the inclusion of flexibility in financial decision-making under risk. It describes the application of the real options methodology with the possibility of sequential multinomial decision-making. The basic intention is to describe and apply a generalized approach and methodology of the flexibility modeling and valuation based on multiple choices and non-symmetrical switching costs under risk. The stochastic dynamic Bellman optimization principle is explained and applied. The optimization criterion of the present expected value is derived and used. Likewise, an option valuation approach based on replication strategy and risk-neutral probability is applied. An illustrative example of the application of the real multinomial flexible non-symmetrical switch options methodology is presented for three chosen modes. The option flexible values are computed. The usefulness, effectiveness, and suitability of applying the generalized flexibility model in company valuation and project evaluation is verified and confirmed. The significance of applying the generalized methodology in transition market economies is discussed and verified.financial options; real options; Discrete Binomial Model; pricing; stochastic dynamic Bellman Optimization Principle; switch options

PRICING ARITHMETIC ASIAN OPTIONS UNDER THE CEV PROCESS

This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price arithmetic Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in CEV process.Exotic options; arithmetic Asian options; binomial tree method; CEV proces

Pricing Options on Commodity Futures: The Role of Weather and Storage

Options on agricultural futures are popular financial instruments used for agricultural price risk management and to speculate on future price movements. Poor performance of Black’s classical option pricing model has stimulated many researchers to introduce pricing models that are more consistent with observed option premiums. However, most models are motivated solely from the standpoint of the time series properties of futures prices and need for improvements in forecasting and hedging performance. In this paper we propose a novel arbitrage pricing model motivated from the economic theory of optimal storage, and consistent with implications of plant physiology on the importance of weather stress. We introduce a pricing model for options on futures based on a Generalized Lambda Distribution (GLD) that allows greater flexibility in higher moments of the expected terminal distribution of futures price. We use times and sales data for corn futures and options for the period 1995-2009 to estimate the implied skewness parameter separately for each trading day. An economic explanation is then presented for inter-year variations in implied skewness based on the theory of storage. After controlling for changes in planned acreage, we find a statistically significant negative relationship between ending stocks-to-use and implied skewness, as predicted by the theory of storage. Furthermore, intra-year dynamics of implied skewness reflect the fact that resolution of uncertainty in corn supply is resolved between late June and middle of October, i.e. during corn growth phases that encompass corn silking through grain maturity. Impacts of storage and weather on the distribution of terminal futures price jointly explain upward sloping implied volatility curves.arbitrage pricing model, options on futures, generalized lambda distribution, theory of storage, skewness, Agribusiness, Agricultural Finance, Crop Production/Industries, Financial Economics, Research Methods/ Statistical Methods, Risk and Uncertainty, G13, Q11, Q14,

Arbitrage with Fixed Costs and Interest Rate Models

In this paper, we study securities market models with fixed costs. We characterize the absence of arbitrage opportunities and we provide fair pricing rules. We then apply these results to extend some popular interest rate and option pricing models, which present arbitrage opportunities in the absence of fixed costs.In particular, we prove that the quite striking result obtained by Dybvig, Ingersoll and Ross (1996), which asserts that, under the assumption of absence of arbitrage, long zero-coupon rates can never fall, is no longer true in models with fixed costs, even arbitrarily small ones. For instance, models where the long-term rate follows a diffusion process are arbitrage-free in the presence of fixed costs (including arbitrarily small ones). We also rationalize models with partially absorbing or reflecting barriers on the price processes. In particular, we propose a version of the Cox, Ingersoll, and Ross (1985) model which, as in Longstaff (1992), produces yield curves with realistic humps but does not assume an absorbing barrier for the short-term rate. This is made possible by the presence of (even arbitrarily small) fixed costs.Arbitrage, fixed costs, contingent claims pricing, interest rate models, long zero-coupon rates, Dybvig Ingersoll and Ross, Brennan and Schwartz, barrier models

Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns

This paper summarizes a program of research we have conducted over the past four years. So far, it has produced two published articles, one forthcoming paper, one working paper currently under review at a journal, and three working papers in progress. The research concerns the recovery of market-wide risk-neutral probabilities and risk aversion from option prices. The work is built on the idea that risk-neutral probabilities (or their related state-contingent prices) are an amalgam of consensus subjective probabilities and consensus risk aversion. The most significant departure of this work is that it reverses the normal direction of previous research, which typically moves from assumptions governing subjective probabilities and risk aversion, to conclusions about risk-neutral probabilities. Our work is partially motivated by the conspicuous failure of the Black-Scholes formula to explain the prices of index options in the post-1987 crash market. First, we independently estimate risk-neutral probabilities, taking advantage of the now highly liquid index option market. We show that, if the options market is free of general arbitrage opportunities and we can at least initially ignore trading costs, there are quite robust methods for recovering these probabilities. Second, with these probabilities in hand, we use the method of implied binomial trees to recover a consistent stochastic process followed by the underlying asset price. Third, we provide an empirical test of implied trees against alternative option pricing models (including “naïve trader” approaches) by using them to forecast future option smiles. Fourth, we argue that realized historical distributions will be a reliable proxy for certain aspects of the true subjective distributions. We then use these observed aspects together with the option-implied risk-neutral probabilities to estimate market-wide risk aversion.Risk Aversion; Option; Realized Returns

A lattice framework for pricing display advertisement options with the stochastic volatility underlying model

Advertisement (abbreviated ad) options are a recent development in online advertising. Simply, an ad option is a first look contract in which a publisher or search engine grants an advertiser a right but not obligation to enter into transactions to purchase impressions or clicks from a specific ad slot at a pre-specified price on a specific delivery date. Such a structure provides advertisers with more flexibility of their guaranteed deliveries. The valuation of ad options is an important topic and previous studies on ad options pricing have been mostly restricted to the situations where the underlying prices follow a geometric Brownian motion (GBM). This assumption is reasonable for sponsored search; however, some studies have also indicated that it is not valid for display advertising. In this paper, we address this issue by employing a stochastic volatility (SV) model and discuss a lattice framework to approximate the proposed SV model in option pricing. Our developments are validated by experiments with real advertising data: (i) we find that the SV model has a better fitness over the GBM model; (ii) we validate the proposed lattice model via two sequential Monte Carlo simulation methods; (iii) we demonstrate that advertisers are able to flexibly manage their guaranteed deliveries by using the proposed options, and publishers can have an increased revenue when some of their inventories are sold via ad options.Comment: Bowei Chen and Jun Wang. A lattice framework for pricing display advertisement options with the stochastic volatility underlying model. Electronic Commerce Research and Applications, 2015, Volume 14, Issue 6, pages 465-479, ISSN: 1567-422

Valuing American Put Options Using Chebyshev Polynomial Approximation

This paper suggests a simple valuation method based on Chebyshev approximation at Chebyshev nodes to value American put options. It is similar to the approach taken in Sullivan (2000), where the option`s continuation region function is estimated by using a Chebyshev polynomial. However, in contrast to Sullivan (2000), the functional is fitted by using Chebyshev nodes. The suggested method is flexible, easy to program and efficient, and can be extended to price other types of derivative instruments. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations. The paper also describes an alternative method based on dynamic programming and backward induction to approximate the option value in each time period

Option Pricing: Real and Risk-Neutral Distributions

The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.Option; Pricing