Valuing real options using implied binomial trees and commodity futures options

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market‐implied probability distributions for commodity prices. In addition, the existence of long‐dated futures options means that good volatility estimates may now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. An example is given using gold futures options and a real option to extract gold from a mine. A detailed out‐of‐sample test is included that shows how IBT option pricing errors evolve on subtrees emanating from future levels of the underlying asset. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:203–226, 2007     

Lévy betas: Static hedging with index futures

This study considers calibration to forward‐looking betas by extracting information on equity and index options from prices using Lévy models. The resulting calibrated betas are called Lévy betas. The objective of the proposed approach is to capture market expectations for future betas through option prices, as betas estimated from historical data may fail to reflect structural change in the market. By assuming a continuous‐time capital asset pricing model (CAPM) with Lévy processes, we derive an analytical solution to index and stock options, thus permitting the betas to be implied from observed option prices. One application of Lévy betas is to construct a static hedging strategy using index futures. Employing Hong Kong equity and index option data from September 16, 2008 to October 15, 2009, we show empirically that the Lévy betas during the sub‐prime mortgage crisis period were much more volatile than those during the recovery period. We also find evidence to suggest that the Lévy betas improve static hedging performance relative to historical betas and the forward‐looking betas implied by a stochastic volatility model.     

SIMPLE PROCESSES AND THE PRICING AND HEDGING OF CLIQUETS

For data on market prices for 246 cliquets we consider pricing these exotic options using a relatively simple path space. The path space is subsequently stressed to market implied stress levels as well as stress levels predicted from contract characteristics. An additive process transitioning from a Sato process to a Levy process is formulated and estimated on vanilla options. Ask prices constructed from predicted stress levels are observed to have an in sample correlation of 92% with market prices. Interestingly, it is observed that capped cash flows have negative stress levels while uncapped products have positive stress levels. We illustrate the effect of hedging cliquet liabilities using call options as hedging assets permitting a 10% reduction in ask prices.     

汇率传导效应的双重传导机制分析

采用2005年8月～2010年12月相关指标的月度数据,以协整方法、误差修正模型及VAR模型等计量方法对汇率传导效应进行了量化,研究结论显示,产品市场传导渠道的汇率传导效果较为显著,而资本市场传导渠道的汇率传导效应较为微弱,但传导速度较为迅速.     

Hat die Einführung der Abgeltungsteuer Aktienkurse beeinflusst?

This paper discusses findings of a current research project whose results indicate that the implementation of the German flat withholding tax on capital gains at the turn of the year 2008–09 led to a temporary but significant increase in trading volumes and share prices on the German stock market. As this capital gains tax reform had already been announced in 2007, corresponding market reactions imply a delayed dissemination of tax information. Hence, our results raise some doubt regarding the information-processing capacity of stock markets. This holds true especially in the following circumstances: 1) extensive trading activities of individual investors with limited information access and attention; 2) a strong focus by a large group of individual investors to a limited number of trading days (herd behaviour); and 3) limited liquidity in the market (e.g. stocks with a small market capitalisation).     

Intraday price formation and bid–ask spread components: A new approach using a cross‐market model

This study examines the intraday formation process of transaction prices and bid–ask spreads in the KOSPI 200 futures market. By extending the structural model of Madhavan, A., Richardson, M., and Roomans, M. ( 1997 ), we develop a unique cross‐market model that can decompose spread components and explain intraday price formation for the futures market by using the order flow information from the KOSPI 200 options market, which is a market that is closely related to the futures market as well as considered to be one of the most remarkable options markets in the world. The empirical results indicate that the model‐implied spread and the permanent component of the spread that results from informed trading tend to be underestimated without the inclusion of options market information. Further, the results imply that trades of in‐the‐money options, which have high delta values, generally incur a more adverse information cost component (the permanent spread component) of the futures market than those of out‐of‐the‐money options, which have relatively low delta values. Finally, we find that the adverse information cost component that is estimated from the cross‐market model exhibits a nearly U‐shaped intraday pattern; however, it sharply decreases at the end of the trading day. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Valuation of futures and commodity options with information costs

In this article, futures and commodity options are analyzed in the context of Merton's (1987) model of capital market equilibrium with incomplete information. First, following Dusak (1973) and Black (1976), the conditions under which Merton's model can be applied to the valuation of forward and futures contracts are proposed. Then an application to futures markets is given. We provide a partial differential equation and the formulas for European commodity options, futures contracts, and American options in the same context. The models are simulated and compared to standard models with no information costs. We find that model prices are not significantly different from standard model prices. However, our models correct for some pricing biases in standard models. In particular, they reduce the overvaluation bias for European and American commodity options. It seems that the costs of gathering and processing information regarding the option and its underlying asset play a role in explaining the biases observed in standard models. This work can be applied to other futures markets. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 645–664, 1999     

Hedging under the influence of transaction costs: An empirical investigation on FTSE 100 index options

The Black–Scholes (BS; F. Black & M. Scholes, 1973) option pricing model, and modern parametric option pricing models in general, assume that a single unique price for the underlying instrument exists, and that it is the mid‐ (the average of the ask and the bid) price. In this article the authors consider the Financial Times and London Stock Exchange (FTSE) 100 Index Options for the time period 1992–1997. They estimate the ask and bid prices for the index, and show that, when substituted for the mid‐price in the BS formula, they provide superior option price predictors, for call and put options, respectively. This result is reinforced further when they .t a non‐parametric neural network model to market prices of liquid options. The empirical .ndings in this article suggest that the ask and bid prices of the underlying asset provide a superior fit to the mid/closing price because they include market maker's, compensation for providing liquidity in the market for constituent stocks of the FTSE 100 index. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:471–494, 2007     

Threshold levels,strike price grid,and other market microstructure issues associated with exchange‐traded equity options

This study addresses a number of important market microstructure issues associated with exchange‐traded equity options having significant research implications for studies investigating clustering on option strike prices. Price threshold levels associated with exchange listing and the automatic exercise of equity options as established by the Securities and Exchange Commission and Options Clearing Corporation (OCC) to carry out their regulatory and oversight responsibilities are examined. Significant changes are documented including motivation for such changes. Market microstructure issues potentially impact equity options research outcomes and one important issue is documenting changes over time to the strike price grid. A chronological outline of the introduction of option strike codes from April 26, 1973, through December 2008 is presented. Pricing discrepancies are documented between Standard & Poor's end‐of‐day updates (closing prices) and similar prices reported by Center for Research in Security Prices, Thompson, and Bloomberg, which is the source of ambiguities associated with the OCC's official settlement price. A number of quirks associated with option databases are identified to be of potential interest to researchers. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:188–201, 2010     

Tapering talk: The impact of expectations of reduced Federal Reserve security purchases on emerging markets

In May 2013, Federal Reserve officials first began to talk of the possibility of tapering their security purchases. This “tapering talk” had a large negative impact on the exchange rate and financial markets in emerging markets. In this paper, we analyze who was hit and why. We find that countries with larger and more liquid markets and larger inflows of capital in prior years experienced more pressure on their exchange rate, foreign reserves, and equity prices. We interpret this as investors being able to rebalance their portfolios more easily when the target country has a large and liquid financial market.     

Bid and ask prices of index put options: Which predicts the underlying stock returns?

In this study, we separately estimate the implied volatility from the bid and ask prices of deep out-of-the-money put options on the S&P500 index. We find that the implied volatility of ask prices has stronger predictive power for stock returns than does the implied volatility of bid prices. We identify two sources of the better performance of the ask price implied volatility: one is its stronger predictive power during economic recessions and in the presence of increasing intermediary capital risk, and the other is its richer information about the future market variance risk premium.     

Is the KOSPI 200 Options Market Efficient? Parametric and Nonparametric Tests of the Martingale Restriction

A number of studies on the S&P 500 index options market claim that the no‐arbitrage assumption cannot be rejected for this market because either the martingale restriction defined in Longstaff (1995) cannot be rejected by the data, or, even when it is rejected, a large proportion of the violation can be explained by market friction factors. The present study singles out the effect of market inefficiency from market friction by testing the martingale restriction for the KOSPI 200 index options market, which is the most liquid and active options market in the world. Not only using the parametric methods adopted in previous studies but also using the nonparametric methods that enable us to avoid the model misspecification problem, we empirically present clear evidence of a violation of the martingale restriction. In addition, in contrast to the S&P 500 options market, regression analyses and robustness tests indicate that market friction factors can explain only a small portion of the percentage differences between option‐implied and market‐observed index prices. Overall, the results do not support the basic no‐arbitrage assumption or the market efficiency in the KOSPI 200 options market.     

ANALYTIC APPROXIMATIONS FOR MULTI‐ASSET OPTION PRICING

We derive general analytic approximations for pricing European basket and rainbow options on N assets. The key idea is to express the option’s price as a sum of prices of various compound exchange options, each with different pairs of subordinate multi‐ or single‐asset options. The underlying asset prices are assumed to follow lognormal processes, although our results can be extended to certain other price processes for the underlying. For some multi‐asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single‐asset option under a modified measure, and in such cases an almost exact analytic price exists. More generally, approximate analytic prices for multi‐asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the subordinate basket options. The analytic formulae for multi‐asset option prices, and their Greeks, are defined in a recursive framework. For instance, the option delta is defined in terms of the delta relative to subordinate multi‐asset options, and the deltas of these subordinate options with respect to the underlying assets. Simulations test the accuracy of our approximations, given some assumed values for the asset volatilities and correlations. Finally, a calibration algorithm is proposed and illustrated.     

The Chinese equity index options market

Using Bakshi et al. (2000), and Bakshi and Kapadia's (2003) methodology, this paper studies the Chinese equity index options market that has been developing since 2015. Empirical evidence shows that the market price of call (put) option is generally lower (higher) than their Black-Scholes prices with historical volatility. The prices of the options do not support the one-dimensional diffusion model properties. We find 61.79% (63.25%) of delta-hedged gains in call (put) options to be negative. The analysis of the non-zero delta-hedged gain suggests that the investors are mainly trading on additional volatility risk in the options market in China.     

Too many options? Theory and evidence on option exchange design

A model of option exchange design is proposed and tested. The model allows investors to choose among several exchange‐traded options based on a trade‐off between standardization costs and liquidity/transaction costs. It employs a spatial economics approach to provide results for the existence of markets for particular option contracts on the exchange, a comparison of exchange design by a social planner and a profit‐maximizing monopolist (corresponding to the idea that most derivatives exchanges centralize the design and creation of option contracts), and comparative statics that can potentially aid decision makers in the design of option exchanges. In the empirical work, open interest is analyzed for Chicago Board Options Exchange (CBOE) options on the stocks in the S&P 100 index. In accordance with the model's predictions, open interest forms a previously undocumented seesaw pattern across strike prices, clustering around certain strike prices, and dropping off for the adjacent strike prices. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:533–570, 2006     

Role of delivery options in basis convergence

The corn futures contract, traded on the Chicago Board of Trade, provides sellers with delivery options about the timing of delivery, the location of delivery, and the grade to be delivered. These options presumably have values that can vary from one delivery month to the next. The joint values of the timing and location options are estimated for each delivery month for the years 1989 through 1997. These estimates are then used in regression models to determine the degree to which they influence basis variability on the first day of the maturity month. Econometric models are also developed to see if the estimated implicit options values are useful in improving the forecasts of basis convergence over the 2‐month period prior to maturity. The results suggested that variation in the delivery options values in the corn futures contract does indeed help explain basis variability on the first day of maturity. An option‐value variable, based on estimated values two months prior to maturity, resulted in occasional, small improvements (from a statistical point of view) in the precision of forecasts. The existence of delivery options increases basis variability at maturity, but it is difficult to use this information to improve forecasts of basis convergence. One limitation of the analysis is that the Chicago cash market had few transactions per day during the sample period, and hence the reported spot prices may be inadequate for making high‐quality estimates of the options values. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:783–809, 2002     

Robust Hedging of Barrier Options

This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion.
We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight.     

Option implied cost of equity and its properties

The estimation of the cost of equity capital (COE) is one of the most important tasks in financial management. Existing approaches compute the COE using historical data, i.e. they are backward‐looking methods. This study derives a method to calculate forward‐looking estimates of the COE using the current market prices of stocks and stock options. Our estimates of the COE reflect the expectation of the market investors about the COE during the life of the investment project. We test empirically our method and compare it with the Fama/French (1993) three‐factor model for the S&P 100 firms. The empirical results indicate that our COE estimates (1) are plausible and stable over the years as required by appropriate discount rates for capital budgeting, (2) yield an equity risk premium close to the market equity risk premium reported by Fama E. F. and French K. R. (2002), (3) generate strong return‐risk relationships, and (4) are significantly related with investor sentiment. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29: 599–629, 2009     

构建多层次资本市场——突破中小企业融资瓶颈

我国中小企业由于自身的原因,使其难以进入资本市场,中小企业在发展过程中面临资金不足而又难以在资本市场融资的问题依旧无法彻底得到解决。政府应构建多层次资本市场,规范和发展现有全国性证券交易所,降低创业板门槛、加强创业板监督管理,拓展中小企业融资渠道,实现新三板扩容,以此来解决这一瓶颈问题。     

Indian equity options: Smile,risk premiums,and efficiency

We study the pricing of equity options in India which is one of the world's largest options markets. Our findings are supportive of market efficiency: A parsimonious smile-adjusted Black model fits option prices well, and the implied volatility (IV) has incremental predictive power for future volatility. However, the risk premium embedded in IV for Single Stock Options appears to be higher than in other markets. The study suggests that even a very liquid market with substantial participation of global institutional investors can have structural features that lead to systematic departures from the behavior of a fully rational market while being “microefficient.”