American contingent claims under small proportional transaction costs

American options are considered in the binary tree model under small proportional transaction costs. Dynamic programming type algorithms, which extend the Snell envelope construction, are developed for computing the ask and bid prices (also known as the upper and lower hedging prices) of such options together with the corresponding optimal hedging strategies for the writer and for the seller of the option. Representations of the ask and bid prices of American options in terms risk-neutral expectations of stopped option payoffs are also established in this setting.     

Option pricing and replication with transaction costs and dividends

This paper derives optimal perfect hedging portfolios in the presence of transaction costs within the binomial model of stock returns, for a market maker that establishes bid and ask prices for American call options on stocks paying dividends prior to expiration. It is shown that, while the option holder's optimal exercise policy at the ex-dividend date varies according to the stock price, there are intervals of values for such a price where the optimal policy would depend on the holder's preferences. Nonetheless, the perfect hedging assumption still allows the derivation of optimal hedging portfolios for both long and short positions of a market maker on the option.     

The valuation of American barrier options using the decomposition technique

In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call ‘symmetry’ relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options. Our implementation of the obtained solution indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and efficiency. In particular, the method is free of the difficulty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.     

Is the nonlinear hedge of options more effective?—Evidence from the SSE 50 ETF options in China

The linear hedging of the options ignores the characteristic of the nonlinear change of option prices with the underlying asset. This paper establishes the nonlinear hedging strategy followed the study by Hull and White (2017) to investigate the effectiveness on the Shanghai Stock Exchange (SSE) 50 ETF options. The results show that the nonlinear hedge of the Chinese option market is less effective than the U.S option market because of the short history and the lower activity of the Chinese option market. The effect of nonlinear hedging strategy is better than the linear hedging strategy for calls in China. But for puts, the effect of the nonlinear hedging strategy is not as significant as it for calls. The difference in the trading volume between calls and puts and the high short-selling cost in the Chinese market are the main factors leading to the difference in hedge effectiveness. This paper suggests that the stock exchange could reduce margin standard of 50 ETF securities lending, promote a more flexible shorting mechanism, and accelerate the process of index options listed, so as to achieve hedging the risk of options more directly and efficiently.     

Multi-step barrier products and static hedging

This paper examines multi-step barrier options with an arbitrary payoff function using extended static hedging methods. Although there have been studies using extended reflection principles to obtain joint distribution functions for barrier options with complex barrier conditions, and static hedging methods to evaluate limited barrier options with well-known payoff functions, we obtain an explicit expression of barrier option price which has a general payoff function under the Black–Scholes framework assumption. The explicit multi-step barrier options prices we discuss in this paper are not only useful in that they can handle different levels and time steps barrier and all types of payoff functions, but can also extend to pricing of barrier options under finite discrete jump–diffusion models with a simple barrier. In the last part, we supplement the theory with numerical examples of various multi-step barrier options under the Black–Scholes or discrete jump–diffusion model for comparison purposes.     

Link-save trading

Transaction costs involved while trading several assets may be described using bid-ask spread of the asset prices. We assume that the prices of several assets may be linked, so that transactions involving several assets have prices that are not necessarily equal to the sums of (bid or ask) prices of the individual assets. The family of possible price combinations forms a convex (random) set which changes in time and is called the set-valued price process. It is shown that the necessary and sufficient condition for no-arbitrage is the existence of a martingale selection, i.e. a martingale that takes values in the set-valued price process. Examples and applications to option pricing are discussed.     

Hedging Foreign Project Risk

We study the firm's hedging problem when there is uncertainty about whether its bid on a foreign project will be accepted. Most treatments of this problem suggest that foreign currency options are the preferred hedging instrument. However, we show that when the uncertainty pertaining to the realization of the foreign cash flow is unrelated to the exchange rate, which typically will be the case, futures dominate options as hedge vehicles.
Conversely, options hedging will be appropriate when the viability of the foreign project depends also on an exchange-rate contingency, as would be the case when the bidding firm can withdraw its bid if the foreign currency depreciates sufficiently.
In many cases, both futures and options will form part of the best hedge position. The general principle in forming the hedge is that futures will best offset exchange-rate exposure the existence of which is not exchange-rate contingent. Options will best hedge any costs or revenues that might occur in a foreign currency depending on the outcome of an exchange-rate contingency.     

Middlemen and Oligopolistic Market Makers

This paper studies the endogenous structure of intermediation when heterogeneous intermediaries choose between becoming a middleman or a market maker, and the relation between the equilibrium market structure and price dispersion. We obtain three main results: First, middlemen and oligopolistic market makers can coexist in the market equilibrium. All market makers publicly post unique ask and bid prices. These prices serve as the high and low bounds, respectively, for the ask and bid prices of middlemen, when capacity cost is sufficiently large. Second, more efficient intermediaries choose to become market makers, whereas less efficient intermediaries choose to become middlemen. Third, if the fixed cost of capacity installation for market makers increases, the number of market makers declines, whereas the number of middlemen increases. As a result, both ask prices and bid prices become more dispersed.     

Equilibrium in a market with intermediation is Walrasian

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer by setting bid and ask prices nearly equal to Walrasian equilibrium prices. In our model agents choose to trade either through the intermediary or privately. Buyers (sellers) trading through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as gains. A buyer or seller who trades privately shares all the gains to trade with this trading partner, but risks costly delay in finding a partner. We show that as the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. Received: 2 February 1996 / Accepted: 28 March 1997     

Exchange options for catastrophe risk management

In this paper, we investigate the pricing issue and catastrophe risk management of exchange options. Exchange options allow the holder to exchange its stocks for another at maturity and can be seen as an extended version of catastrophe equity put options with another traded asset price as strike prices. Since option holders have to issue new shares to exercise the option, we illustrate the differences between option prices calculated using pre-exercise and post-exercise share prices. The effects of default risk on option prices and risk management are also considered. Finally, risk management analysis shows that exchange options can effectively hedge catastrophe risk.     

Fake news

This analysis uses Twitter stock and options prices sampled at a 30 s frequency around the fake news announcement, of a bid for a controlling stake in Twitter stock, to investigate how noise trading and informed trading is disseminated into equity and option markets. We find reaction to the fake news occurred in the equity market, and the option market reacted with a delay. This differs from many analyses of actual news events, which found informed traders prefer the options market, and information from their trades then leaks into the equity market. We conclude uninformed traders, and those aware of the hoax, prefer to trade in equity over option markets. This result has implications for isolating informed trading around actual news events.     

Tradability,closeness to market prices,and expected profit: their measurement for a binomial model of options pricing in a heterogeneous market

A reliable method of options pricing in real time would help various players, including hedgers and speculators, to make informed decisions. In this study, we develop an extensive simulation with multiple business environments, which includes the use of real data from the S&P 500 Index between the years 2010–2017 for the 30 days prior to expiration of the options. Forecasted tradability is computed based on the SH model: a theoretical model of real-time options pricing that takes into account players’ heterogeneity with regard to their willingness to accept offers proposed by the opposing player. The quality of the model is examined for the scenario in which the model players are speculators who act against the real market prices. We show that the equilibrium prices predicted by the SH model are close to the market prices (a deviation of up to approx. 3%) in an In-The-Money environment. Additionally, the tougher the players (i.e., the greater their level of unwillingness to accept a bid from the opposing player), the higher the average tradability. We also find that the level of willingness of the players has a greater effect on tradability than does option moneyness or the market trend.

     

Option pricing with discrete time jump processes

In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist.     

Monetary general equilibrium with transaction costs

Commodity money arises endogenously in a general equilibrium model with separate budget constraints for each transaction. Transaction costs imply differing bid and ask (selling and buying) prices. The most liquid good—with the smallest proportionate bid/ask spread—becomes commodity money. General equilibrium may not be Pareto efficient. If zero-transaction-cost money is available then the equilibrium allocation is Pareto efficient. Fiat money is an intrinsically worthless instrument. Its positive price comes from acceptability in paying taxes, and its use as a medium of exchange is based on low transaction cost.     

Profit opportunities with the American put-call parity when dividends are not expected

The objective of this research is to study borrowing and lending profit opportunities with the put-call parity of American options when dividends on the stock are not expected. Studying profit opportunities embedded in the put-call parity is intriguing because of their relative simplicity. The only assumptions necessary for the parity to hold are that option markets are frictionless and generate efficient prices of puts and calls around the underlying stock price. For this reason alone (parsimony of postulates) the put-call parity is a tempting vehicle for studying option market efficiency. In this work it is shown that both synthetic lending and borrowing parities (before and after transaction costs), on average and ex post, have negative expected profits (i.e. put-call parity implied rates are inferior to the observed riskless rate). When certain trading rules are established, however, empirical evidence of substantial profit opportunities with both lending and borrowing with the American parity (even after considering transaction costs) is observed. It is also shown that these opportunities are greater for some stocks than for others. The existence of these disparities might be an indication that the pricing mechanism of the respective options is not always in sync. The duration of disequilibrium between the options market and the stock market suggests that such occurrences are not just random bursts.     

Pricing exotic options using the Wang transform

The Wang transform allows for a simple, yet intuitive approach to pricing options with underlying based on geometric Brownian motion. This paper shows how the approach by Hamada and Sherris can be used to price some exotic options. Examples showing the convergence of the Wang price to the Black–Scholes price for a Margrabe option, a geometric basket option and an asset-or-nothing option are given. We also take a look at the range of prices achievable using the Wang transform for these options.     

Comparative empirical study of binomial call-option pricing methods using S&P 500 index data

In this paper, several binomial models are tested empirically on S&P500 Index on the levels of tradability, proximity to market (RMS) prices and profitability, especially close to expiration day. These comparisons will be carried out for many different business environments, including different market trends and moneyness levels traded. Among the models under analysis we assess the quality of the SH model, developed by the authors in previous work, in relation to other models. The option price in the SH model is affected by the players’ assessments about the behavior of the prices of the underlying asset up to the expiration day and by their “eagerness” levels (i.e., players’ readiness to respond to a given bid proposed by their opponent). We found that for all models, the higher the moneyness, the greater the proximity of models prices to actual market prices and that, eagerness parameters have a decisive effect on tradability. We also found that there was no correlation between the degree of proximity of modeled prices to actual prices and the expected profit gained by players that act according to a given model and that the SH model traded relatively small number of options. The expected profit is highest for the SH model in the ITM and ATM for days that are far from the expiration day.     

Search and Trading in Intermediated Markets

This paper examines the effect of a middleman on the search and trading behavior of the traders. It is shown that the buyer and seller types with middle valuations choose to search for each other, while the buyer and seller types with high or low valuations drop out of the search market and choose to trade directly with the middleman. The ask and bid prices of the middleman act as an outside option for the buyer and seller, and influence the outcome of the bargaining between the two. The model generalizes Gehrig (1993) by endogenizing the traders' search intensities, by allowing the traders to go to an intermediary even if thy have engaged in search, and by enabling the intermediary to provide the service of immediacy.     

Approximate analytic solution for Asian options with stochastic volatility

The valuation of Asian options is complicated because the arithmetic average of lognormal random variables is no longer lognormal. Furthermore, the stochastic volatility inherent in financial asset prices is easily observed. However, few academic studies consider the pricing and hedging of Asian options with stochastic volatility, despite the popularity of such options. This study extends the work of Hull and White (1987) and integrates the Taylor series expansion technique to derive an approximate analytic solution for Asian options with stochastic volatility. Numerical experiments show that the proposed approximate analytic solution performs favorably and is computationally efficient compared with large-sample simulations. The approximate analytic solution provides a practical approach for pricing and hedging Asian options with stochastic volatility and is both easy to implement and desirable in terms of computing speed.