Semistatic hedging and pricing American floating strike lookback options

We price an American floating strike lookback option under the Black–Scholes model with a hypothetic static hedging portfolio (HSHP) composed of nontradable European options. Our approach is more efficient than the tree methods because recalculating the option prices is much quicker. Applying put–call duality to an HSHP yields a tradable semistatic hedging portfolio (SSHP). Numerical results indicate that an SSHP has better hedging performance than a delta-hedged portfolio. Finally, we investigate the model risk for SSHP under a stochastic volatility assumption and find that the model risk is related to the correlation between asset price and volatility.     

Robustness of the Black and Scholes Formula

Consider an option on a stock whose volatility is unknown and stochastic. An agent assumes this volatility to be a specific function of time and the stock price, knowing that this assumption may result in a misspecification of the volatility. However, if the misspecified volatility dominates the true volatility, then the misspecified price of the option dominates its true price. Moreover, the option hedging strategy computed under the assumption of the misspecified volatility provides an almost sure one-sided hedge for the option under the true volatility. Analogous results hold if the true volatility dominates the misspecified volatility. These comparisons can fail, however, if the misspecified volatility is not assumed to be a function of time and the stock price. The positive results, which apply to both European and American options, are used to obtain a bound and hedge for Asian options.     

On Feedback Effects from Hedging Derivatives

This paper proposes a new explanation for the smile and skewness effects in implied volatilities. Starting from a microeconomic equilibrium approach, we develop a diffusion model for stock prices explicitly incorporating the technical demand induced by hedging strategies. This leads to a stochastic volatility endogenously determined by agents' trading behavior. By using numerical methods for stochastic differential equations, we quantitatively substantiate the idea that option price distortions can be induced by feedback effects from hedging strategies.     

Derivative pricing model and time‐series approaches to hedging: A comparison

This research compares derivative pricing model and statistical time‐series approaches to hedging. The finance literature stresses the former approach, while the applied economics literature has focused on the latter. We compare the out‐of‐sample hedging effectiveness of the two approaches when hedging commodity price risk using futures contracts. For various methods of parameter estimation and inference, we find that the derivative pricing models cannot out‐perform a vector error‐correction model with a GARCH error structure. The derivative pricing models' unpalatable assumption of deterministically evolving futures volatility seems to impede their hedging effectiveness, even when potentially foresighted optionimplied volatility term structures are employed. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:613–641, 2005     

PARTIAL HEDGING IN A STOCHASTIC VOLATILITY ENVIRONMENT

We consider the problem of partial hedging of derivative risk in a stochastic volatility environment. It is related to state-dependent utility maximization problems in classical economics. We derive the dual problem from the Legendre transform of the associated Bellman equation and interpret the optimal strategy as the perfect hedging strategy for a modified claim. Under the assumption that volatility is fast mean-reverting and using a singular perturbation analysis, we derive approximate value functions and strategies that are easy to implement and study. The analysis identifies the usual mean historical volatility and the harmonically averaged long-run volatility as important statistics for such optimization problems without further specification of a stochastic volatility model. The approximation can be improved by specifying a model and can be calibrated for the leverage effect from the implied volatility skew. We study the effectiveness of these strategies using simulated stock paths.     

Bounds on European Option Prices under Stochastic Volatility

In this paper we consider the range of prices consistent with no arbitrage for European options in a general stochastic volatility model. We give conditions under which the infimum and the supremum of the possible option prices are equal to the intrinsic value of the option and to the current price of the stock, respectively, and show that these conditions are satisfied in most of the stochastic volatility models from the financial literature. We also discuss properties of Black–Scholes hedging strategies in stochastic volatility models where the volatility is bounded.     

Volatility spillover effects and cross hedging in corn and crude oil futures

Using a volatility spillover model, we find evidence of significant spillovers from crude oil prices to corn cash and futures prices, and that these spillover effects are time‐varying. Results reveal that corn markets have become much more connected to crude oil markets after the introduction of the Energy Policy Act of 2005. Furthermore, when the ethanol–gasoline consumption ratio exceeds a critical level, crude oil prices transmit positive volatility spillovers into corn prices and movements in corn prices are more energy‐driven. Based on this strong volatility link between crude oil and corn prices, a new cross‐hedging strategy for managing corn price risk using oil futures is examined and its performance is studied. Results show that this cross‐hedging strategy provides only slightly better hedging performance compared with traditional hedging in corn futures markets alone. The implication is that hedging corn price risk in corn futures markets alone can still provide relatively satisfactory performance in the biofuel era. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Volatility and trading demands in stock index futures

In this study we examine how volatility and the futures risk premium affect trading demands for hedging and speculation in the S&P 500 Stock Index futures contracts. To ascertain if different volatility measures matter in affecting the result, we employ three volatility estimates. Our empirical results show a positive relation between volatility and open interest for both hedgers and speculators, suggesting that an increase in volatility motivates both hedgers and speculators to engage in more trading in futures markets. However, the influence of volatility on futures trading, especially for hedging, is statistically significant only when spot volatility is used. We also find that the demand to trade by speculators is more sensitive to changes in the futures risk premium than is the demand to trade by hedgers. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:399–414, 2003     

Volatility dynamics of NYMEX natural gas futures prices

We examine the volatility dynamics of NYMEX natural gas futures prices via the partially overlapping time‐series model of Smith (2005. Journal of Applied Econometrics, 20, 405–422). We show that volatility exhibits two important features: (1) volatility is greater in the winter than in the summer, and (2) the persistence of price shocks and, hence, the correlations among concurrently traded contracts, displays substantial seasonal and cross‐sectional variation in a way consistent with the theory of storage. We demonstrate that, by ignoring the seasonality in the volatility dynamics of natural gas futures prices, previous studies have suggested sub‐optimal hedging strategies. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:438–463, 2008     

Leland's Approach to Option Pricing: The Evolution of a Discontinuity

A claim of Leland (1985) states that in the presence of transaction costs a call option on a stock S , described by geometric Brownian motion, can be perfectly hedged using Black–Scholes delta hedging with a modified volatility. Recently Kabanov and Safarian (1997) disproved this claim, giving an explicit (up to an integral) expression of the limiting hedging error, which appears to be strictly negative and depends on the path of the stock price only via the stock price at expiry S _T . We prove in this paper that the limiting hedging error, considered as a function of S _T , exhibits a removable discontinuity at the exercise price. Furthermore, we provide a quantitative result describing the evolution of the discontinuity: Hedging errors, plotted over the price at expiry, show a peak near the exercise price. We determine the rate at which that peak becomes narrower (producing the discontinuity in the limit) as the lengths of the revision intervals shrink.     

Market volatility and the demand for hedging in stock index futures

This study examines the relation between stock market volatility and the demand for hedging in S&P 500 stock index futures contracts. Open interest is used as a proxy for hedging demand. The analysis employs unique data that identify separately the open interest of large hedgers, large speculators, and smaller traders. Volatility estimates are decomposed into expected and unexpected components, to assess whether traders’ reactions to volatility depend upon its predictability. Results indicate that daily open interest for hedgers increases when unexpected volatility increases. Increases in unexpected volatility may cause hedgers to raise their estimates of future expected volatility, and hence increase their demand for hedging. Open interest of speculators is not related to expected volatility, and is only weakly related to unexpected volatility. The increase in the participation of hedgers in periods of higher volatility is significantly larger than the increase in the participation of speculators. The results suggest that increases in stock market volatility increase the demand for hedging. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 105–125, 2000     

Mean-Variance Hedging for Stochastic Volatility Models

In this paper we discuss the tractability of stochastic volatility models for pricing and hedging options with the mean-variance hedging approach. We characterize the variance-optimal measure as the solution of an equation between Doléans exponentials; explicit examples include both models where volatility solves a diffusion equation and models where it follows a jump process. We further discuss the closedness of the space of strategies.     

The Asymmetric Commodity Inventory Effect on the Optimal Hedge Ratio

Hedging strategies for commodity prices largely rely on dynamic models to compute optimal hedge ratios. This study illustrates the importance of considering the commodity inventory effect (effect by which the commodity price volatility increases more after a positive shock than after a negative shock of the same magnitude) in modeling the variance–covariance dynamics. We show by in‐sample and out‐of‐sample forecasts that a commodity price index portfolio optimized by an asymmetric BEKK–GARCH model outperforms the symmetric BEKK, static (OLS), or naïve models. Robustness checks on a set of commodities and by an alternative mean‐variance optimization framework confirm the relevance of taking into account the inventory effect in commodity hedging strategies.     

BitMEX bitcoin derivatives: Price discovery,informational efficiency,and hedging effectiveness

BitMEX is the largest unregulated bitcoin derivatives exchange, listing contracts suitable for leverage trading and hedging. Using minute-by-minute data, we examine its price discovery and hedging effectiveness. We find that BitMEX derivatives lead prices on major bitcoin spot exchanges. Bid–ask spreads, interexchange spreads, and relative trading volumes are important determinants of price discovery. Further analysis shows that BitMEX derivatives have positive net spillover effects, are informationally more efficient than bitcoin spot prices, and serve as effective hedges against spot price volatility. Our evidence suggests that regulators prioritize the investigation of the legitimacy of BitMEX and its contracts.     

OPTIMAL STATIC–DYNAMIC HEDGES FOR BARRIER OPTIONS

We study optimal hedging of barrier options, using a combination of a static position in vanilla options and dynamic trading of the underlying asset. The problem reduces to computing the Fenchel–Legendre transform of the utility-indifference price as a function of the number of vanilla options used to hedge. Using the well-known duality between exponential utility and relative entropy, we provide a new characterization of the indifference price in terms of the minimal entropy measure, and give conditions guaranteeing differentiability and strict convexity in the hedging quantity, and hence a unique solution to the hedging problem. We discuss computational approaches within the context of Markovian stochastic volatility models.     

A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets

This paper provides comparative theoretical and numerical results on risks, values, and hedging strategies for local risk-minimization versus mean-variance hedging in a class of stochastic volatility models. We explain the theory for both hedging approaches in a general framework, specialize to a Markovian situation, and analyze in detail variants of the well-known Heston (1993) and Stein and Stein (1991) stochastic volatility models. Numerical results are obtained mainly by PDE and simulation methods. In addition, we take special care to check that all of our examples do satisfy the conditions required by the general theory.     

A new scheme for static hedging of European derivatives under stochastic volatility models

This study proposes a new scheme for static hedging of European path‐independent derivatives under stochastic volatility models. First, we show that pricing European path‐independent derivatives under stochastic volatility models is transformed to pricing those under one‐factor local volatility models. Next, applying an efficient static replication method for one‐dimensional price processes developed by Takahashi and Yamazaki (2008), we present a static hedging scheme for European path‐independent derivatives. Finally, a numerical example comparing our method with a dynamic hedging method under Heston's (1993) stochastic volatility model is used to demonstrate that our hedging scheme is effective in practice. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:397–413, 2009     

Delivery horizon and grain market volatility

We study the difference in the volatility dynamics of CBOT corn, soybeans, and oats futures prices across different delivery horizons via a smoothed Bayesian estimator. We find that futures price volatilities in these markets are affected by inventories, time to delivery, and the crop progress period and that there are important differences in the effects across delivery horizons. We also find that price volatility is higher before the harvest starts in most cases compared to the volatility during the planting period. These results have implications for hedging, options pricing, and the setting of margin requirements. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 30:846–873, 2010     

The impact of net buying pressure on index options prices

This study examines whether the demand for options, as measured by the net buying pressure of index options, explains the implied volatility structure created by options prices. We decompose the buying pressure into the direction‐motivated (i.e., delta‐informed) and the volatility‐motivated (i.e., vega‐informed) demand for options. After controlling for options traders' hedging demand, we find that both delta‐ and vega‐informed trading play significant roles in explaining changes in implied volatility. Foreign institutions are more directionally informed in index options trading than their domestic counterparts are. Domestic investors effectively implement volatility trading using put options.     

Is volatility risk priced in the KOSPI 200 index options market?

The negative volatility risk premium is understood as a result for a hedging demand against market declines. Although this negative volatility risk premium is observed in most index options markets, there are some doubts about its presence in the KOSPI 200 index options market. The majority of KOSPI 200 index option holders do not possess any position in the underlying market; the composition of trading groups of the KOSPI 200 index options significantly differs from that of its underlying index; in this circumstance, the presence of a hedging demand is questionable. This study shows that volatility risk does not require a premium in the KOSPI 200 index options market. Rather, jump fears influence KOSPI 200 options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:797–825, 2009