Static versus dynamic hedges: an empirical comparison for barrier options

We conduct an empirical comparison of static versus dynamic hedges of barrier options. Using more than five years of data, we compare a number of static hedges from the literature with dynamic hedges based on the local volatility model. The main result is that the variability of profit-and-loss distributions from certain static hedges is significantly smaller than that of dynamic hedges and robust to changing market scenarios. Furthermore, these static hedges are able to provide a robust tracking of barrier options’ sensitivities. This article reflects the authors’ personal opinion and not necessarily the opinion of their employers.     

Modelling exchange-traded barrier options traded in the Australian options market

Barrier options traded in the Australian market vary considerably in terms of the extent to which the barrier is monitored and in terms of the location of the barrier level relative to the exercise price. This paper examines the impact of these differences on prices and also on deltas and gammas. We find that it is not possible to generalize results concerning hedge parameter values to all barrier options. We find that options examined by Easton et al. (2004) do not display discontinuity of deltas at the barrier levels and that their apparent overpricing cannot be attributed to hedging difficulties.     

Valuation of American partial barrier options

This paper concerns barrier options of American type where the underlying asset price is monitored for barrier hits during a part of the option’s lifetime. Analytic valuation formulas of the American partial barrier options are provided as the finite sum of bivariate normal distribution functions. This approximation method is based on barrier options along with constant early exercise policies. In addition, numerical results are given to show the accuracy of the approximating price. Our explicit formulas provide a very tight lower bound for the option values, and moreover, this method is superior in speed and its simplicity.     

Analytical pricing formulae for vulnerable vanilla and barrier options

Review of Quantitative Finance and Accounting - This paper proposes analytically vulnerable vanilla option pricing formulae that simultaneously consider the premature default, the correlation...     

Local time and the pricing of time-dependent barrier options

A time-dependent double-barrier option is a derivative security that delivers the terminal value φ(S _T ) at expiry T if neither of the continuous time-dependent barriers b _±:[0,T]→ℝ₊ have been hit during the time interval [0,T]. Using a probabilistic approach, we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions φ, barrier functions b _± and linear diffusions (S _t ) _t∈[0,T]. We show that the barrier premium can be expressed as a sum of integrals along the barriers b _± of the option’s deltas Δ _±:[0,T]→ℝ at the barriers and that the pair of functions (Δ ₊,Δ ₋) solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.     

A simple approach for pricing barrier options with time-dependent parameters

Abstract

In this paper we present a simple and easy-to-use method for computing accurate estimates (in closed form) of Black-Scholes barrier option prices with time-dependent parameters. This new approach is also able to provide tight upper and lower bounds (in closed form) for the exact barrier option prices.     

Valuation of FX barrier options under stochastic volatility

This paper describes European-style valuation and hedging procedures for a class of knockout barrier options under stochastic volatility. A pricing framework is established by applying mean self-financing arguments and the minimal equivalent martingale measure. Using appropriate combinations of stochastic numerical and variance reduction procedures we demonstrate that fast and accurate valuations can be obtained for down-and-out call options for the Heston model.     

Analytical pricing of single barrier options under local volatility models

This paper considers a single barrier option under a local volatility model and shows that any down-and-in option can be priced by a combination of three standard European options whose volatility functions are connected through symmetrization. The symmetrized volatility function is approximated by a sequence of smooth functions that converges to the original one. An approximation formula is developed to price the standard European options with the approximated volatility functions. Finally, we apply the Aitken convergence accelerator to obtain an approximate price of the down-and-in option. Other single barrier options are priced in a similar fashion.     

Efficient willow tree method for European-style and American-style moving average barrier options pricing

Moving average options are widely traded in financial markets, but exiting methods for pricing this type of option are too slow. This paper proposes two efficient willow tree methods for pricing European-style and American-style moving average barrier options (MABOs). We first solve the finite-dimensional partial differential equation model for discretely monitored MABOs by willow tree methods, and then compute the value of continuously monitored MABOs by Richardson’s two-point extrapolation. Our new willow tree method employs the interpolation error minimization technique to reduce complexity. The corresponding convergence rate and error bounds are also analyzed. It shows that our proposed methods can provide the same accuracy as the binomial tree approach and Monte Carlo simulation, but require much less computing time. The numerical experiments support our claims.     

Long-term care financing: options for the future

The aging of the baby boomers will have an enormous impact on the future of long-term care costs. This article projects the magnitude of that impact, discusses sources of financing, and considers the cost and feasibility of three options for financing future long-term care services. The authors investigate the alternatives of increasing personal savings, raising payroll taxes and expanding employer-sponsored private long-term care insurance coverage, respectively.     

Pricing double barrier options under a volatility regime-switching model with psychological barriers

The prices of lots of assets have been proved in literature to exhibit special behaviors around psychological barriers, which is an important fact needed to be considered when pricing derivatives. In this paper, we discuss the valuation problem of double barrier options under a volatility regime-switching model where there exist psychological barriers in the prices of underlying assets. The volatility can shift between two regimes, that is to say, when the asset price rises up or falls down through the psychological barrier, the volatility takes two different values. Using the Laplace transform approach, we obtain the price of the double barrier knock-out call option as well as its delta. We also provide the eigenfunction expansion pricing formula and examine the effect of the psychological barrier on the option price and delta, finding that the gamma of the option is discontinuous at such barriers.     

Information content of options trading volume for future volatility: Evidence from the Taiwan options market

This study follows the approach of Ni et al. [Ni, S.X., Pan, J., Poteshman, A.M., 2008. Volatility information trading in the option market. Journal of Finance 63, 1059–1091] – based upon the vega-weighted net demand for volatility – to determine whether volatility information exists within the Taiwan options market. Our empirical results show that foreign institutional investors possess the strongest and most direct volatility information, which is realized by the delta-neutral options/futures trades. In addition, a few individual investors (less than 1% of individuals’ trades) might be informed and realize their volatility information using the strangle strategy. Surprisingly, we find no evidence to support the predictive ability of the volatility demand from straddle trades, despite the widespread acknowledgement that such trades are sensitive to volatility.     

Managing earnings risk under SFAS 133/IAS 39: the case of cash flow hedges

Whereas empirical studies suggest that firm hedging is influenced by accounting standards such as SFAS 133 and IAS 39, the nature of earnings risk management remains a puzzle. I develop a model that shows how non-financial firms that prefer predictable earnings jointly optimize their hedging strategy and the choice between fair-value and hedge accounting. I also examine the implications of these decisions for earnings predictability under SFAS 133/IAS 39. In this model, which has two accounting periods, earnings uncertainty arises from economic shocks and accounting mismatches. The specific influence of accounting mismatches is isolated with two benchmarks, one for firm hedging (cash flow hedging) and another for an accounting system that fully complies with the matching principle. In this forward-looking analysis, most firms significantly decrease the hedging of long-term earnings when faced with persistent price dynamics. Under non-persistent price dynamics, the levels of long-term earnings hedging are only slightly reduced. Therefore, the influence of accounting mismatches on firm hedging is highly dependent on the economic environment in which a firm operates, which suggests that the potential influence of accounting on firm hedging may be difficult to identify in archival studies. The analysis also offers a forward-looking perspective on the changing properties of earnings since the late 1970s that supplements the existing body of archival accounting studies. For example, under persistent price dynamics, forward-looking short-term earnings volatility may increase tenfold or more for cash flow hedging under fair-value accounting compared with a perfectly matched accounting system.     

Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs

In this paper, we propose a new algorithm to find the optimal static replicating portfolios for general path-independent nonlinear pay-off functions and give an estimate for the rate of convergence that is absent in the literature. We choose the static replication by designing an adaptation function arising in the error bound between the nonlinear pay-off function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strikes. The numerical tests for variance swaps, swaptions, static quadratic hedges and also for a jump-diffusion process, allowing for the default of the underlying asset, show that the proposed iterative equidistribution equation algorithm is simple, fast and accurate. The paper generalizes and improves the results on static replication and approximation in the literature.     

Reducing reporting risk: Designating foreign currency forward contracts as cash flow hedges

We present an example that compares the effects on earnings of designating a foreign currency forward contract as either a cash-flow or fair-value hedge of a foreign currency denominated receivable. Entities engaging in exchange transactions not denominated in their functional currency frequently enter into foreign currency forward contracts in order to mitigate their foreign exchange rate risk exposure. The aggregate effect on earnings of the transaction gain or loss on the foreign currency receivable and the gain or loss on the forward contract is known on the date the forward contract is initiated. The effect on each period’s earnings during the term of a forward contract designated as a cash-flow hedge is also known on the date the contract is initiated; whereas the effect on each periods’ earnings from a fair-value hedge cannot be determined until the respective balance sheet dates. Therefore, designating forward contracts as cash-flow hedges may suppress volatility in reported earnings compared to designating forward contracts as fair-value hedges. In addition, the reporting risk (the amount of uncertainty surrounding the pending measure of an item to be reported in the financial statements) is lower when a forward contract is designated as a cash-flow hedge relative to designating it as a fair-value hedge. This suggests foreign currency forward contracts designated as cash-flow hedges are more consistent with the purpose of hedge accounting: to mitigate the effects on earnings of applying different measurement criteria for the hedge and the hedged item.