UNDERSTANDING BID-ASK SPREADS OF DERIVATIVES UNDER UNCERTAIN VOLATILITY AND TRANSACTION COSTS

2001 ◽  
Vol 04 (03) ◽  
pp. 467-489 ◽  
Author(s):  
THIERRY ANÉ ◽  
VINCENT LACOSTE
Keyword(s):  
Transaction Costs ◽  
Portfolio Diversification ◽  
Uncertain Parameters ◽  
Price Determination ◽  
Options Markets ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Equilibrium Prices ◽  
Bid Ask Spreads ◽  
Random Nature

The classical option valuation models assume that the option payoff can be replicated by continuously adjusting a portfolio consisting of the underlying asset and a risk-free bond. This strategy implies a constant volatility for the underlying asset and perfect markets. However, the existence of non-zero transaction costs, the consequence of trading only at discrete points in time and the random nature of volatility prevent any portfolio from being perfectly hedged continuously and hence suppress any hope of completely eliminating all risks associated with derivatives. Building upon the uncertain parameters framework we present a model for pricing and hedging derivatives where the volatility is simply assumed to lie between two bounds and in the presence of transaction costs. It is shown that the non-arbitrageable prices for the derivatives, which arise in this framework, can be derived by a non-linear PDE related to the convexity of the derivatives. We use Monte Carlo simulations to investigate the error in the hedging strategy. We show that the standard arbitrage is exposed to such large risks and transaction costs that it can only establish very wide bounds on equilibrium prices, obviously in contradiction with the very tight bid-ask spreads of derivatives observed on the market. We explain how the market spreads can be compatible with our model through portfolio diversification. This has important implications for price determination in options markets as well as for testing of valuation models.

A Simulation Analysis on the Tradeoff Between Cost and Risk in Replicating ELS (Equity-Linked Securities) with Transactions Costs: The Early Redeemable Case

2009 ◽  
Vol 17 (2) ◽  
pp. 1-47
Author(s):  
Jun Young Park ◽  
Chongseok Hyun
Keyword(s):  
Transaction Costs ◽  
Simulation Analysis ◽  
Transactions Costs ◽  
Proportional Transaction Costs ◽  
Underlying Asset ◽  
Trade Off ◽  
Computational Burden ◽  
Considerable Impact ◽  
The Right ◽  
Mean Variance

The trade-off between cost and risk of discretely rebalanced ELS hedges is analyzed under the proportional transaction costs. The analysis shows that the transaction costs have a considerable impact on the hedging performance. The trade-off, or mean-variance graphs move in the right and lower directions in cases that the drift or the volatility of the underlying asset increases, the redemption level of the ELS decreases, or the maturity of the ELS gets longer. The underlying asset move-based strategy (UAMB) reveals better performances than the time-based strategy (TS), while the delta move-based strategy (DMB) shows worse results. However, as the volatility of the underlying asset grows, the time-based strategy shows worse performances than the other two strategies does. The difficulty of computational burden in simulating the hedge procedure is alleviated using the vectorized scheme, which makes the simulation analysis in feasible time.

The Behavior of Bid-Ask Spreads and Volume in Options Markets during the Competition for Listings in 1999

2003 ◽  
Vol 58 (6) ◽  
pp. 2437-2463 ◽  
Author(s):  
Patrick De Fontnouvelle ◽  
Raymond P. H. Fishe ◽  
Jeffrey H. Harris
Keyword(s):  
Options Markets ◽  
Bid Ask Spreads

scholarly journals How Firms Can Hedge Against Market Risk

2014 ◽  
Vol 37 (1) ◽  
pp. 39-49
Author(s):  
Krzysztof Echaust
Keyword(s):  
Absolute Risk ◽  
Future Price ◽  
Utility Model ◽  
Forward Contracts ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Absolute Risk Aversion ◽  
Black Scholes ◽  
Expected Utility Model ◽  
Constant Absolute Risk Aversion

Abstract The article presents a problem of proper hedging strategy in expected utility model when forward contracts and options strategies are available. We consider a case of hedging when an investor formulates his own expectation on future price of underlying asset. In this paper we propose the way to measure effectiveness of hedging strategy, based on optimal forward hedge ratio. All results are derived assuming a constant absolute risk aversion utility function and a Black-Scholes framework.

scholarly journals The Extended Black-Scholes Model with-LAGS-and “Hedging Errors”

2003 ◽  
Author(s):  
Mondher Bellalah
Keyword(s):  
Stock Price ◽  
Standard Form ◽  
Small Time ◽  
Market Model ◽  
Short Term ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Elapsed Time ◽  
Black Scholes Model ◽  
Black Scholes

The Black-Scholes model is derived under the assumption that heding is done instantaneously. In practice, there is a “small” time that elapses between buying or selling the option and hedging using the underlying asset. Under the following assumptions used in the standard Black-Scholes analysis, the value of the option will depend only on the price of the underlying asset S, time t and on other Variables assumed constants. These assumptions or “ideal conditions” as expressed by Black-Scholes are the following. The option us European, The short term interest rate is known, The underlying asset follows a random walk with a variance rate proportional to the stock price. It pays no dividends or other distributions. There is no transaction costs and short selling is allowed, i.e. an investment can sell a security that he does not own. Trading takes place continuously and the standard form of the capital market model holds at each instant. The last assumption can be modified because in practice, trading does not take place in-stantaneouly and simultaneously in the option and the underlying asset when implementing the hedging strategy. We will modify this assumption to account for the “lag”. The lag corresponds to the elapsed time between buying or selling the option and buying or selling - delta units of the underlying assets. The main attractions of the Black-Scholes model are that their formula is a function of “observable” variables and that the model can be extended to the pricing of any type of option. All the assumptions are conserved except the last one.

Bifractional Black-Scholes Model for Pricing European Options and Compound Options

2020 ◽  
Vol 8 (4) ◽  
pp. 346-355
Author(s):  
Feng Xu
Keyword(s):  
Empirical Studies ◽  
Asset Price ◽  
European Options ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Bifractional Brownian Motion ◽  
Compound Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Delta Hedging

AbstractRecent empirical studies show that an underlying asset price process may have the property of long memory. In this paper, it is introduced the bifractional Brownian motion to capture the underlying asset of European options. Moreover, a bifractional Black-Scholes partial differential equation formulation for valuing European options based on Delta hedging strategy is proposed. Using the final condition and the method of variable substitution, the pricing formulas for the European options are derived. Furthermore, applying to risk-neutral principle, we obtain the pricing formulas for the compound options. Finally, the numerical experiments show that the parameter HK has a significant impact on the option value.

Sign in / Sign up

Export Citation Format

Share Document