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The Pricing of Options in a Financial Market Model With Transaction Costs and Uncertain Volatility
"... This paper introduces a financial market model with transactions costs and uncertain volatility. This model is a modification of the wellknown BlackScholes model. The solution to the problem of the pricing of the European call option is obtained by solving a nonlinear parabolic partial differentia ..."
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This paper introduces a financial market model with transactions costs and uncertain volatility. This model is a modification of the wellknown BlackScholes model. The solution to the problem of the pricing of the European call option is obtained by solving a nonlinear parabolic partial differential equation. The presented option pricing formula relates the price of an option to the underlying asset price and the bounds of the volatility of the underlying asset. 1. Introduction
HEDGING DEMANDS IN HEDGING CONTINGENT CLAIMS
"... Abstract—Minimumvariance hedging of a contingent claim in discrete time is suboptimal when the contingent claim is hedged for multiple periods and the objective is to maximize the expected utility of cumulative hedging errors. This is because the hedging errors are not independent. The difference b ..."
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Abstract—Minimumvariance hedging of a contingent claim in discrete time is suboptimal when the contingent claim is hedged for multiple periods and the objective is to maximize the expected utility of cumulative hedging errors. This is because the hedging errors are not independent. The difference between a minimumvariance hedge and the optimal multiperiod hedge is called the hedging demand and depends on the hedger’s preferences, the characteristics of the contingent claim, the trading frequency and horizon, and most importantly the joint distribution of the contingent claim and the underlying security prices. Since modeling this joint distribution is empirically controversial, I examine nonparametrically the economic importance of hedging demands in the case of hedging Standard & Poor’s 500 index options. I.
A Bounded Risk Strategy for a Market With NonObservable Parameters
, 2002
"... The paper investigates the investment problem in a financial market model with the risk free asset (bond) and the risky asset (stock). A hedging investment strategy is proposed and investigated. This strategy depends on the current prices only and does not require any market forecasting and volatili ..."
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The paper investigates the investment problem in a financial market model with the risk free asset (bond) and the risky asset (stock). A hedging investment strategy is proposed and investigated. This strategy depends on the current prices only and does not require any market forecasting and volatility estimation. Moreover, this strategy gives a positive average gain for the classic stochastic CoxRossRubinstein market model and for the diffusion market model in any case of nonriskneutral probabilistic measure. In the case of the diffusion model, a number of transactions is fixed and finite, but stopping time is a random value which has a finite expectation. Keywords: Portfolio choice, Stochastic market model, Uncertain deviations, Nonobservable volatility 1 Introduction The paper investigates the investment problem for a discretetime model and for a diffusion model of a financial market which consist of the risk free bond or bank account and the risky stock. Such models have been...
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"... There is no institutionalised derivative market in Slovenia on which it would be possible to trade with standardized derivatives. Like in every modern marketoriented economy, there ..."
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There is no institutionalised derivative market in Slovenia on which it would be possible to trade with standardized derivatives. Like in every modern marketoriented economy, there
Growth Optimal Investment and Pricing of Derivatives
, 1999
"... We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growthoptimal strategies should be particularly relevant to the problem of pricing derivatives. Under the assumption ..."
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We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growthoptimal strategies should be particularly relevant to the problem of pricing derivatives. Under the assumptions of no trading costs, and no restrictions on lending, we find an appropriate equivalent martingale measure that prices the underlying and the derivative security. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is check with a smallscale empirical test. 1 This work was supported by the NFR contract SFO 1778302 2 and by I.N.F.M. grantinaid Preprint submitted to Elsevier Preprint 1 February 2008 1
Asymptotic Arbitrage in a Stochastic Economic Model
"... The paper investigates the investment problem in a diffusion stochastic economic model with an infinitive number of commodities. Hedging investment strategies are proposed and investigated. These strategies do not require forecasting of the volatility coefficient and depend on the historical volatil ..."
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The paper investigates the investment problem in a diffusion stochastic economic model with an infinitive number of commodities. Hedging investment strategies are proposed and investigated. These strategies do not require forecasting of the volatility coefficient and depend on the historical volatility only, and the volatility coefficient is estimated at current time. It is shown that these strategies converge to arbitrage as the number of the traded stocks increases. Hence it is an example of asymptotic arbitrage ("free lunch") without borrowing. Keywords: Portfolio choice, Diffusion market model, Historical volatility, Asymptotic arbitrage 1 Introduction The paper investigates the investment problem in a stochastic diffusion model of a securities market which consists of the risk free bond or bank account and infinite number of risky stocks. It is assumed that the dynamics of the stocks is given by random processes with some standard deviations of the stock returns (the volatility c...
Overstatement of Implied Variance in the Dollar/Yen Currency Option Market
, 1996
"... This paper investigates the predictive power of implied variances extracted from the dollar/yen option prices. Implied variances are estimated from transaction prices of currency options traded on PHLX using the option pricing model of Garman and Kohlhagen (1983). In contrast to recent findings on s ..."
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This paper investigates the predictive power of implied variances extracted from the dollar/yen option prices. Implied variances are estimated from transaction prices of currency options traded on PHLX using the option pricing model of Garman and Kohlhagen (1983). In contrast to recent findings on stock and stock index options, the outofsample tests indicate that the implied variance is an upward biased estimator of future variance; and that the variance forecasts from GARCH and historical models do not contain significant incremental information in predicting future variance. Trading strategies are also developed to exploit the observed overstatement of variance in the dollar/yen option market. Traders that can execute the deltaneutral trading strategies at the observed market transaction prices could lock in a significant profits during the period examined. However, for investors that facing higher transaction costs, the magnitude of the profits is generally not large enough to al...
Analytical Approximate Solutions for the Prices of American Exotic Options
, 1997
"... of the Dissertation Analytical Approximate Solution for the Prices of American Exotic Options. by Tatiana S. Taksar in Applied Mathematics and Statistics State University of New York at Stony Brook 1997 Dissertation Advisor: Professor Qiang Zhang In this thesis we will present analytical approximate ..."
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of the Dissertation Analytical Approximate Solution for the Prices of American Exotic Options. by Tatiana S. Taksar in Applied Mathematics and Statistics State University of New York at Stony Brook 1997 Dissertation Advisor: Professor Qiang Zhang In this thesis we will present analytical approximate solutions to the values of American barrier, lookback and Asian options. Both "out" barrier and "in" barrier options have been considered. At an "out" ("in") barrier, an option becomes worthless (starts to exist). A pathdependent option is an option iii whose payoff at exercise or maturity depends on the past history of the price of the underlying asset. Lookback options are one of the most common types of pathdependent options. They are pathdependent options whose payoff depends on the maximum or the minimum realized price of the underlying asset over the life of the option. Asian options are pathdependent options whose payoff depends on the average stock price observed during the li...
Approximate Series and Claim Replicating Problems for a Market With Time Varying Random Volatility
"... The paper investigates a contingent claim replicating problem for a diffusion market model. It is proposed an approach which does not call to solve the backward parabolic equation, unlike for the classical method, and this approach is applied for a case when the volatility coefficient is random and ..."
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The paper investigates a contingent claim replicating problem for a diffusion market model. It is proposed an approach which does not call to solve the backward parabolic equation, unlike for the classical method, and this approach is applied for a case when the volatility coefficient is random and depends on time. The replicating strategy is decomposed to series of explicit strategies which does not use current estimations of volatility. A mean variance convergence of the series is proved. Keywords: diffusion market model, option pricing, time varying random volatility, approximate series 1 Introduction The paper investigates optimal investment problem and hedging problem for a market which consists of a risks free bond and a risky stock. It is assumed that the dynamics of the stock is described by a diffusion random process. The dynamics of the bond is deterministic and exponentially increasing with a given risk free rate. The most wellknown strategies for this market model were ob...
Static Hedging of Standard Options
, 2002
"... We consider the hedging of derivative securities when the price movement of the underlying asset can exhibit jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter term options written on the same ass ..."
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We consider the hedging of derivative securities when the price movement of the underlying asset can exhibit jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter term options written on the same asset. In the portfolio of shorter term options, the portfolio weights do not vary with changes in stock price or time. We then implement this static relation using a finite set of shorter term options based on a quadrature rule and use Monte Carlo simulation to determine the hedging error thereby introduced. We compare this hedging error to that of a delta hedging strategy based on daily rebalancing in the underlying futures. The simulation results indicate that the two types of hedging strategies exhibit comparable performance in the classic BlackScholes environment, but that our static hedge strongly outperforms deltahedging when the underlying asset price is governed by Merton (1976)'s jumpdi#usion model. Further simulation exercises indicate that these results are robust to model misspecification, so long as one performs ad hoc adjustments based on the observed implied volatility.