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tire dynamic trading strategy replicating the option from time 0 to maturity T. Suppose there are only three securities traded in our world: a stock; a European option on the stock expiring at time T and paying off an amount at maturity equal to F(ST), where F is a given payoff function and ST is the stock price at T; and a riskfree money market account A. We start at time 0. The stock price is S0, and the quoted option price is f0. We also set up a money market account at time 0 with one share priced at A0 = $1. At time 0, we set up our portfolio as follows: We (1) sell one option (short) for f0; (2) buy 0 shares of stock; and (3) sell short N0 shares of the money market account (this is equivalent to borrowing N0 dollars at the riskfree money market rate r, since the MMA shares are worth $1 at time 0). The value of our portfolio at time 0 is: 0 = 0S0 N0 f0 (1.40)

The two fundamental problems related to reliable transmission of information [Ref. 3-8] were identified by C.E. Shannon: the use of a minimal number of bits to represent the information given by a source in accordance with a fidelity criterion; the recovery as exact as possible of the information after its transmission through a communication channel in the presence of noise and other interferences.

Finally, it is important to keep in mind whether the purpose of the design is to communicate and illustrate results or explore the data. There are no rules that can be rigidly applied and it may take several iterations and some experimentation before getting it right.

updating Ui = Ui+1 after each iteration until | Ui+1 Ui | < where is arbitrarily small (i.e., 0.0001) and (Ui ) = Pi +1 = Ui

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KDE is nice, but it can be annoying too. Sometimes you ll pop a CD in and KDE will see that it has content and mount it, and not allow the MythTV app to eject it. Once again, Jarod s guide to the rescue. Logged into KDE as the mythtv user, just nuke KDE s autorun feature for the desktop media, like this:

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olatility is the one unobservable factor affecting option prices. Modeling volatility structures is important for practitioners and traders since it can capture observable skews and smirks where low-strike options are seen to exhibit higher implied volatilities than higher-strike options. Volatility structures in the market seen to exhibit such skews and smirks give traders an indication of the relative liquidity and degree of riskiness placed by the marketplace on various strikes and maturities. There may be vol arbitrage opportunities if implied volatilities from observable market prices differ from volatilities implied from calibrated models. The focus of this chapter is to discuss various techniques for measuring and extracting implied volatilities from market option prices. We initially examine deterministic (constant) volatility and then discuss how to model stochastic volatility nondeterministic parametric forms that can be used in diffusion processes to capture observable market volatility structures. In section 7.1, we discuss implied volatility and how to compute it using an iterative numerical method like Newton-Raphson. In section 7.2, volatility skews and smiles are discussed. In section 7.3, empirical explanations are given for why such skews are observed. In section 7.4, we discuss constructing and tting implied volatility surfaces from market data using numerical procedures like nonparametric methods. In section 7.5, one-factor parametric volatility structures are discussed. In section 7.6, constant elasticity variance (CEV) models are discussed for modeling volatility structures. In section 7.7, we discuss recovering implied vol surfaces. In section 7.8, we discuss an approach by Brigo and Mercurio for constructing local volatility surfaces. In section 7.9, we discuss jump-diffusion models for modeling volatility. In section 7.10, two-factor parametric volatility structures are examined. In two-factor models, correlation is incorporated to capture co-movements in factors not captured by one-factor models. Finally, in section 7.11, we discuss the important topic of hedging with stochastic volatility.

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and log f (t + , T ) log f (t , T ) 2 2 2 2 Vart = (t , T ) (t ) (t , T )

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