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the minimum distance increases. The set of minimum distances indexed by increasing truncated length is called the distance profile. The free distance is defined as the distance between sequences with semi-infinite length. For a linear code, free is the distance from the code sequence generated by a "0" information sequence but beginning with a "1", and all the other code sequences. In a distance profile, the biggest term is the free distance. For sequential decoding, the codes with an optimum distance profile are the best choices. The optimum distance profile (ODP) codes have been found and listed in [Ref. 3-9]. As an example, refer to Figure AP3.2-3b). The distance profile can be found by inspection. The result is {2, 3, 4, 5, 5, ...}: the free distance is 5. The weight spectrum of a convolutional code is useful for determining its performance over the AWGN channel. It is defined as the sequence of the number of coded sequences {ai} of weight i, of the code, i=df, df+1, df+2, ... , df is the free distance.

The following formula returns the number of cells containing a logical value (TRUE or FALSE):

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and the sum of pu and pd gives: m 2 t + 1 N 2 t (12.92)

Lending institutions typically advertise their headline rates to make them appear as low as possible. A savvy borrower is able to interpret these rates to determine how much the loan is really costing. The only safe and constant comparison is to look at the effective cost in terms of the annual effective interest rate, or some other common rate such as the annual nominal rate compounded monthly. This section presents four examples that demonstrate how to calculate the effective cost of loans.

Auditing Show Formula Auditing Toolbar. Click the Trace Precedents button to draw arrows to indicate a cell s precedents. Click this button multiple times to see additional levels of precedents. Figure 21-8 shows a worksheet with precedent arrows drawn to indicate the precedents for the formula in cell C13.

double price : initial stock price double strike : strike price double vol : stock volatility double rate : risk-free rate double div : dividend yield double T : time to maturity char type : (C)all or (P)ut int M : number of simulations int N : number of time steps [out]: double : price of arithmetic Asian option **********************************************************************************/ double AsianOption::calcMCAAsianPrice(double price, double strike, double vol, double rate, double div, double T, char type, int M, int N) { // initialize variables double A = 0.0; // arithmetic average double mu = 0.0; // drift int i, j; double deviate; // normal deviate double stddev = 0.0; // standard deviation double stderror = 0.0; // standard error double S = 0.0; // stock price double sum = 0.0; // sum of payoffs double sum1 = 0.0; // sum of stock prices double sum2 = 0.0; // sum of squared payoffs double payoff = 0.0; // payoff of option deltat = T/N; // step size mu = rate - div - 0.5*vol*vol; // compute drift cout.precision(4); // set output decimal format srand(time(0)); long seed = (long) rand() % 100; long *idum = &seed; // initializer RNG // generate seed