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The interaction effect will be small unless there are large changes in both local prices and exchange rates. Because of this, analysts sometimes work with an approximation of the relationship by just adding the currency return to the local return to derive the base returns. Base return Local return + Currency return The exact currency return can also be derived geometrically by Equation (15.6). ( 1 + Base return ) Currency return = --------------------------------------------- 1 ( 1 + Local return ) (15.6)

/********************************************************************************** buildTwoVarBinomialTree : computes the value of an American spread option using a 2 variable binomial tree [in]: double S1 : asset price 1 double S2 : asset price 2 double strike : strike price of spread option double rate : risk-free interest rate double div1 : dividend yield of asset 1 double div2 : dividend yield of asset 2 double rho : correlation of asset 1 and asset 2 double vol1 : volatility of asset 1 double vol2 : volatility of asset 2 double T : time to maturity int N : number of time steps char exercise : E uropean or A merican char type : C all or P ut [out]: double : value of spread option **********************************************************************************/ double TwoDimBinomialTree::buildTwoVarBinomialTree (double S1, double S2, double strike, double rate, double div1, double div2, double rho, double vol1, double vol2, double T, int N, char exercise, char type) { double dt = T/N; // time step double mu1 = rate div1 0.5*vol1*vol1; // drift for stock 1 double mu2 = rate div2 0.5*vol2*vol2; // drift for stock 2 double dx1 = vol1*sqrt(dt); // state step for stock 1 double dx2 = vol2*sqrt(dt); // state step for stock 2

The procedure for setting up a BZFlag server in this chapter focuses on setting up the server for a self-contained LAN or other protected environment. A protected environment lets you get the full feel for the gaming environment, without having the security issues that come with making your server public (and allowing strangers to play who may cheat!).

Echo suppressor*

AP9.2-7 Coordination distance for propagation mode (1)

The Modi ed Dietz return is, however, still lower than the price-to-price return because we traded at a higher price than the beginning of month price, with the effect of lowering the return Now consider the same case, except that we have valuations available for the end of day for each day that we traded the security With valuations available, we can calculate a true time-weighted return Exhibit 153 illustrates the calculation of the security level time-weighted return The TWR is calculated by compounding the subperiod growth rates in between valuation dates While we might expect the time-weighted return to equal the price-to-price return, it does not The time-weighted return is lower than the price-to-price return for two reasons: 1 The trade prices are different from the prior night closing price In our case, with a rising market, the higher trade prices serve to lower the return 2.

where = 1 for a payer quanto swaption and = 1 for a receiver quanto swaption. We can compute the value at time t, by choosing C(t) as the numeraire and taking the expectation, denoted EC under the domestic forward-swap QC measure: QS(t, T, X) = C(t)EC{max( Sf (T) S(T) K, 0) | t} While the forward-swap process Sf is a martingale under the foreign forwardswap measure, it is not under QC and has a drift computed by Hunt and Pelsser (1998) by assuming that under QC the following martingales M1 (t ) = M2 (t ) = (t )(P f (t , T ) P f (t , tn )) C (t ) (t )C f (t ) C (t )

(4.59)