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O 105

Scheme 5-29

Interference geometry between GSO and non-GSO satellite networks (FBW case)

As in the standard normal case, we can express the probably measure P through the probability measure P0 , or simple P, with the zero-mean vector as: (Z)P{Z1 dz1, . . . , Zn dzn} (9.12)

class FiniteDifferenceOption : public SingleAssetOption { public: FiniteDifferenceOption(Option::Type type, double underlying, double strike, Spread dividendYield, Rate riskFreeRate, Time residualTime, double volatility, Size gridPoints); // accessors virtual void calculate() const = 0; double value() const; double delta() const; double gamma() const; Array getGrid() const{return grid_;} protected: // methods virtual void setGridLimits(double center, double timeDelay) const; virtual void initializeGrid() const; virtual void initializeInitialCondition() const; virtual void initializeOperator() const; // input data Size gridPoints_; // results mutable double value_, delta_, gamma_; mutable Array grid_; mutable FiniteDifferences::BlackScholesOperator niteDifferenceOperator_; mutable Array initialPrices_; typedef FiniteDifferences::BoundaryCondition< FiniteDifferences::TridiagonalOperator> BoundaryCondition; mutable std::vector<Handle<BoundaryCondition> > BCs_; // temporaries mutable double sMin_, center_, sMax_; private: // temporaries mutable double gridLogSpacing_; Size safeGridPoints(Size gridPoints, Time residualTime); }; // This is a safety check to be sure we have enough grid points. #de ne QL_NUM_OPT_MIN_GRID_POINTS 10 // This is a safety check to be sure we have enough grid points. #de ne QL_NUM_OPT_GRID_POINTS_PER_YEAR 2 // The following is a safety check to be sure we have enough grid // points.

If pricing a newly written lookback put at contract inception, the initial stock price, S0, is substituted in place of Smax Lookbacks can also be priced numerically by two-state variable binomial or trinomial trees We will illustrate by example of a oating-strike lookback put option Pricing a lookback in a trinomial tree is similar to pricing a vanilla (plain) option We use backward induction However, when we step back through the tree, we have to deal with the possibility of more than one maximum asset price at each node We store the maximum asset prices achievable on paths leading to the node At each interior node, we only store two maximum values For each node (i, j) in the upper half of the tree, the maxima are the current stock price as well as the maximum reached at node (i 1, j + 1).

Table 6.3 LINE From: User A <sip:usera@here.com> ;tag=34kd92kfs (continued) DESCRIPTION The From header contains a display name (User A) followed by the URI of the request recipient enclosed in < > (sip:usera@here.com). The tag parameter is a pseudo random string generated uniquely for each dialog. The Call-ID header contains a unique identifier for this call (session). It is usually made up of a locally unique pseudorandom string. All requests and responses during the call will contain this same Call-ID. The Max-Forwards header field is a hop count that is decremented by each proxy server that forwards a request. When the count goes to zero, a 483 Too Many Hops response is returned. CSeq is the Command Sequence number, which contains an integer (1) a space, then the request method (INVITE). Each successive request (command) during the call will have a higher CSeq number. The caller and called parties each maintain their own separate CSeq counts. Contact contains one or more SIP URIs that provide information for the other party in the session to contact User A. Content-Length is the octet (byte) count of the message body (126) that follows the list of SIP headers and is separated from the headers by a single CRLF. A ContentLength of 0 indicates no message body.

(10.34)