American-transaction costs 1.0.0.0
American option pricer under proportional transaction costs
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00001 /* 00002 American option pricer under proportional transaction costs 00003 Copyright (C) 2011 Alet Roux alet.roux@york.ac.uk 00004 00005 This program is free software: you can redistribute it and/or modify 00006 it under the terms of the GNU General Public License as published by 00007 the Free Software Foundation, either version 3 of the License, or 00008 (at your option) any later version. 00009 00010 This program is distributed in the hope that it will be useful, 00011 but WITHOUT ANY WARRANTY; without even the implied warranty of 00012 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00013 GNU General Public License for more details. 00014 00015 You should have received a copy of the GNU General Public License 00016 along with this program. If not, see <http://www.gnu.org/licenses/>. 00017 00018 */ 00019 00020 #ifndef TREEPRODUCT_AMERICAN_SELLERNOOPTIONAL_H 00021 #define TREEPRODUCT_AMERICAN_SELLERNOOPTIONAL_H 00022 00023 #include "american.h" 00024 #include "randomexercisable.h" 00025 00027 00031 class TreeProductAmericanSeller : public TreeProductAmerican, public TreeProductRandomExercisable 00032 { 00033 00034 public: 00035 TreeProductAmericanSeller (const coefficient expiry, const PayoffBridge& payoff) : TreeProductAmerican (expiry, payoff) {}; 00036 00037 PiecewiseLinear final_hedge (const Spot& spot) const 00038 { 00039 return payoff_hedge (expiry(), spot); 00040 } 00041 00042 PiecewiseLinear interim_hedge (const coefficient time, const Spot& spot, const PiecewiseLinear& future_hedge) const 00043 { 00044 #ifdef USE_ASSERT 00045 assert (time < expiry()); 00046 #endif 00047 00048 PiecewiseLinear current = future_hedge; 00049 current.restrict_slope (-spot.ask(), -spot.bid()); 00050 00051 PiecewiseLinear reference = payoff_hedge (time, spot); 00052 return maximum (current, reference); 00053 } 00054 00055 coefficient current_price(const PiecewiseLinear& current, const Portfolio& holdings = Portfolio (0,0)) const 00056 { 00057 return sellers_price(current, holdings); 00058 } 00059 00063 coefficient random_exercise (const coefficient t, const Spot& spot, const PiecewiseLinear& current_hedge, const PiecewiseLinear& future_hedge, const coefficient x, coefficient& y, coefficient& S, const Portfolio& portfolio) const 00064 { 00065 if (equal (t, expiry())) 00066 { 00067 y = x; 00068 S = x; 00069 return 1.0; 00070 } 00071 00072 std::vector<PiecewiseLinear> g; 00073 g.push_back (payoff_hedge (t, spot)); 00074 g.push_back (future_hedge); 00075 g[1].restrict_slope (-spot.ask(), -spot.bid()); 00076 00077 std::vector<coefficient> p, X; 00078 00079 coefficient shares = portfolio.shares(); 00080 untangle_maximum (current_hedge, g, x, shares, p, X); 00081 00082 S = X[0]; 00083 y = X[1]; 00084 00085 return p[0]; 00086 } 00087 00088 }; 00089 00090 #endif // TREEPRODUCT_AMERICAN_SELLERNOOPTIONAL_H