28{
32
33 const std::string american_option_binomial_model_program =
34 " var dt := t / n; "
35 " var z := exp(r * dt); "
36 " var u := exp(v * sqrt(dt)); "
37 " var p_up := (z * u - 1) / (u^2 - 1); "
38 " var p_down := 1 - p_up; "
39 " var discount := 1 / z; "
40 " "
41 " var option_price[n + 1] := [0]; "
42 " "
43 " for (var i := 0; i <= n; i += 1) "
44 " { "
45 " var base_price := s * u^(2 * i - n); "
46 " "
47 " option_price[i] := "
48 " switch "
49 " { "
50 " case callput_flag == 'call' : max(base_price - k, 0); "
51 " case callput_flag == 'put' : max(k - base_price, 0); "
52 " }; "
53 " }; "
54 " "
55 " for (var j := n - 1; j >= 0; j -= 1) "
56 " { "
57 " for (var i := 0; i <= j; i += 1) "
58 " { "
59 " var base_price_at_node := s * u^(2 * i - j); "
60 " "
61 " var intrinsic_value := "
62 " switch "
63 " { "
64 " case callput_flag == 'call' : base_price_at_node - k; "
65 " case callput_flag == 'put' : k - base_price_at_node; "
66 " }; "
67 " "
68 " var expected_value := discount * "
69 " (p_up * option_price[i + 1] + p_down * option_price[i]); "
70 " "
71 " option_price[i] := max(expected_value, intrinsic_value); "
72 " } "
73 " }; "
74 " "
75 " option_price[0]; ";
76
77 T s = T( 100.00);
78 T k = T( 110.00);
79 T v = T( 0.30);
80 T t = T( 2.22);
81 T r = T( 0.05);
82 T n = T(1000.00);
83
84 std::string callput_flag;
85
86 symbol_table_t symbol_table(symbol_table_t::e_immutable);
87 symbol_table.add_variable("s", s);
88 symbol_table.add_variable("k", k);
89 symbol_table.add_variable("t", t);
90 symbol_table.add_variable("r", r);
91 symbol_table.add_variable("v", v);
92 symbol_table.add_constant("n", n);
93 symbol_table.add_stringvar("callput_flag",callput_flag);
94
95 expression_t expression;
96 expression.register_symbol_table(symbol_table);
97
98 parser_t parser;
99 parser.compile(american_option_binomial_model_program,expression);
100
101 callput_flag = "call";
102
103 const T binomial_call_option_price = expression.value();
104
105 callput_flag = "put";
106
107 const T binomial_put_option_price = expression.value();
108
109 printf("American BinomialPrice(call, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %22.18f\n",
110 s, k, t, r, v,
111 binomial_call_option_price);
112
113 printf("American BinomialPrice(put , %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %22.18f\n",
114 s, k, t, r, v,
115 binomial_put_option_price);
116
117
118 const T callput_diff = (binomial_call_option_price - binomial_put_option_price);
119 const T basestrike_diff = s - k;
120 const T basepv_diff = s - k * std::exp(-r * t);
121 const bool put_call_parity = (basestrike_diff < callput_diff) &&
122 (callput_diff < basepv_diff ) ;
123
124 const T call_price_r0 = binomial_put_option_price + basestrike_diff;
125 const T call_price_r1 = binomial_put_option_price + basepv_diff;
126
127 const T put_price_r0 = binomial_call_option_price - basepv_diff;
128 const T put_price_r1 = binomial_call_option_price - basestrike_diff;
129
130 printf("Put-Call parity: %s\n", put_call_parity ? "True" : "False");
131
132 printf("Call price range: %7.4f < %7.4f < %7.4f\n",
133 call_price_r0,
134 binomial_call_option_price,
135 call_price_r1);
136
137 printf("Put price range: %7.4f < %7.4f < %7.4f\n",
138 put_price_r0,
139 binomial_put_option_price,
140 put_price_r1);
141}
