calcoli

calcolo.py

#!/usr/bin/env python3

from decimal import *

def main():
    getcontext().prec = 30
    getcontext().rounding = ROUND_HALF_EVEN

    s0 = Decimal(0.16670847)
    sigma = Decimal(0.0427111)
    k = Decimal(0.0630307823077064)

    r = Decimal(0.02 / 365)
    e = Decimal(2.7182818284590452353602874713526624977572)
    dt = Decimal(1)
    q = Decimal(0)


    df = e**(-r * dt)
    u = e**(sigma*dt.sqrt())
    d = Decimal(1)/u
    p = ((e**(r-q) * dt) - d) / (u - d)

    lattice = lattice_evolution(s0, 1095, u, d)
    reduced_l = lattice_valuation(lattice, k, p, df)
    print(len(reduced_l))
    print(len(reduced_l[0]))

    v0 = reduced_l[-1]
    print("aaa", v0)

def lattice_evolution(s0, days, u, d):
    lattice = []
    last = []
    for day in range(days):
        if day == 0:
            last = [s0 * u, s0 * d]
            lattice.append(last)
        else:
            head = last[0]
            tail = last[1::]
            head = [head * u, head * d]
            tail = list(map(lambda x: x * d, tail))
            last = head + tail
            lattice.append(last)
    lattice = [[3]] + lattice
    return lattice

def lattice_valuation(lattice, k, p, df):
    lattice.reverse()
    reduced = []
    last = []
    for (i, day) in enumerate(lattice):
        if i == 0:
            last = list(map(lambda x: max((x - k), 0), day))
            reduced.append(last)
        else:
            last = list(map(
                lambda x:
                    max((x[1] - k), 0) + (last[x[0]] * p * df) + (last[x[0] + 1] * (1 - p) * df),
                enumerate(day)))
            reduced.append(last)
    return reduced

def test_reduce_lattice():
    k = 1
    p = 4
    df = 8
    u = 10
    d = 9
    def rr(val, a, b):
        return max((val - k), 0) + (a *  p * df) + (b * (1 - p) * df)
    lattice = [
        [3],
        [3*u, 3*d],
        [3*u*u, 3*u*d, 3*d*d],
        [3*u*u*u, 3*u*u*d, 3*u*d*d, 3*d*d*d],
        [3*u*u*u*u, 3*u*u*u*d, 3*u*u*d*d, 3*u*d*d*d, 3*d*d*d*d]
    ]
    expected = [
        [   rr(
                3,
                rr(
                    3*u,
                    rr(
                        3*u*u,
                        rr(3*u*u*u,max((3*u*u*u*u - k), 0),max((3*u*u*u*d - k), 0)),
                        rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
                    ),
                    rr(
                        3*u*d,
                        rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
                        rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
                    )
                ),
                rr(
                    3*d,
                    rr(
                        3*u*d,
                        rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
                        rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
                    ),
                    rr(
                        3*d*d,
                        rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
                        rr(3*d*d*d,max((3*u*d*d*d - k), 0),max((3*d*d*d*d - k), 0))
                    )
                )
        )
        ],
        [
            rr(
                3*u,
                rr(
                    3*u*u,
                    rr(3*u*u*u,max((3*u*u*u*u - k), 0),max((3*u*u*u*d - k), 0)),
                    rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
                ),
                rr(
                    3*u*d,
                    rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
                    rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
                )
            ),
            rr(
                3*d,
                rr(
                    3*u*d,
                    rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
                    rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
                ),
                rr(
                    3*d*d,
                    rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
                    rr(3*d*d*d,max((3*u*d*d*d - k), 0),max((3*d*d*d*d - k), 0))
                )
            )
        ],
        [
            rr(
                3*u*u,
                rr(3*u*u*u,max((3*u*u*u*u - k), 0),max((3*u*u*u*d - k), 0)),
                rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
            ),
            rr(
                3*u*d,
                rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
                rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
            ),
            rr(
                3*d*d,
                rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
                rr(3*d*d*d,max((3*u*d*d*d - k), 0),max((3*d*d*d*d - k), 0))
            )
        ],
        [
            rr(3*u*u*u,max((3*u*u*u*u - k), 0),max((3*u*u*u*d - k), 0)),
            rr(3*u*u*d,max((3*u*u*u*d - k), 0),max((3*u*u*d*d - k), 0)),
            rr(3*u*d*d,max((3*u*u*d*d - k), 0),max((3*u*d*d*d - k), 0)),
            rr(3*d*d*d,max((3*u*d*d*d - k), 0),max((3*d*d*d*d - k), 0))
        ],
        [
            max((3*u*u*u*u - k), 0),
            max((3*u*u*u*d - k), 0),
            max((3*u*u*d*d - k), 0),
            max((3*u*d*d*d - k), 0),
            max((3*d*d*d*d - k), 0)
        ]
    ]
    result = lattice_valuation(lattice, k, p, df)
    expected.reverse()
    if expected != result:
        print(expected)
        print(result)
        assert False
    else:
        print("test_lattice_evolution OK")

def test_lattice_evolution():
    start = 3
    days = 4
    u = 10
    d = 9
    expected = [
        [3],
        [3*u, 3*d],
        [3*u*u, 3*u*d, 3*d*d],
        [3*u*u*u, 3*u*u*d, 3*u*d*d, 3*d*d*d],
        [3*u*u*u*u, 3*u*u*u*d, 3*u*u*d*d, 3*u*d*d*d, 3*d*d*d*d]
    ]
    result = lattice_evolution(start, days, u, d)
    if expected != result:
        print(expected)
        print(result)
        assert False
    else:
        print("test_lattice_evolution OK")

if __name__ == "__main__":
    test_lattice_evolution()
    test_reduce_lattice()
    main()