Question

I have a function that generates a lattice of prices and a function that uses that lattice to price the associated option. The generate_lattice function dynamically allocates space for an array, and a pointer to that array is returned. This pointer is what is passed to price_from_tree. Here is the code:

#include <iostream>
#include <math.h>

using std::cout;
using std::endl;
using std::max;
using std::nothrow;

double* generate_lattice(double asset_price, double u, double d, int periods)
{
    int nodes = (periods * (periods + 1)) / 2; //Number of nodes = sum(1, # of periods)
    double * lattice; 

    lattice = new (nothrow) double[nodes]; 
    double up, down;
    int price_index = 0;
    for (int period = 0; period < periods + 1; period++) {
        for (int exp = 0; exp < period + 1; exp++) {
            up = pow(1 + u, exp);
            down = pow(1 - d, period - exp);
            lattice[price_index] = asset_price * up * down;
            price_index++;
        }
    }
    return lattice;
}

double price_from_tree(double* lattice, int periods, double strike, double risk_free, double period_len_years, bool euro = true, bool call = true)
{
    int num_prices = ((periods + 1) * (periods + 2)) / 2;
    double asset_max = lattice[num_prices - 1];
    double asset_min = lattice[num_prices - (periods + 1)];
    double asset_t0 = lattice[0];
    double u = pow(asset_max / asset_t0, pow(periods, -1));
    double d = pow(asset_min / asset_t0, pow(periods, -1));
    double p = (exp(risk_free * period_len_years) - d) / (u - d);
    double p_minus1 = 1 - p;
    int start_node;
    if (euro == true) { start_node = num_prices - periods - 1; }
    else { start_node = 0; }
    int sign;
    if (call == true) { sign = 1; }
    else { sign = -1; }
    for (int node = start_node; node < num_prices; node++) {
        lattice[node] = max(sign * (lattice[node] - strike), 0.0);
    }
    int price_index = num_prices - 1;
    double pv_mult = exp(-risk_free * period_len_years);
    double down_payoff, up_payoff, prev_payoff;
    for (int period = periods + 1; period > 0; period--) {
        for (int node = 0; node < period - 1; node++) {
            down_payoff = lattice[price_index - (node + 1)];
            up_payoff = lattice[price_index - node];
            prev_payoff = pv_mult * (p * up_payoff + p_minus1 * down_payoff);
            if (euro == false) {
                prev_payoff = max(lattice[price_index - (node + 1) - (period - 1)], prev_payoff);
            }
            lattice[price_index - (node + 1) - (period - 1)] = prev_payoff;
        }
        price_index -= period;
    }
    return lattice[0];
}

int main(int argc, char** argv)
{
    double* lattice = generate_lattice(100, 0.10, 0.10, 2);
    double option1 = price_from_tree(lattice, 2, 105, 0.05, 1, true, true);
    cout<<"option 1: "<<option1<<endl;
    double* lattice2 = generate_lattice(100, 0.10, 0.10, 2);
    return 0;
}

When I run the code, I get this output:

option 1: 8.28214
test: malloc.c:3096: sYSMALLOc: Assertion `(old_top == (((mbinptr) (((char *) &((av)->bins[((1) – 1) * 2])) – __builtin_offsetof (struct
malloc_chunk, fd)))) && old_size == 0) || ((unsigned long) (old_size)

= (unsigned long)((((__builtin_offsetof (struct malloc_chunk, fd_nextsize))+((2 * (sizeof(size_t))) – 1)) & ~((2 * (sizeof(size_t)))
– 1))) && ((old_top)->size & 0x1) && ((unsigned long)old_end & pagemask) == 0)’ failed.
Aborted

------------------
(program exited with code: 134)

All I can find on error 134 is descriptions along the lines of The job is killed with an abort signal. The code returns the correct value for price_from_tree in every case I’ve tried, but if I include multiple calls to generate_lattice it fails with the stated error. Is there a problem with my price_from_tree function that causes confusion within memory? Am I better off using vectors in this case?

Answer 1

You’re corrupting your heap pretty badly. If you run with valgrind (assuming you’re on a Linux machine) there are tons of errors.

==23357== Invalid write of size 8
==23357==    at 0x400B9E: generate_lattice(double, double, double, int) (so.cpp:21)
==23357==    by 0x400FC4: main (so.cpp:68)
==23357==  Address 0x595b058 is 0 bytes after a block of size 24 alloc'd
==23357==    at 0x4C27FFB: operator new[](unsigned long, std::nothrow_t const&) (vg_replace_malloc.c:325)
==23357==    by 0x400B1A: generate_lattice(double, double, double, int) (so.cpp:14)
==23357==    by 0x400FC4: main (so.cpp:68)