Binomial Tree Option Pricer (CRR)

A C++ implementation of the Cox-Ross-Rubinstein binomial tree model for pricing European and American options. This repo is part of a larger portfolio of option pricing methods; companion implementations include a LSM Monte Carlo pricer

Supported Instruments

Type	Style	Method
Call	European	Combinatorial closed-form over terminal nodes
Put	European	Combinatorial closed-form over terminal nodes
Call	American	Backward induction with early exercise check
Put	American	Backward induction with early exercise check

Methodology

Up/down factors follow the CRR parameterization: $u = e^{\sigma\sqrt{\Delta t}}$, $d = 1/u$, with risk-neutral probability $p = \frac{e^{r\Delta t} - d}{u - d}$. American options are priced by backward induction — at each node the option value is $\max(\text{intrinsic value},\ e^{-r\Delta t}(p \cdot V_u + (1-p) \cdot V_d))$. European option prices are computed directly from the terminal distribution using the binomial formula, avoiding the full backward pass.

Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.

Validation

Benchmark prices are generated from QuantLib's Crank-Nicolson PDE solver at 3200×3200 grid resolution. The validation suite covers all four option types across a range of strikes, maturities, volatilities, and moneyness levels.

Accuracy is reported as mean absolute percentage error (MAPE) at varying step counts $N$.

Results

Option Type	N = 50	N = 100	N = 250	N = 1000
European Call	1.147	0.594	0.255	0.056
European Put	0.987	0.397	0.144	0.037
American Call	1.114	0.577	0.248	0.054
American Put	0.866	0.379	0.139	0.034

Key Findings

MAPE decreases steadily as $N$ increases across all four instrument types. At $N = 1000$ all instruments price within 0.06% MAPE of the QuantLib Crank-Nicolson reference.

American call and European call MAPE are nearly identical at every step count (e.g., 0.054% vs. 0.056% at $N = 1000$), consistent with the result that an American call on a non-dividend-paying asset carries no early exercise premium. American puts converge at a similar rate to European puts despite the added early exercise boundary.

Usage

#include "Pricers.h"

// Parameters
double S = 100.0;   // spot price
double K = 100.0;   // strike
double T = 1.0;     // time to expiry (years)
double r = 0.05;    // continuous risk-free rate
double v = 0.20;    // annualised volatility
int    N = 500;     // number of time steps

double american_put = priceAmericanPut(S, v, T, N, K, r);
double american_call = priceAmericanCall(S, v, T, N, K, r);
double european_put = priceEuropeanPut(S, v, T, N, K, r);
double european_call = priceEuropeanCall(S, v, T, N, K, r);

Validation runner

1. Select a validation dataset from the validation folder and assign path to 'datasetPath' variable in main
2. Select option type by assigning pricingType to one of the following values:

1 = European Call,
2 = European Put,
3 = American Call,
4 = American Put

3. Compile and run both Tester and Pricer together. After running the user will be prompted and allowed to select number of time steps used.
4. Mean absolute percent error between the dataset price and the model price is returned

References

1. Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.
2. Shreve, S. E. (2004). Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer.
3. QuantLib Development Team. (2024). QuantLib: A free/open-source library for quantitative finance. https://www.quantlib.org