Financial Engineering: Derivatives Design and Pricing

Module: Fintech AI | Difficulty: Advanced

Exotic Options

Model Risk

Hedging Error

import numpy asnp

class ExoticPricer:
    def __init__(self, s0, r, sigma, T):
        self.s0 = s0; self.r = r; self.sigma = sigma; self.T = T
    def monte_carlo_price(self, payoff_fn, n_sims=100000):
        dt = self.T / 252
        paths = np.zeros((n_sims, 252))
        paths[:, 0] = self.s0
        for t in range(1, 252):
            z = np.random.standard_normal(n_sims)
            paths[:, t] = paths[:, t-1] * np.exp(
                (self.r - 0.5*self.sigma**2)*dt + self.sigma*np.sqrt(dt)*z)
        payoffs = payoff_fn(paths)
        return np.exp(-self.r * self.T) * payoffs.mean()
    def asian_option(self, strike, n_sims=100000):
        dt = self.T / 252
        paths = np.zeros((n_sims, 252))
        paths[:, 0] = self.s0
        for t in range(1, 252):
            z = np.random.standard_normal(n_sims)
            paths[:, t] = paths[:, t-1] * np.exp(
                (self.r - 0.5*self.sigma**2)*dt + self.sigma*np.sqrt(dt)*z)
        avg_price = paths.mean(axis=1)
        payoffs = np.maximum(avg_price - strike, 0)
        return np.exp(-self.r * self.T) * payoffs.mean()

Research Insight: Exotic options require complex pricing models and hedging strategies. The key challenge is model risk — the pricing model may not match market reality. Robust hedging and regular model recalibration are essential for managing exotic derivatives portfolios.