Exotic Options & Structured Derivatives Research

Quantitative research on pricing and risk analysis of exotic options and structured derivatives using Monte Carlo simulation. The primary case study is an Auto-Callable Reverse Convertible (worst-of) note linked to a basket of three U.S. equities (TSLA, META, NFLX), combining barrier features, autocall triggers, and worst-of payoff mechanics that require simulation-based valuation.

Product Structure

The note is a 2-year Auto-Callable Reverse Convertible linked to TSLA, META, and NFLX. It pays a 14% p.a. coupon quarterly while outstanding. On monthly observation dates, if all underlyings are at or above their initial levels (100% trigger), the note autocalls at par plus accrued coupon. At maturity, the worst-performing underlying determines redemption: full principal if the worst-of ratio is above the 70% strike barrier, otherwise principal scales proportionally to the worst performer's terminal return.

Monte Carlo Methodology

Pricing employs correlated geometric Brownian motion under the risk-neutral measure, with a Cholesky-decomposed correlation matrix estimated from historical daily log-returns. The simulation handles path-dependent features: monthly autocall barrier monitoring, continuous coupon accrual, and terminal worst-of payoff evaluation. The risk-free rate is calibrated to the 2-year U.S. Treasury yield (3.54% as of issue date). Variance reduction techniques including antithetic variates are applied to improve convergence.

Market Calibration

Annualized volatilities are estimated from historical returns: TSLA 57.7%, META 37.9%, NFLX 43.4%. The correlation structure shows moderate cross-correlation (0.33–0.45), which is critical for worst-of pricing since lower correlations increase the probability of barrier breach. Sensitivity analysis examines how the note's fair value responds to shifts in volatility, correlation, and the risk-free rate.

Risk and Scenario Analysis

Scenario analysis covers three canonical outcomes: early autocall under bullish conditions (all stocks above trigger), moderate decline with principal protection (worst-of above 70%), and significant decline with principal loss (worst-of below barrier). Greek sensitivities and probability distributions of terminal payoffs are computed to characterize the risk-return profile from both the investor and issuer perspective.