To what extent can deep out-of-the-money put options enhance downside protection for equity portfolios while preserving cost efficiency under different market regimes?
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- This thesis examines whether deep out-of-the-money put options can improve downside protec- tion for equity portfolios while preserving cost efficiency across different market regimes. The analysis compares an unhedged long SPX Index portfolio with a hedged portfolio that adds Euro- pean put options on the same underlying over a one-year horizon, subject to a maximum option budget of 5%. DOOM puts are defined through a target probability under the risk-neutral mea- sure. The same target probability represents the same risk-neutral tail quantile across models, even though each model produces different strikes and premia. The analysis is conducted in two steps. First, the model-based benchmark compares three pricing frameworks, Black-Scholes-Merton, Merton jump-diffusion and Heston stochastic volatility, at three option-surface calibration dates: 16 March 2020, 8 April 2025 and 30 June 2026. For each date, physical dynamics are estimated from historical SPX returns and used to generate one-year portfolio scenarios. The corresponding risk-neutral pricing specifications are calibrated to the dated SPX option surfaces and used to construct DOOM strikes, option premia and static hedge allocations through the ES95%-based optimization. Second, the resulting model-based allocations are evaluated on historical SPX one-year rolling windows classified into Crash, Stress and Normal market regimes. The allocations are applied without re-optimization to these realized scenarios. This second evaluation tests whether the model-selected hedges remain effective outside the simulated environment and therefore ex- poses model risk. The results show that DOOM puts can reduce downside losses, but only when the selected strike region matches the market regime. This match depends on the volatility level and downside skew priced in the option surface, which shape the cost of protection across strikes. The best hedge does not necessarily come from the deepest puts. Low-strike puts create a far-tail floor, while higher-strike puts can be more effective in crash or stress regimes when they pay across a wider range of realized losses. Overall, effective DOOM puts rely on the alignment between the strike region, the option-surface regime and the losses targeted by the hedge, relative to the investor’s objective.