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|Title||Optimal Delta Hedging Frequency for Equity Options|
|Institution||University of Zurich|
|Faculty||Faculty of Business, Economics and Informatics|
|Number of Pages||98|
|Zusammenfassung||Executive Summary The aim of this master’s thesis was to investigate various delta hedging frequencies and procedures in order to evaluate if an optimal rebalancing frequency exists for single stock options. It is known from theory that continuous hedging results in the lowest hedging errors. However, riskless replication of option payoffs as envisioned by Black and Scholes (1973) is not possible in practice. This thesis adds to the literature not only by providing a detailed examination of delta-hedged option positions’ risk and return characteristics but also does so in the scarcely researched field of single stock options. Furthermore, it was examined whether an optimum can be found between P&L and hedging errors under real-life constraints (e.g. discrete time, transaction costs, stochastic volatility, jumps). A new data set for Swiss stocks was compiled and analyzed over a ten-year period. Using a self-programmed lattice model that incorporated discrete dividend payments, implied volatilities were inferred from market prices and the corresponding hedge ratios calculated. The model as well as its implementation were based on approaches and methodologies that were found to generate effective and promising results in prior research. Daily hedging proved to be the most hedging error-reducing frequency empirically and can also be recommended from a combined risk-return perspective. This finding is robust across different error measures. Rebalancing less frequently did generally not result in a better performance except for static hedges which can be beneficial if transaction costs are very high. However, returns for static hedges are heavily skewed and feature a fat left tail. Although individual P&Ls sometimes departed markedly from zero, the null hypothesis of their population mean being equal to zero could usually not be rejected. Moreover, all delta hedging frequencies greatly reduced hedging errors relative to unhedged option returns. Furthermore, adjusted hedge ratios were calculated and tested and were found to improve hedging performance in terms of P&L as well as accuracy. Especially smile adjustments showed significant improvements over implied Black-Scholes deltas and performed specifically well in times of crises and steady rallies.|