ON THE NUMERICAL ASPECTS OF OPTIMAL OPTION HEDGING WITH TRANSACTION COSTS

We present a numerical study of non-self-financing hedging of European options under proportional transaction costs. We describe an algorithmic approach based on a discrete time financial market model that extends the classical binomial model. We review the analytical basis for our algorithm and present a variety of empirical results using real market data. The performance of the algorithm is evaluated by comparing to a Black–Scholes delta hedge with transaction costs incorporated. We also evaluate the impact of recalibrating the hedging strategy one or more times during the life of the option using the most recent market data. These results are compared to a recalibrated Black–Scholes delta hedge modified for transaction costs.

Capital Structure Arbitrage under a Risk Neutral Calibration

By reinterpreting the calibration of structural models, a reassessment of the importance of the input variables is undertaken. The analysis shows that volatility is the key parameter to any calibration exercise by several orders of magnitude. In order to maximize the sensitivity to volatility, a simple formulation of Merton’s model is proposed that employs deep out-of-the-money option implied volatilities. The methodology also eliminates the use of historic data to specify the default barrier thereby leading to a full risk neutral calibration. Subsequently, a new technique for identifying and hedging capital structure arbitrage opportunities is illustrated. The approach seeks to hedge the volatility risk, or vega, as opposed to the exposure from the underlying equity itself, or delta. The results question the efficacy of the common arbitrage strategy of only executing the delta hedge.

IMPLICATIONS FOR HEDGING OF THE CHOICE OF DRIVING PROCESS FOR ONE-FACTOR MARKOV-FUNCTIONAL MODELS

In this paper, we study the implications for hedging Bermudan swaptions of the choice of the instantaneous volatility for the driving Markov process of the one-dimensional swap Markov-functional model. We find that there is a strong evidence in favor of what we term "parametrization by time" as opposed to "parametrization by expiry". We further propose a new parametrization by time for the driving process which takes as inputs into the model the market correlations of relevant swap rates. We show that the new driving process enables a very effective vega-delta hedge with a much more stable gamma profile for the hedging portfolio compared with the existing ones.