Partial Hedging for Options Based on Extreme Values and Passage Times
A hedger of a contingent claim may decide to partially replicate on some states of nature and not on the others: A partial hedge initially costs less than a perfect hedge. However, a partial hedge may lead to a default position. It is of interest in that context to estimate the gain and the default risk. Some partial hedging strategies based on the final primitive asset price, its maximum over the trading period, and the time to maximum, are analyzed. Closed-form solutions are derived in the Black and Scholes  model and efficient Monte Carlo estimates are computed using a stochastic volatility model. The results show how the gain and the default risk inversely change depending on the hedging event.
KeywordsCall Option Default Risk Contingent Claim Stochastic Volatility Model Initial Wealth
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