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A related term, delta hedging, is the process of setting or keeping a portfolio as close to delta-neutral as possible. In practice, maintaining a zero delta is very complex because there are risks associated with re-hedging on large movements in the underlying stock's price, and research indicates portfolios tend to have lower cash flows if re ...
Nevertheless, both arbitrage free pricing and risk neutral valuation deliver identical results. In fact, it can be shown that "delta hedging" and "risk-neutral valuation" use identical formulae expressed differently. Given this equivalence, it is valid to assume "risk neutrality" when pricing derivatives.
As a result, under normal market conditions, the arbitrageur expects the combined position to be insensitive to small fluctuations in the price of the underlying stock. However, maintaining a market-neutral position may require rebalancing transactions, a process called dynamic delta hedging. This rebalancing adds to the return of convertible ...
Over the holding period, the trader will realize a profit on the trade if the underlying's realized volatility is closer to his forecast than it is to the market's forecast (i.e. the implied volatility). The profit is extracted from the trade through the continuous re-hedging required to keep the portfolio delta-neutral.
Since the delta of underlying asset is always 1.0, the trader could delta-hedge his entire position in the underlying by buying or shorting the number of shares indicated by the total delta. For example, if the delta of a portfolio of options in XYZ (expressed as shares of the underlying) is +2.75, the trader would be able to delta-hedge the ...
For instance, a seller of a call may hedge by buying just enough of the underlier to create a delta neutral portfolio. As time passes, the option seller adjusts his hedge position by buying or selling some quantity of the underlier to counteract changes in the price of the underlier. At expiration, usually either
(Note that the alternative valuation approach, arbitrage-free pricing, yields identical results; see “delta-hedging”.) This result is the "Binomial Value". It represents the fair price of the derivative at a particular point in time (i.e. at each node), given the evolution in the price of the underlying to that point.
The rationale behind the above formulation of the Vanna-Volga price is that one can extract the smile cost of an exotic option by measuring the smile cost of a portfolio designed to hedge its Vanna and Volga risks. The reason why one chooses the strategies BF and RR to do this is because they are liquid FX instruments and they carry mainly ...