静态对冲Barrier期权在实际中的应用（原创）－从做CQF Project 得到的启示
Derivatives markets have become an essential part of the global economic and financial system in the past decade. Growth in trading activity has been particularly fast in over-the-counter (OTC) markets, which have become the dominant force in the finance industry.
One factor in the success of OTC markets has been their ability to offer new, “exotic” derivatives customized to customers’ needs. Among the most successful OTC option products are barrier options. The payoff of a barrier option depends on whether the price of the underlying asset crosses a given threshold (the barrier) before maturity.The simplest barrier options are “knock-in” options which come into existence when the price of the underlying asset touches the barrier and “knock-out” options which come out of existence in that case. For example, an up-and-out call has the same payoff as a regular plain vanilla call if the price of the underlying asset remains below the barrier over the life of the option but becomes worthless as soon as the price of the underlying asset crosses the barrier.
Barrier options fulfil different economic needs and have been widely used in foreign exchange and fixed-income derivatives markets since the mid 1990s. Barrier options reduce the cost of modifying one’s exposure to risk because they are cheaper than their plain-vanilla counterparts. It helps traders who place directional bets enhancing their leverage and investors who accept to keep some residual risk on their books reducing their hedging costs. More generally speaking, barrier options allow market participants to tailor their trading strategies to their specific market views. Traders who believe in a market upswing of limited amplitude prefer to buy up-and-out calls rather than more expensive plain vanilla calls. In contrast, fund managers who use options to insure only against a limited downswing prefer down-and-out puts. Using barrier options, investors can easily translate chartist views into their trading strategies. Options with more complex barrier features are also traded. Naturally, traders who use barrier options to express their directional views on the market do not want to hedge their positions; they use such options to gain leveraged exposure to risk.
In contrast, their counterparties may not be directional players with opposite views but rather dealers who provide liquidity by running barrier option books and hedge their positions. Barrier options are difficult to hedge because they combine features of plain vanilla options and of a bet on whether the underlying asset price hits the barrier. Merely adding a barrier provision to a regular option significantly impacts the sensitivity of the option value to changes in the price or the volatility of the underlying asset: The Greeks of barrier options behave very differently from those of plain vanilla options. The discontinuity in the payoff of barrier options complicates hedging, especially those that are in the money when they come out of existence (such as up-and-out calls and down-and-out puts). Delta hedging these options is particularly unpractical. For example, when the price nears the barrier and the option is about to expire, the Delta (and the Gamma) of an up-and-out call takes large negative values because the option payoff turns into a spike in this region. Vega also turns negative when the price of the underlying asset is close to the barrier because a volatility pickup near the barrier increases the likelihood of the price passing through it. In contrast, the Delta, Gamma, and Vega of regular options are always positive and well behaved functions.
Despite the difficulties associated with impact from the sensitivity of the volatility on the price of barrier options or hedging barrier options, banks write large amounts of those instruments to accommodate customer demand and typically prefer to hedge their positions. Moreover, when devising pricing models or hedging strategies, banks have to face the limitations of real markets, like transaction costs, discrete trading, and lack of liquidity. The literature has highlighted various strategies in order to address these concerns. For instance, addressed in CQF, one way of addressing the sensitivity to volatility is to use the Uncertain Volatility Model, where the financial parameters are assumed to lie between some known upper and lower bound. Solving the problem for the worst case scenario leads to a non-linear generalisation of the classical Black-Scholes equation. Another important issue is how the barrier option can be hedged. In CQF, one way is to use static hedge, which is carried out by limited trading highly liquid regular options instead of with the underlying asset and a riskless bond. The static hedge outperforms delta hedge in practice from the following perspective.(i)Transaction cost are reduced because the hedging is undertaken by limited times.(ii) Improves hedging effects because regular options are more closely related to barrier options than underlying asset itself.(iii)As a result of (ii) liquidity are enhanced. The isolated barrier option has very limited liquidity, it is very difficult for bank to hedge its position. By hedging with other liquid product, banks have more freedom trade barrier option, the major effect is that the bid-ask spread is narrowed so that the market is becoming more competitive.
[ 本帖最后由 EnglandWhite 于 2008-1-31 09:28 PM 编辑 ]
