| 摘要(英) |
This paper investigates static hedge portfolios for barrier options with volatility “smile.” We try to value the option with an implied binomial tree approach. We replace the traditional dynamic hedging strategy with a static replication under this volatility structure. Moreover, in valuing options with barriers, we use the enhanced numerical method to make the value approach the analytic result much more rapidly.
We define the smile in terms of implied volatility by giving a formula relating strike price to implied volatility, assuming the smile to be time independent. In constructing the implied binomial tree, “bad probability” is a big problem. We replace the bad nodes that generate a violation of the probabilities with the good nodes, which keep the implied local volatility function smooth. In addition, barrier options valued on an implied tree have no analytic solution. The enhanced method saves computing time and provides greater accuracy than an unenhanced binomial solution.
When we hedge the options with a static replicating portfolio, the number of options should be chosen to balance an inaccurate replication against the options’ cost. The more options there are in our replication portfolio, the better the replication is, and the greater the transaction costs are as well. In the example, our findings show that the replication mismatch is much smaller when using ten options to replicate the target option instead of a five-option replication portfolio. We also compare the effect of the static replication between the implied volatility approach and the constant volatility framework. |
| 參考文獻 |
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