Pricing and Replication of Interest Rate Options with Transaction Costs
Date Issued
2004
Date
2004
Author(s)
Ho, Po-Wen
DOI
zh-TW
Abstract
Abstract
Leland has proposed a replication strategy of stock option with transaction costs in 1985. He gave a pricing formula and replication strategy as same as Black-Scholes-Merton’s except employing a volatility modified by transaction costs and rebalance time step. He also derive the relationship between hedge error and dynamic rebalance time step, and has proved that when rebalance time step approaches zero, i.e. almost doing continuous time hedge, hedge error will approach zero too if executing rebalances with the modified volatility. After Leland (1985), there were many articles kept studying the replication strategy and pricing method of stock option when transaction costs being considered, but it seems that there were almost not any other articles to consider interest rate options with transaction costs.
This article tries to include transaction costs in pricing method and replication strategy of the most popular interest rate derivatives in market, Cap and Floor. The research is under Miltersen, Sandmann, and Sondermann (1997) framework. Firstly we extend the continuous time replication strategy to discrete time with no transaction costs existing as foundation for further studies, and then try to derive the replication strategy of Cap and Floor when there are transaction costs needed for hedging. And finally use Monte-Carlo simulation method to analysis the relationship of hedge error and model parameters.
We have some conclusions in this research:
1.If there is no transaction costs needed for hedging, we found with the smaller the rebalance time step and the higher the rebalance frequency, then the closer to zero the expectation and variance of total hedge error will be.
2.With transaction costs in market, the replication strategy of Cap and Floor has close connection with transaction costs、rebalance time step and forward price of the forward contracts. Following the strategy proposed in this article, expectation and variance of total hedge error would approach zero when hedge frequency approach infinity.
3.After doing Monte-Carlo simulation with transaction costs included, we found it’s much harder and more costly to replicate Cap and Floor when transaction costs are higher or the options are more out-of-the-money.
4.There is upper and lower bound of Cap and Floor been proposed here when transaction costs are included.
Subjects
市場模型
交易成本
利率上(下)限選擇權
Cap&Floor
Market Model
Transaction Costs
Type
thesis
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